The example problems are all uniquely numbered for easy reference. The problem statement is given, and then the solution is provided as a PDF file which you can download.

If you want to review the theory behind all these problems, I conveniently cover that on this website, in the kinematics and dynamics pages. If you're studying engineering, there's a problems page on engineering mechanics. Even if you're not studying engineering, it's very useful to study the kinematics problems on that page, if nothing else. They are greatly beneficial in that they give a much deeper coverage of kinematics that also extends into three dimensions. That, in addition to the content on this page, will be of great benefit to you in your overall understanding of mechanics.

To see the example problems click on the category you are interested in:

Kinematics – 1-D problems involving free-fall acceleration (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving constant acceleration (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving average velocity and average speed (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving instantaneous velocity and speed (motion along a straight line) – Senior high school and first year college/university

Kinematics – 1-D problems involving average acceleration and instantaneous acceleration (motion along a straight line) – Senior high school and first year college/university

Kinematics – 2-D and 3-D problems involving position and displacement – Senior high school

Kinematics – 2-D and 3-D problems involving instantaneous velocity, average velocity, and average speed – Senior high school and first year college/university

Kinematics – 2-D and 3-D problems involving instantaneous acceleration and average acceleration – Senior high school and first year college/university

Kinematics – Projectile motion problems – Senior high school and first year college/university

Kinematics – Uniform circular motion – Senior high school and first year college/university

Kinematics – 1-D problems involving relative motion – Senior high school and first year college/university

Kinematics – 2-D problems involving relative motion – Senior high school and first year college/university

Force and motion – Problems involving Newton's laws – Senior high school and first year college/university

Force and motion – Problems involving pulleys – Senior high school and first to upper year college/university

Force and motion – Problems involving friction – Senior high school and first to upper year college/university

Force and motion – Problems involving uniform circular motion – Senior high school and first to upper year college/university

Force and motion – Problems involving rotation, rolling, and torque – First to upper year college/university

Energy – Problems involving work and energy – Senior high school and first to upper year college/university

Energy – Problems involving conservation of energy – Senior high school and first to upper year college/university

Systems – Problems involving systems of particles – Senior high school and first to upper year college/university

Systems – Problems involving momentum – Senior high school and first to upper year college/university

Equilibrium – Problems involving static equilibrium – Senior high school and first to upper year college/university

Problem # 1:

A building is under construction, and a construction worker is standing on top of a 130 m high elevator shaft. The worker accidentally drops his hammer down the shaft.

(a) At what speed does the hammer hit the ground?

(b) How much time passes between when the hammer is dropped and when it hits the ground?

(c) What fraction of the total airborne time does the hammer spend in the top 75% of the falling distance?

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Problem # 2:

A model rocket is launched vertically, and has a constant acceleration of 5.0 m/s

(a) What is the maximum height reached by the rocket?

(b) How much time passes between when the rocket is launched and when it lands?

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Problem # 3:

An object is dropped from rest, and one second before it lands it is at half its initial drop height.

(a) What is the falling time?

(b) What is the drop height?

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Problem # 4:

A ball is thrown vertically upward. On its way up it passes point A at a speed

(a) What is the speed

(b) What is the distance between point A and the peak height reached by the ball?

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Problem # 5:

A drop tower at an amusement park rises at 5 m/s and is 45 m above the ground when one of the riders drops her phone.

(a) How long does it take for the phone to fall to the ground?

(b) At what speed does the phone hit the ground?

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Problem # 6:

A girl is standing in an elevator moving upward at 5 m/s. She places a launch toy on the floor of the elevator, which then launches a ball straight up at 5.5 m/s relative to the elevator. The girl catches the ball 1.0 seconds later. At the instant the ball is caught, the floor of the elevator is 32 m above the ground.

(a) What is the height of the ball above the ground at the instant it is caught?

(b) What is the height of the elevator floor above the ground at the instant the ball is launched?

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Problem # 7:

A child is standing in an elevator with glass walls, at a mall. She throws a ball in the air at a vertical upward speed of 4.5 m/s relative to the elevator, and from a height of 1.3 m relative to the elevator floor. At the same time, the elevator is moving upward at 3 m/s, starting from ground level.

(a) From the perspective of the child, what is the maximum height reached by the ball?

(b) From the perspective of someone in the mall (outside the elevator), what is the maximum height reached by the ball?

