Exam 5: Kinetic Energy, work, and Power

A spring of negligible mass is compressed by 0.250 m.Then a steel ball bearing of mass 0.05 kg is put on the spring,and the spring is released.The spring and ball bearing are aligned horizontally and friction is negligible.In addition,assume that the ball bearing will come off the spring exactly as the spring returns to its equilibrium position.The speed of the ball bearing right after the ball bearing loses contact with the spring is 12.9 m/s.What is the spring constant of the spring?

If the kinetic energy of a sub-atomic particle was doubled,then by what factor would its speed increase?

A rope that makes an angle of 28 degrees with respect to the horizontal is used to pull a sled.The sled has a mass of 35 kg and the tension in the rope is 17 N.How much work is done by the force of the rope if the sled moves a horizontal distance of 5.6 m?

A force has the dependence F_x = -ax⁴ on the position x.The work performed by this force when the position of its point of application changes from 0.75 m to 1.50 m is -32.2 J.the constant a is

Two boats are travelling along a river.Boat A is half as massive as boat B,but is going 3 times as fast.What is the ratio of kinetic energies K_A/K_B?

A 1.2-kg toy train is moving with a speed of 2.0 m/s.What is its kinetic energy?

What is the force that a baseball pitcher must apply to a 145 g baseball over a distance of 2.2 m to give it a speed of 144 km/hr when the ball is released? Assume that the force is constant.

An electron's initial position is zero and its final position is 1.00 m.The electric force on the electron is to the left and its magnitude is ,where F is measured in newtons and x is measured in meters.How much work does the electric force do on the electron as it moves?

A 10.0-g bullet traveling at 200 m/s strikes a fixed wooden block.The bullet comes to rest 22 cm inside the block.The magnitude of the force exerted on the bullet by the block over its 22-cm travel is shown in graph.Find the value of F_max.

The force acting on a 30.0 kg ball is -1.20  10¹⁶ r ^-2 (the force pulls the ball towards r = 0).An externally applied force moves the ball slowly from an initial distance of r_i = 6.38  10⁶ m to a final position of r_f= 6.39  10⁶.The work done by the applied force is

The Statue of Freedom stands above the US Capital Dome.She is made of bronze,has a mass of 6800 kg,and stands 6.0 m tall and the top of her head is 88 m above the ground.How much work was done in lifting her up to the top of the Capital Dome (assume she was in the standing position when they started lifting her)?

Initially an object of mass 1.00 kg is moving to the left at 10.0 m/s.If 150 J of work is done on the object,then how fast will it be moving?

What is the average power output of an engine when a car of mass m accelerates from rest to a final speed v over a distance d on flat,level ground? Ignore energy lost due to friction and air resistance.

A mass of 0.75 kg is suspended from a spring.If 1.41 J of work is done against the spring as the mass is pulled 0.15 m away from its equilibrium position,what is the spring constant of the spring?

A spring of negligible mass and with spring constant 200.0 N/m is compressed by 0.250 m.Then a steel ball bearing of mass 0.05 kg is put on the spring,and the spring is released.The spring and ball bearing are aligned horizontally and friction is negligible.In addition,assume that the ball bearing will come off the spring exactly as the spring returns to its equilibrium position.The speed of the ball bearing right after the ball bearing loses contact with the spring is

A 1000-kg car starts from rest and accelerates to 60 mph (27 m/s)in 6.0 s.How much horsepower is required for this to occur?

An ideal spring is attached to the ceiling.Without anything attached to the bottom of the spring,the bottom of the spring is 40 cm below the ceiling.When a 3.0 kg mass is attached to the bottom of the spring,the bottom of the spring (at rest)is 65 cm below the ceiling.What is the spring constant of the spring?

A 30.0 kg ball is released from rest and is acted upon by a net force of -1.40  10¹⁶ r ^-2 (the force pulls the ball towards r = 0).The ball starts from rest at an initial position of r_i = 6.39  10⁶ m and moves under the influence of the force to a final position of r_f= 6.38  10⁶.What is the speed of the ball when it reaches its final position,r_f?

When a 2 kg object is at x = 2 m it has a velocity 2.5 m/s in the positive x-direction.The object is subjected to a single force of the form F=3x² + 2x + 5 N as it moves from x = 2 m to x = 4 m.what is the speed of the object when its location is x = 4 m?

A lift is used to raise objects to the back of a moving truck.If the maximum power the lift is capable of delivering is 98 W,what is the maximum constant speed with which this lift can raise a 5.0 kg crate straight up from the ground to the back of the moving truck? The back of the moving truck is 5.0 m above the ground.