Two solid uniform cylinders are connected with a belt wrapped around both cylinders, as shown in the figure below. The mass and radius of the smallest cylinder is

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In the previous problem, suppose that the distance between the center of both cylinders, A and B, is equal to

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In the figure below, a liquid is shown flowing through a horizontal pipe in steady-state fashion. The cross-sectional area of the pipe at location A is larger than at location B. Using the Bernoulli equation and the concept of mass conservation, explain why there is a difference in the kinetic energy of the liquid between locations A and B.

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In the figure below, wind is blowing through a wind turbine at constant velocity

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The figure below shows a linkage with a wheel on each end, and each wheel can move freely inside two slots that are perpendicular to each other. The mass of the linkage is

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A car is traveling on the highway at a speed

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A plane is flying in a straight line at a velocity of

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Answer for Problem # 1

The kinetic energy of the smallest cylinder is

Answer for Problem # 2

Let's say the length of the belt is

Answer for Problem # 3

According to the Bernoulli equation, (1/2)

Answer for Problem # 4

The answer is 59.3%. The solution to this problem comes from the well known Betz' Law for wind turbines, which can be easily referenced online. Take the time to look this up, since it's an interesting problem, originally solved by Albert Betz in 1919.

Answer for Problem # 5

To make things easier to visualize, first imagine an xy-coordinate system with origin located at the bottom right corner, where the line of travel of the center-point of both wheels meet, and positions to the left of, and above, this point are considered positive. Then, the x-position of the center of mass of the linkage is x = (1/2)

Answer for Problem # 6

The total kinetic energy of the car is equal to the kinetic energy of the car body + driver + wheels. Therefore,

Answer for Problem # 7

The kinetic energy of the propeller is equal to

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