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Problem # 8:

A mischievous student drops an egg from the window of his dorm room. The egg falls straight down onto the hood of a car parked below. A few floors below, someone is recording a video on their webcam, which is facing the window. The egg is recorded falling past the window. The person recording the video is a physics student, and she sees an opportunity to solve an interesting physics problem while also determining the height, and consequently the room, that the egg was dropped from. She analyzes the video, and determines that it took the egg 0.14 seconds to fall from the top of the window to the bottom. She then measures the height of the window to be 1.30 meters. From what height, measured from the top of the window, was the egg dropped?

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Problem # 9:

A game is played by two children, in which one child, at a height of 10 m above the ground, drops a rock with no initial speed. The second child also drops a rock, from a height of 15 m above the ground. The second child drops the rock

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Here are additional free fall problems for you to work on.

Problem # A-1:

A car travelling on a straight road at 25 m/s undergoes constant acceleration until it reaches a speed of 40 m/s. The car then maintains this speed for 6.0 seconds. The brakes are then applied, causing the car to undergo constant deceleration until it once more reaches a speed of 25 m/s. If it takes the car 25 seconds from the time that it starts accelerating to the time that it slows down to 25 m/s, how far does it travel in this time?

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Problem # A-2:

A train is moving at high speed on a straight track, while at the same time a locomotive is moving in the opposite direction on the same track. In order to avoid a collision, the locomotive must move on to the siding before a collision becomes unavoidable. At the same time, the train must decelerate by putting the brakes on. At the instant shown, the front of the train is 0.35 mi from the back of the locomotive, the back of the locomotive is 0.1 mi from the siding entrance, the speed of the train is 80 mi/h, and the maximum speed of the locomotive is 20 mi/h. What is the minimum deceleration of the train?

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Problem # A-3:

Given the above graph of

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Problem # A-4:

The takeoff speed of a commercial jet is 260 km/h. If the runway is 2.1 km long, what is the minimum constant acceleration of the jet?

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Problem # A-5:

A truck driving on a paved road is capable of decelerating at a constant value of 5 m/s

(a) If the truck is initially travelling at 27.4 m/s, how long does it take to come to a complete stop?

(b) How far does the truck travel in this time?

(c) Sketch a graph of distance vs. time and speed vs. time, when the brakes are applied.

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Problem # A-6:

A distracted driver is cruising at 25 m/s when she suddenly notices a truck directly ahead moving at 15 m/s, in the same direction. At the instant she brakes, the distance between the front of the car and the back of the truck is

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Problem # A-7:

A distracted driver is cruising at 25 m/s when he suddenly notices a truck directly ahead moving at 15 m/s, in the same direction. At the instant he brakes, the distance between the front of the car and the back of the truck is 15 m. If the car decelerates at

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Problem # A-8:

A distracted driver is cruising at 25 m/s when he suddenly notices a truck directly ahead moving at 15 m/s, in the same direction. At the instant he brakes, the distance between the front of the car and the back of the truck is 9 m. The car decelerates at 5 m/s

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Problem # A-9:

A distracted driver is driving on the wrong side of the road, when he notices an oncoming vehicle moving towards him. He quickly applies the brakes, causing his car to decelerate at 4.5 m/s

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Problem # B-1:

The speed of sound in air is 330 m/s at 0 degrees Celsius. If the average velocity of a jet plane is 2.3 times the speed of sound, how far does it travel in 0.25 seconds?

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Problem # B-2:

A delivery truck travels up a hill at a constant speed of 50 km/h, in order to deliver a package. After the package is delivered, the truck travels down the same hill at 80 km/h. What is the average speed of the truck for the round trip?

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Problem # B-3:

The graph shown above shows velocity vs. time for a particle moving along a straight line. What is the average velocity and average speed for the particle for the entire time the particle is in motion?

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Problem # B-4:

A particle is moving along the

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Problem # B-5:

The position of an object moving along the

(a) Find the position of the object at

(b) What is the displacement of the object between

(c) What is the average velocity of the object between

(d) What is the average speed of the object between

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Problem # B-6:

The position of an object moving along the

(a) What is the average velocity of the object between 0 and

(b) What is the average speed of the object between 0 and

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Problem # B-7:

A delivery truck drives 6.5 km along a straight road. The driver then exits the truck, walks 1.5 km to deliver a package at one house, and then continues walking another 2 km to deliver a package to another house. The driver then walks back to the truck. The driving speed of the truck is 70 km/h, and the walking speed of the driver is 5 km/h.

