What is the escape speed from the surface of Earth? Assume there is no energy loss from air resistance. Compare this to the escape speed from the Sun, starting from Earth's orbit. (1.12 x 104 m/s, 4.21 x 104 m/s)

How would you have to adjust the starting height to have the same amount of energy among the Earth, Moon, and Jupiter?

A basketball player throws a basketball m = 1 kg straight up with an initial speed of v0 = 9.5 m/s. The ball leaves his hand at shoulder height h0 = 2.2 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g.

A 43-kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.5 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.

Problem 3:   A hiker of mass 57 kg is going to climb to the top of Mount Tam, which has an elevation of 2,574 ft. Part (a)  If the hiker starts climbing at an elevation of 495 ft, what will their change in gravitational potential energy be, in joules, once they reach the top? Assume the zero of gravitational potential energy is at sea level.  ΔVg = ______ Part (b)  Repeat the above calculation for the change in gravitational potential energy, but assume the gravitational potential is zero at the top of the mountain.  ΔVg = ______

A particle of mass 4.0 kg moves under the influence of the force F(x) = (-5x + 7x) N. If its speed at x = -2.4 m is v = 24.0 m/s, what is its speed (in m/s) at x = 2.4 m? m/s

A 59-kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.3 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.

Kepler’s laws of planetary motion can be derived from Newton’s laws of motion and Newton’s universal law of gravitation. Since gravity is a conservative force, mechanical energy is conserved throughout a planet’s orbit. a) Is the gravitational potential energy of the planet-Sun system greater at perihelion (the point of closest approach to the Sun) or aphelion (the point of farthest approach from the Sun)? b) Is the kinetic energy of the planet-Sun system greater at perihelion or aphelion? c) Is your answer consistent with Kepler’s second law of planetary motion? Justify your answers.

In a futuristic scenario, you are assigned the mission of making an enemy satellite that is in a circular orbit around Earth inoperative. You know you cannot destroy the satellite, as it is well protected against attack, but you can try to knock it out of its orbit so it will fly away and never return. What is the minimum amount of work ?W applied to the satellite that is required to accomplish that? The satellite's mass and altitude are 969 kg969 kg and 241 km.241 km. Earth's mass and radius are 5.98×1024 kg5.98×1024 kg and 6370 km.

A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground- Utop).  What is the child's final speed, vf in m/s?