Question

A ball with an unknown mass mA is initially a distance hA above the surface of the planet Alderaan. A box with an unknown mass mE is initially a distance hE above the surface of the Earth. Both the ball on Alderaan and the box on Earth have the same gravitational potential energy (GPE) relative to the surface of each respective planet. Both the ball on Alderaan and the box on Earth are then dropped from rest, and each is caught by a person standing on the surface of that planet. The person on Alderaan and the person on Earth each apply the same impulse while catching the ball and the box, respectively. If the ball on Alderaan was dropped from an initial height of hA = 10.1 m, what was the initial height hE of the box on Earth before it was dropped? The mass of Alderaan is 7.2 × 10^24 kg, its radius is 6.36 × 10^6 m, and G = 6.67 × 10^−11 Nm^2/kg^2. (Ignore any air resistance and use 9.8 m/s^2 for the gravitational field strength of the Earth). Answer in units of meters." A) hE = 10.1 m

B) hE = 20.2 m
C) hE = 30.3 m
D) hE = 40.4 m

Answer 1

To find the initial height hE of the box, equate the gravitational potential energy on Alderaan with that on Earth using the formula G.P.E. = mgh, and calculate the gravitational acceleration on Alderaan to solve for hE.

Step-by-step explanation:

The student is asked to determine the initial height hE of a box on Earth using the concept of gravitational potential energy (GPE) and provided that the GPE is the same for both the box on Earth and a ball on the planet Alderaan when dropped from their respective heights. The GPE is given by the equation G.P.E. = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above ground. Since both objects experience the same impulse upon being caught and have the same initial gravitational potential energy, we can equate the GPEs of both the box on Earth and the ball on Alderaan to solve for the unknown height hE.

To find hE, we first need to calculate the gravitational force on Alderaan using the formula F = G(mA)(mAlderaan)/r^2, where G is the gravitational constant, mA is the unknown mass of the ball, mAlderaan is the mass of Alderaan, and r is the radius of Alderaan. The acceleration due to gravity on Alderaan is then gA = F/mA. Knowing the value of gA and the height hA, we can calculate the GPE on Alderaan: G.P.E.Alderaan = mAgAhA. As the GPE for the box on Earth is the same, G.P.E.Earth = mEgEhE where gE = 9.8 m/s^2 and mE is the unknown mass of the box on Earth, and we solve for hE.