(a) What is the average velocity and average speed of the driver from the start of the drive until the time that the package is delivered to the second house?

(b) What is the average velocity and average speed of the driver from the start of the drive until the time that the driver returns to the truck?

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Problem # B-8:

An object moves along the positive

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Problem # B-9:

An object moves along the positive

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Problem # C-1:

The position of a particle is given by

(a) What is the velocity of the particle at

(b) Is the position of the particle increasing or decreasing at

(c) What is the speed of the particle at

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Problem # C-2:

A particle's position is given by

(a) At what time is the velocity of the particle equal to -1.5 m/s ?

(b) At what time is the speed of the particle equal to 1.5 m/s ?

(c) What is the minimum velocity and minimum speed of the particle?

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Problem # D-1:

A particle's position is given by

(a) What is the average acceleraton of the particle between

(b) What is the acceleraton of the particle at

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Problem # D-2:

A particle is moving towards the right at 21 m/s, at a time of 3.1 s, and is moving towards the left at 18 m/s, at a time of 6.4 s. What is the average acceleration of the particle from 3.1 s to 6.4 s ?

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Problem # D-3:

A particle moves in a straight line, as represented by the above graph of velocity vs. time. Sketch a graph representing the acceleration of this particle.

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Problem # D-4:

A particle moves in a straight line, as represented by the above graph. Sketch a graph representing the acceleration of this particle.

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Problem # D-5:

A particle moves in a straight line at 12 m/s, and some time later it is moving at −21 m/s. If the average acceleration of the particle is −2.5 m/s

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Problem # E-1:

A particle has the following coordinates:

(a) Find the position vector in unit-vector notation.

(b) What is the magnitude of this vector?

(c) Sketch the vector on a right-handed coordinate system.

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Problem # E-2:

A particle has the following coordinates initially:

(a) Find the displacement vector of the particle.

(b) Sketch the initial, final, and displacement vector of the particle.

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Problem # E-3:

A particle has the following coordinates initially:

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Problem # F-1:

A plane flies 350 mi east from airport A to airport B in 50 min, and then flies 500 mi south from airport B to airport C in 1.8 h.

(a) Determine the displacement vector, for the total trip.

(b) Determine the average velocity vector, for the total trip.

(c) Determine the average speed, for the total trip.

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Problem # F-2:

In 4.2 h, a weather balloon drifts 10.2 km west, 18.7 km south, and 3.1 km upward.

(a) Determine the magnitude of the balloon's average velocity, and the angle that this vector makes with the horizontal.

(b) Determine the average speed of the balloon.

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Problem # F-3:

The position of a particle is given by

(a) What is the instantaneous velocity of the particle at

(b) What is the magnitude of the instantaneous velocity at

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Problem # G-1:

A particle has initial velocity

(a) What is the average acceleration over the 5.0 s interval?

(b) What is the magnitude of the average acceleration, and show the orientation of the average acceleration.

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Problem # G-2:

A particle is initially located at the origin and has an initial velocity of

(a) What is the velocity of the particle when its y-coordinate is a maximum?

(b) Where is the particle located at this instant?

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Problem # G-3:

The position of a particle is given by

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Problem # H-1:

A ball rolls down a ramp that is inclined at 15° with the horizontal. At the edge of the ramp (point A), the velocity of the ball is

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Problem # H-2:

A remote controlled toy car is driven off the edge of a table, at point A, at a speed of 2.2 m/s. It lands at point B. If the table is 1.1 m high, what is the horizontal distance,

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Problem # H-3:

A remote controlled toy car is driven off the edge of a ramp, at point A, at a speed of 3 m/s. It lands at point B. If the edge of the ramp is at a height of 0.8 m, and it is inclined at 20° with the horizontal, what is the horizontal distance,

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Problem # H-4:

A person standing at the top of a hill throws a rock with an initial velocity of 12 m/s at an angle of 20° below the horizontal.

(a) Calculate the horizontal displacement of the rock 1.5 s later.

(b) Calculate the vertical displacement of the rock 1.5 s later.

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Problem # H-5:

In order to calculate the height,

(a) What is the height,

(b) What is the peak height,

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Problem # H-6:

A person standing at the top of a hill throws a rock with an initial velocity of 14 m/s at an angle of 30° above the horizontal.

