10. Conservation of Energy

Which of the following quantities is required to calculate the gravitational potential energy of an object near $E’s$ surface?

Energy stored in a system due to its position is what kind of energy?

As a planet approaches the perihelion of its orbit around the Sun, which of the following best describes the change in its gravitational potential energy?

According to the standard reference point where the ground is chosen as zero height, what is the gravitational potential energy of an object resting on the ground?

By how much does the gravitational potential energy of a 58-kg pole vaulter change if her center of mass rises 4.0 m during the jump?

A sphere of radius r₁ has a concentric spherical cavity of radius r₂ (Fig. 8–42). Assume this spherical shell of thickness r₁ - r₂ is uniform and has a total mass M. Show that the gravitational potential energy of a mass m at a distance r from the center of the shell ( r > r₁) is given by U = - (GmM/r).

The free-fall acceleration on a large asteroid, in the vacuum of space, is 0.15 m/s². A spacecraft hovering 500 m above the surface drops a 25 kg payload wrapped in a padded jacket. What is the payload's impact speed?

A binary star system has two stars, each with the same mass as our sun, separated by 1.0 ✕ 10¹² m. A comet is very far away and essentially at rest. Slowly but surely, gravity pulls the comet toward the stars. Suppose the comet travels along a trajectory that passes through the midpoint between the two stars. What is the comet's speed at the midpoint?

A 66.5-kg hiker starts at an elevation of 1150 m and climbs to the top of a peak 2660 m high. What is the hiker’s change in potential energy?

A uniform 2.00-m ladder of mass 9.00 kg is leaning against a vertical wall while making an angle of 53.0° with the floor. A worker pushes the ladder up against the wall until it is vertical. What is the increase in the gravitational potential energy of the ladder?

CALC A particle of mass m has the wave function ψ(x) = Ax exp (−x²/a²) when it is in an allowed energy level with E = 0. Find and graph the potential-energy function U(x).

A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?