Exam 10: Energy and Work

A futuristic design for a car is to have a large flywheel within the car to store kinetic energy. The flywheel is a solid uniform disk of mass 370 kg with a radius of 0.50 m, and it can rotate up to $200 \mathrm { rev } / \mathrm { s }$ Assuming all of this stored kinetic energy could be transferred to the linear speed of the $1500 - \mathrm { kg }$ car, find the maximum attainable speed of the car.

A toy rocket that weighs 10 N blasts straight up from ground level with an initial kinetic energy of 40 J. At the exact top of its trajectory, its total mechanical energy is 140 J. To what vertical height above the ground does it rise, assuming no air resistance?

When you throw a pebble straight up with initial speed V, it reaches a maximum height H with no air resistance. At what speed should you throw it up vertically so it will go twice as high?

A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?

A solid uniform cylinder is rolling without slipping. What fraction of its kinetic energy is rotational?

Joe and Bill throw identical balls vertically upward. Joe throws his ball with an initial speed twice as high as Bill. If there is no air resistance, the maximum height of Joe's ball will be

A 5.0-N projectile leaves the ground with a kinetic energy of 220 J. At the highest point in its trajectory, its kinetic energy is 120 J. To what vertical height, relative to its launch point, did it rise if there was no air resistance?

A 550-g ball traveling at 8.0 m/s undergoes a sudden head-on elastic collision with a 250-g ball traveling toward it also at 8.0 m/s. What is the speed of the 250-g mass just after the collision?

A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first?

An ideal spring with a spring constant (force constant) of $22 \mathrm {~N} / \mathrm { m }$ is stretched from equilibrium to 2.9 m. How much work is done in the process?

How much kinetic energy does a 0.30-kg stone have if it is thrown at $44 \mathrm {~m} / \mathrm { s } \text { ? }$

A sled having a certain initial speed on a horizontal surface comes to rest after traveling 10 m. If the coefficient of kinetic friction between the object and the surface is 0.20, what was the initial speed of the object?

A solid uniform 3.33-kg disk has thin string of negligible mass wrapped around its rim, with one end of the string tied to the ceiling, as shown in the figure. The disk is released from rest, and as it falls, it turns as the string unwraps. At the instant its center has fallen 2.25 m, (a) how fast is the center moving, and (b) how much rotational kinetic energy does the disk have?

How fast must a 6.0-kg cat run to have a kinetic energy of 150 J?

Three cars (car L, car M, and car N) are moving with the same speed and slam on their brakes. The most massive car is car L, and the least massive is car N. If the tires of all three cars have identical coefficients of kinetic friction with the road surface, for which car is the amount of work done by friction in stopping it the greatest?

When you drop a pebble from height H, it reaches the ground with speed V if there is no air resistance. From what height should you drop it so it will reach the ground with twice speed?

A sand mover at a quarry lifts 2,000 kg of sand per minute a vertical distance of 12 m. The sand is initially at rest and is discharged at the top of the sand mover with speed 5.0 m/s into a loading chute. What minimum power must be supplied to this machine?

If the units of your answer are kg ∙ m²/s³, which of the following types of quantities could your answer be? (There could be more than one correct choice.)

A block of mass m = 4.4 kg, moving on frictionless surface with a speed $v _ { \mathrm { i } } = 9.2 \mathrm {~m} / \mathrm { s }$ makes a sudden perfectly elastic collision with a second block of mass M, as shown in the figure. The second block is originally at rest. Just after the collision, the 4.4-kg block recoils with a speed of $v _ { \mathrm { f } } = 2.5 \mathrm {~m} / \mathrm { s }$ What is the mass M of the second block?

A small 1.4-N stone slides down a frictionless bowl, starting from rest at the rim. The bowl itself is a hemisphere of radius 75 cm. Just as the stone reaches the bottom of the bowl, how hard is the bowl pushing on it?