(a) Calculate the horizontal displacement of the rock 1.7 s later.

(b) Calculate the vertical displacement of the rock 1.7 s later.

(c) How long does it take the rock to fall 3.5 m below its initial launch height?

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Problem # H-7:

A ball is launched from the ground into the air. At a height of 7.3 m, the velocity of the ball is observed to be

(a) What is the maximum height reached by the ball?

(b) What will be the total horizontal distance traveled by the ball?

(c) At the instant just before the ball hits the ground, what is the magnitude and direction of its velocity?

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Problem # H-8:

A stuntman rides his motorcycle at 25 m/s off a ramp that is inclined at 30°. He intends to land on the back of a truck. The driver of the truck must wait

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Problem # H-9:

A baseball player throws a ball at an initial speed of 20 m/s, from point A, which is 1.4 m above the ground and 14 m from a wall. What is the launch angle

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Problem # H-10:

A ball is launched at ground level at a speed of 20 m/s, at an angle of 35° above the horizontal. A hill is located 25 m from the launch point, where it has an inclination of 20°. How far up the hill,

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Problem # H-11:

In a competition held in a high school gym, the goal is to launch a ball from floor level so that it passes through two rings suspended from the ceiling, as shown. One of the competitors is a physics student who calculates the value of

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Here are additional projectile motion problems for you to work on.

Problem # I-1:

A sprinter is running around the bend of a track with radius of 30 m, at a speed of 11 m/s. What is the acceleration of the sprinter and in what direction does the acceleration

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Problem # I-2:

A charged particle moves in a circular path in a magnetic field, with a radial acceleration of 2.5 × 10

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Problem # I-3:

A fan rotates at 1000 revolutions per minute. The tip of the blades have a radius of 0.20 m.

(a) What is the distance traveled by the tip of a blade during one full revolution?

(b) What is the speed of a blade tip?

(c) What is the acceleration of a blade tip?

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Problem # I-4:

A high speed train goes around a curve at a speed of 250 km/h. What is the smallest radius of curvature of the track so that the maximum acceleration experienced by the passengers is 0.05

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Problem # I-5:

A high speed train goes around a curve with a radius of 1.5 km. What is the maximum speed of the train so that the maximum acceleration experienced by the passengers is 0.05

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Problem # I-6:

A tether car is going around a track at a speed of 200 mph. To prevent the car from going off the track it is tethered to a center post with a cable. The diameter of the track is 21.3 m, and the wheel diameter of the car is 5 cm.

(a) What is the acceleration of the car?

(b) How fast do the car wheels rotate, in revolutions per minute?

(c) Looking at the car from above, how fast does it go around the track, in revolutions per minute?

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Problem # J-1:

A boat is traveling in a river in the upstream direction, at 15 km/h with respect to the water of the river. The water in the river is flowing at 7 km/h with respect to the ground.

(a) What is the velocity of the boat with respect to ground?

(b) A person on the boat walks from the front of the boat to the back of the boat at 5 km/h with respect to the boat. What is the person's velocity with respect to the ground?

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Problem # J-2:

A person walks up an escalator that has stopped, in 100 seconds. When the escalator is moving, it takes the person 75 seconds to be carried up when they are standing on it. If the escalator is 20 m long, how long would it take that same person to walk up the moving escalator?

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Problem # J-3:

A cameraman is standing on the back of a pickup truck filming a scene for a movie. He videotapes a car traveling directly ahead of him moving at 45 mi/h faster than the truck. Suddenly, the car slows down, stops, and begins moving in the opposite direction at 60 mi/h, as measured by someone on the ground. If the pickup truck is moving at 35 mi/h, and the change in the car's velocity took 2.5 seconds, what was the acceleration of the car from the perspective of (a) the cameraman, and (b) the person on the ground?

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Problem # K-1:

Two cars, A and B, are approaching an intersection as shown. Car A is 600 m from the intersection and is moving at 80 km/h. Car B is 700 m from the intersection and is moving at 90 km/h.

(a) In unit vector notation, what is the velocity of car A with respect to car B?

(b) How does the direction of the velocity found in (a) compare to the line of sight between the two cars?

(c) How does the answer to (a) and (b) change as the cars move closer to the intersection?

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Problem # K-2:

A train travels in the north direction at 25 m/s relative to the ground. At the same time it is raining. An observer on the ground sees that the raindrops make an angle of 18° with the vertical. A passenger on the train sees the raindrops fall in a perfectly vertical direction. What is the speed of the raindrops relative to the ground?

