Gravitational Potential Energy Practice Problems

A spacecraft is located at a distance from the sun equal to that of Jupiter's orbit and it needs to escape the solar system. Determine the minimum speed for the spacecraft to escape the gravitational pull of the sun.

In a two-star system, two stars of equal mass are separated by a distance of 1.5 × 10¹² m. An asteroid is approaching the stars with negligible speed. What will be its speed at the point when it is twice as close to one star as the other? Consider the mass of the two stars as 3.0 × 10²⁶ kg.

In a science fiction film, a skyscraper is under construction on a planet where the gravitational acceleration is 1.35 m/s². A worker drops his 7.00-kg toolbox from a height of 300 m above the ground. Find the speed of the toolbox just before hitting the ground.

If the center of mass of a 59-kg pole jumper rises 5.0 m during the jump, what is the change in gravitational potential energy?

A large hollow ball of outer radius R₁ was put into space. Its inner radius is R₂. The shell of the hollow ball of thickness R₁-R₂ is uniform in mass distribution and has a total mass of m. If another mass m' was placed at a distance of R (R > R1) away from the center of the hollow ball, calculate the gravitational potential energy of this mass m'.

A painter of mass 56.5 kg is painting a building's wall at an altitude of 26.4 m. If he gradually reaches the top of the building at an altitude of 40.2 m, calculate the change in his potential energy. [Hint: Assume that the gravitational acceleration is 9.80 m/s².]

A uniform plank, 5.00 m in length and weighing around 12.0 kg, rests against a smooth surface at an angle of approximately 30.0° to the ground. If the plank is pushed to a vertical position, how much will its gravitational potential energy increase?