Exam 6: Conservation of Energy

A spring-powered launcher has a spring with a constant of 50.0 N/cm. The launcher is prepared by compressing the spring by 5.00 cm. If the mass of the projectile is 10.0 grams, what is the speed of the projectile when it is launched?

A 1 kg mass is attached to a vertical spring, stretching it by 10 cm from its equilibrium position. With the spring secured in the same stretched position, the 1 kg mass is removed and replaced with a 0.50 kg mass. If the spring is then released, how high will the 0.50 kg mass rise above the point where it was released?

An 8000 kg satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of 100 km above the surface of the Earth. The kinetic energy of the satellite in the circular orbit is (G = 6.67 × 10⁻¹¹ N·m²/kg², M_E = 5.97 × 1024 kg, R_E = 6.37 × 10⁶ m)

A blob of clay of mass M is dropped onto a spring from a height h above the end of the spring. If the spring compresses by an amount d as the blob comes to rest, what is the spring constant k?

A 2500 kg car accelerates from rest to a velocity of 30.0 m/s in 8.00 seconds. The work done by the engine to accelerate the car is

A spring-powered dart gun is unstretched and has a spring constant 16.0 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The velocity of the projectile when it is shot from the gun is

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 4.00 m/s when the support string makes an angle of 30.0 degrees with the vertical. What is the speed of the bob at the bottom of the swing?

A horizontal force of 12 newtons is applied to a 4.0 kg box that slides on a horizontal surface. The box starts from rest, moves a horizontal distance of 10 meters, and obtains a velocity of 5.0 m/s. The surface has friction. The friction force, assumed constant, is

A road bicycle racer rides down the highway from Pike's peak. During one stretch of the ride, he descends 150 m while accelerating from 35 km/hr to some final speed. Assuming friction and air resistance to be negligible, and treating kinetic energy as purely translational (i.e., ignoring any rotational part), what is his final speed?

The graph shows the force on an object as it moves a distance x. What is the work done by the force as the object moves from 0.0 m to 4.0 m?

A 200 N box is pushed at a constant velocity up an incline that is 5.00 m long and rises 1.00 m. The incline has a coefficient of kinetic friction of 0.200, and the pushing force is parallel to the incline. The work done by the pushing force is

A 20.0 kg box slides down a 12.0 m long incline at an angle of 3.0 degrees with the horizontal. A force of 50.0 N is applied to the box to try to prevent it from sliding down the incline. The applied force makes an angle of 0.00 degrees to the incline. If the incline has a coefficient of kinetic friction of 0.100, then the increase in the kinetic energy of the box is

A 90.0 kg person is running up some stairs at 0.500 m/s. If the staircase is angled at 45.0° to the horizontal, then the power needed to run up the stairs is

An airplane has a mass of 30,000 kg and travels at 300 m/s. If the drag force is 1000 N, then the power the engines have to provide to keep flying at a constant speed is

The graph shows the force on an object as it moves a distance x. What is the work done by the force as the object moves from 0.0 m to 10.0 m?

A 200 N box is pushed at a constant velocity up an incline that is 5.00 m long and rises 1 m. If the incline is frictionless, then the work done by the pushing force is

A 20.0 kg box slides up a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 150 N is applied to the box to pull it up the incline. The applied force makes an angle of 10.0 degrees to the incline. What is the change in gravitational potential energy of the box?

A spring-powered dart gun is unstretched and has a spring constant 16.0 N/m. The spring is compressed by 8.0 cm and a 5.0 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is

A 120 N horizontal force is applied to a 4.00 kg box on a frictionless surface. The box moves a horizontal distance of 8.00 meters. The change in the kinetic energy of the box is

A 20 N horizontal force is applied to a 4.0 kg box. Friction is negligible. The box moves a horizontal distance of 3.0 meters. The work done by the 20 N force is