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Problem # K-3:

The pilot of a plane intends to fly directly east in the presence of a wind, a distance of 950 km. The plane has an airspeed of 630 km/h, and the pilot calculates that the plane must fly with a heading of 15° south of east. If the plane arrives at the destination 1.8 hours later, what was the velocity vector of the wind?

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Problem # K-4:

A 350 m wide river flows in the east direction at 2.5 m/s. A boat with a speed of 9.5 m/s relative to the water sets a course that is pointed in a direction 25° west of north.

(a) What is the velocity of the boat relative to the Earth?

(b) How long does it take the boat to cross the river, starting from the south bank?

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Problem # K-5:

A river flows in the east direction at 3.5 m/s. A boat with a speed of 8.5 m/s relative to the water sets a course that is pointed in a direction 30° north of east. Once the boat is in motion, one of the passengers walks from the left side of the boat directly to the right side of the boat at a speed of 1.5 m/s relative to the boat. What is the velocity of the passenger relative to the ground?

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Here are additional relative velocity problems for you to work on.

Problem # L-1:

Three forces are applied to a 2 kg slab, as shown. What is the slab's acceleration in unit-vector notation, and expressed as a magnitude and direction?

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Problem # L-2:

Suppose a force of 10.5 N is acting on the mass

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Problem # L-3:

A block of mass 2 kg is sliding along a flat frictionless surface at a velocity of 5 m/s. A force of 6 N is applied opposite the direction of motion of the block, and the block slows down to a velocity of 2 m/s. What is the travel distance of the block over the time period that the force is applied?

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Problem # L-4:

A block of mass

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Problem # L-5:

Two masses,

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Problem # L-6:

At an amusement park, a drop tower falls with an acceleration of 8.1 m/s

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Problem # L-7:

A helicopter is accelerating upward at 1.5 m/s

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Problem # L-8:

A space capsule simultaneously fires three of its thrusters, denoted by 1, 2, 3. If the thrusters fire for 9.5 s, and

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Problem # L-9:

A sphere of mass

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Problem # M-1:

In the pulley system shown, block 1 has a mass of 80 kg and block 2 has a mass of 30 kg. If the system is released from rest, what is the speed of block 2 after 1.5 seconds? Neglect the mass of the pulleys and rope.

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Problem # M-2:

In the pulley system shown, block

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Problem # M-3:

In the pulley system shown, the two blocks are released from rest. The sliding surfaces are frictionless, and the mass of the rope and pulleys is negligible. Determine the acceleration of each block and the tension in the rope. Note that

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Problem # M-4:

In the pulley system shown, the two blocks are released from rest. The sliding surface is frictionless, and the mass of the rope and pulleys is negligible. Determine the acceleration of each block and the tension in the rope. Note that

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Problem # M-5:

In the pulley system shown, block

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Problem # M-6:

Block

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Problem # M-7:

In the pulley system shown, two blocks are released from rest. The sliding surfaces are frictionless, and the mass of the pulleys and rope are negligible. After 1.3 s, what is the velocity of each block? Note that

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Problem # N-1:

In the system shown, the coefficient of static friction between all contact surfaces is 0.15, and the coefficient of kinetic friction between all contact surfaces is 0.10. Determine the acceleration of the blocks and the tension in the rope. Note that

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Problem # N-2:

Two blocks are sitting on a wheeled platform which is initially stationary. The coefficient of kinetic friction between the left block and the platform is 0.15, and the coefficient of kinetic friction between the right block and the platform is 0.10. The platform is given a sudden push to the right causing slippage between it and the blocks. Determine the acceleration of the blocks and the force between them. Note that

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Problem # N-3:

In the pulley system shown,

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Problem # N-4:

A disk is launched at an initial speed

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Problem # N-5:

A platform is accelerating to the right at 5 m/s

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Problem # N-6:

A force

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Problem # N-7:

In the pulley system shown,

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Problem # N-8:

Two masses,

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Problem # N-9:

A block of mass 2 kg is sitting on top of a conveyor belt moving at 5 m/s. The block is prevented from moving with the belt with a plate, as shown. As a result, the belt slides underneath the block with a speed of 5 m/s relative to the block. The coefficient of kinetic friction between the block and belt is 0.20, and there is no friction between the block and the plate. Suppose that someone were to push the block in the tranverse direction at a speed

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Here are additional friction problems and pulley problems for you to work on.

