Exam 10: Energy and Work

A block of mass m = 9.0 kg and speed V and is behind a block of mass M = 27 kg and speed of $0.50 \mathrm {~m} / \mathrm { s }$ as shown int the figure. The surface is frictionless, and the blocks suddenly collide and couple. After the collision, the blocks have a common speed of 0.90 m/s. How much kinetic energy of the blocks is lost due to the collision?

A uniform solid disk is released from rest and rolls without slipping down an inclined plane that makes an angle of 25° with the horizontal. What is the forward speed of the disk after it has rolled 3.0 m, measured along the plane?

A family goes on vacation for one week but forgets to turn off an electric fan that consumes electricity at the rate of 200 W. If the cost of electricity is 12.0¢/kW∙h how much does it cost (to the nearest penny) to run the fan for the week?

A baseball pitcher is employing a ballistic pendulum to determine the speed of his fastball. A $\text { 3.3-kg }$ lump of clay is suspended from a cord 2.0 m long. When the pitcher throws his fastball aimed directly at the clay, the ball suddenly becomes embedded in the clay and the two swing up to a maximum height of 0.080 m. If the mass of the baseball is 0.21 kg, find the speed of the pitched ball.

Two cyclists who weigh the same and have identical bicycles ride up the same mountain, both starting at the same time. Joe rides straight up the mountain, and Bob rides up the longer road that has a lower grade. Joe gets to the top before Bob. Ignoring friction and wind resistance, which one of the following statements is true?

An 8.0-g bullet is suddenly shot into a 4.0-kg block that is at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then moves against a spring and compresses it by 3.7 cm. The force constant (spring constant) of the spring is $2500 \mathrm {~N} / \mathrm { m }$ What was the initial speed v of the bullet?

A traveler pulls on a suitcase strap at an angle 36° above the horizontal. If $555 \mathrm {~J}$ of work are done by the strap while moving the suitcase a horizontal distance of $15 \mathrm {~m} \text {, }$ what is the tension in the strap?

If a spring-operated gun can shoot a pellet to a maximum height of 100 m on Earth, how high could the pellet rise if fired on the Moon, where g = 1.6 m/s²?

A 100-N force has a horizontal component of 80 N and a vertical component of 60 N. The force is applied to a cart on a level frictionless floor. The cart starts from rest and moves 2.0 m horizontally along the floor due to this force. What is the cart's final kinetic energy?

You do 116 J of work while pulling your sister back on a fritctionless swing, whose chain is $5.10 \mathrm {~m}$ long, until the swing makes an angle of 32.0° with the vertical. What is your sister's mass?

A heavy frog and a light frog jump straight up into the air. They push off in such away that they both have the same kinetic energy just as they leave the ground. Air resistance is negligible. Which of the following statements about these frogs are correct? (There could be more than one correct choice.)

A 0.32-kg ball is moving horizontally at 30 m/s just before suddenly bouncing off a wall Just after the bounce, it is moving horizontally at 25 m/s but in the opposite direction. (a) What is the magnitude of the change in momentum of the ball during the bounce? (b) What percentage of the ball's original kinetic energy was lost in the collision?

NASA puts a satellite into space that consists of two small 32-kg balls connected by a 12-m long light cable, as shown in the figure. The entire system is initially rotating at 4.0 rpm about an axis perpendicular to the cable at the center of mass. Motors in each mass reel out more cable so that the masses double their separation to 24 m. (a) What is the final rotational speed (in rpm) of the balls? (b) If the initial rotational kinetic energy of the system was K, what is the final rotational kinetic energy in terms of K?

In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

A 100%-efficient engine is being used to raise a 89-kg crate vertically upward at a steady rate. If the power output of the engine is 1620 W, how long does it take the engine to lift the crate a vertical distance of 18.7 m? Friction in the system is negligible.

Jill does twice as much work as Jack does and in half the time. Jill's power output is

A block of mass m = 3.6 kg, moving on a frictionless surface with a speed $\mathrm { v } _ { \mathrm { i } } = 9.3 \mathrm {~m} / \mathrm { s }$ makes a sudden perfectly elastic collision with a stationary block of mass M, as shown in the figure. Just after the collision, the 3.6-kg block recoils with a speed of $v _ { \mathrm { f } } = 2.7 \mathrm {~m} / \mathrm { s }$ What is the speed V of the other block?

A certain battery charger uses 12 W of power. At 6.0 cents per kilowatt-hour, how much does it cost to charge batteries for a full day?

A 1000-kg car is moving at 15 km/h. If a 2000-kg truck has 23 times the kinetic energy of the car, how fast is the truck moving?

In a certain nuclear reactor, neutrons suddenly collide with carbon nuclei, which have 12 times the mass of neutrons. In a head-on elastic collision with a stationary carbon nucleus, what fraction of its initial speed does the neutron have after the collision?