Problem # O-1:

A 3 kg ball is attached to a string of length

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Problem # O-2:

A 3 kg ball is going around in a horizontal circle of radius

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Problem # O-3:

A 3 kg ball is going around in a horizontal circle of radius

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Problem # O-4:

A block is sitting on the inside of a wheel rim, which has radius

(a) What is the minimum value of

(b) What is the minimum value of

(c) For each of the values of

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Problem # O-5:

A person riding a Gravitron at an amusement park can be modelled as a block, as shown. It is given that

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Problem # O-6:

A hollow sphere with a block of mass 0.500 kg inside of it is rotating with an angular velocity,

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Problem # O-7:

A block of mass

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Problem # P-1:

In the pulley system shown, the two blocks have a mass

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Problem # P-2:

In the pulley system shown,

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Problem # P-3:

In the pulley system shown, determine the acceleration of the block. The mass of the belt and pulley is negligible.

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Problem # P-4:

A cylinder is rolling down an incline, as shown. What is the minimum coefficient of static friction between the cylinder and surface so that the cylinder rolls without slipping? Suppose the coefficient of kinetic friction between the cylinder and surface is 0.10. What is the angular acceleration of the cylinder and what is the acceleration of its center of mass? Compare this to the no-slipping case. Note that

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Problem # P-5:

A cord is wound around the inner drum of a spool and pulled with a horizontal force of 120 N. The mass of the spool is 40 kg, and its radius of gyration is 60 mm. If

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Problem # P-6:

A hoop and solid cylinder are initially in contact on an incline, as shown. The mass of each is 50 kg and the radius of each is 30 cm. Is it possible for the hoop and cylinder to both remain stationary, and in contact, on the incline? If the coefficient of kinetic friction between the hoop and cylinder is 0.10, what is the angular acceleration of each, and what is the acceleration of the center of mass of each? How many rotations does the hoop and cylinder complete after each has rolled a distance of 1 meter?

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Here are additional problems for you to work on related to force and motion:

Force problems

Inclined plane problems

Torque problems

Here are examples of force and motion analysis in three-dimensions:

Bowling

Euler's disk

Gyroscopes

Problem # Q-1:

A truck is going down a hill that has an inclination of 20°. If the truck is travelling at constant speed

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Problem # Q-2:

A mass

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Problem # Q-3:

A 5 kg mass is slowly placed on a 3 kg mass that is initially at rest while supported by a spring underneath. If the spring stiffness is 250 N/m, what is the maximum compression amount of the spring, and what is the maximum velocity of the masses?

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Problem # Q-4:

A block of mass

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Problem # Q-5:

A mass

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Problem # Q-6:

A block on a flat horizontal surface has a force

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Problem # Q-7:

A block on the back of a truck, traveling at a constant velocity of 18 m/s, has a force

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Problem # R-1:

A cylinder is attached to a spring, while on an incline, as shown. The cylinder is released from rest when the spring is neither stretched nor compressed. The mass of the cylinder is 25 kg, its radius is 8 cm, and the spring stiffness is 500 N/m. What is the maximum and minimum speed of the cylinder, and the corresponding stretch amount of the spring? Assume the cylinder rolls without slipping.

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Problem # R-2:

A board of mass 16 kg is suspended from two cables, each of length 0.8 m, and each making an angle of 30° with the horizontal. While in this position, the board is released from rest. What is the velocity of the board when it is at its lowest position? Ignore the mass of the cables.

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Problem # R-3:

A board is supported by two cylinders on an incline, as shown. The mass of the board is 12 kg, the mass of each cylinder is 5 kg and their radius is 5 cm. If the system is released from rest and there is no slipping anywhere, what is the velocity of the board after it has moved a distance of 1.2 meters? Assume the board stays in contact with the cylinders.

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Problem # R-4:

In the pulley system shown,

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Problem # R-5:

A board is supported by two cylinders on a horizontal surface, as shown. The mass of the board is 13 kg, the mass and radius of the smaller cylinder is 5 kg and 5 cm, and the mass and radius of the larger cylinder is 10 kg and 7 cm. If the system is released from rest and there is no slipping anywhere, what is the velocity of the board after the cylinders have moved a distance of 30 cm ? Assume the board stays in contact with the cylinders.

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Here are additional problems for you to work on related to energy:

Energy problems

Kinetic energy problems

Problem # S-1:

Two masses,

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Problem # S-2:

In the system shown, a mass

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Problem # S-3:

An underwater capsule is stationary relative to the sea floor. The capsule has a mass of 2,200 kg. An 80 kg passenger in the capsule stands up, causing his center of mass to rise 40 cm relative to the capsule. The passenger then walks to the left a distance of 1.8 m relative to the capsule. What is the displacement of the capsule as a result of the movement of the passenger?

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Problem # S-4:

A cannon of mass 1,400 kg fires a ball of mass 60 kg in the horizontal direction with a velocity of 53 m/s relative to the cannon. What is the velocity of the cannon and ball relative to the Earth?

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Problem # S-5:

A water container of initial mass 120 kg is being lifted at constant velocity,

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Problem # S-6:

Two masses,

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Problem # S-7:

A chute is dumping sand onto a conveyor belt at the rate of 5 kg/s. The belt has a linear speed of 1.3 m/s. What is the power produced by the motor running the conveyor belt?

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Problem # S-8:

A 2-stage rocket has an initial mass of 1,250 kg. At the end of its first stage, the rocket has a mass of 500 kg. At this point, the lower section of the rocket separates, and the top section of the rocket begins firing. The lower section of the rocket has a mass of 200 kg. At the end of the second stage, the mass of the rocket (consisting only of the top section) is 140 kg. For both stages, the rocket consumes fuel at the rate of 2.4 kg/s. The speed of the exhaust gases relative to the rocket engine is 2,800 m/s. What is the speed increase of the rocket at the end of the second stage, and what is the thrust produced by the rocket? The rocket is in deep space where there is negligible gravitational force acting on it.

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Problem # T-1:

A mass

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Problem # T-2:

A golfer hits a golf ball, giving it an initial velocity of 60 m/s with a launch angle of 40° above the horizontal. The club and ball are in contact for 1.9 ms, and the mass of the ball is 45 g. Determine, (a) the impulse acting on the ball and the club, (b) the average force acting on the ball, and (c) the work done on the ball.

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Problem # T-3:

A child throws a ball having a mass of 150 g against a wall, with a speed of 6 m/s. The ball rebounds with a 40% reduction in its kinetic energy. Determine, (a) the speed of the ball immediately after rebounding, (b) the impulse acting on the ball and wall, and (c) the average force exerted on the ball if the contact time between ball and wall was 8.3 ms.

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Problem # T-4:

A space capsule separates into two parts, as a result of detonating the explosive bolts holding the two parts together. The magnitude of impulse acting on each part is 350 N·s. If the masses of the two parts are 1,300 kg and 1,900 kg, what is the relative speed of separation of the two parts?

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Problem # T-5:

As a result of an impact, an average force of 120 N acts on an object of mass 1.5 kg, in the

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Problem # T-6:

A toy consists of 3 rubber balls of mass

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Problem # T-7:

A 3.5 ton weight falls a distance of 1.8 m, and then impacts a 0.6 ton pile. As a result of this completely inelastic collision, the pile is driven 3 cm into the ground. Find the average force exerted on the pile by the ground?

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Problem # T-8:

A 40 ton train car collides with another train car that is stationary. The two cars couple together as a result, and 32% of the initial kinetic energy is lost during the collision. Determine the mass of the second train car.

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Problem # T-9:

Ball A is moving towards two balls, B and C, as shown, at a velocity of 5 m/s. Friction is negligible and the collision is elastic. If the balls are all identical, determine the velocities of all 3 balls after the collision.

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Problem # T-10:

Two rotating cylinders are brought into contact, as shown. Due to friction between the cylinders, they eventually reach the same angular velocity. What is this angular velocity? Note that the cylinders are initially rotating in opposite directions.

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Problem # T-11:

A block is initially at rest on a horizontal surface, and a force

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Here are additional momentum problems for you to work on.

Problem # U-1:

Identical blocks of length

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Problem # U-2:

In the system shown, the coefficient of static friction between the mass

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Problem # U-3:

A uniform board of length

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Problem # U-4:

A uniform board of length

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Problem # U-5:

In the system shown, determine the forces acting on the rod at point O, and the beam at point A.

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Here are additional statics problems for you to work on.

Here are additional mechanics problems for you to work on which cover different topics, so they are a good review.

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