Question

A 2-kg block is thrown upward from a point 20 m above the Earth's surface. At what height above Earth's surface will the gravitational potential energy of the Earth-block system have increased by 500 J?

Answer 1

Answer:

45.5 m

Explanation:

m = 2 kg, h = 20 m, E = 500 J, radius of earth = R, mass of earth = M

find the new height H

at h, the potential energy = -GMm/(R + h)

at H, the potential energy = -GMm/(R + H)

increase of the potential energy

= [-GMm/(R + H)] - [-GMm(R + h)]

= GMm[1/(R + h) - 1/(R + H)] = E

1/(R + h) - 1/(R + H) = E/(GMm)

(H - h)/[(R + H)(R + h)] = E/(GMm)

R + h ≈ R, R + H ≈ R

so (H - h)/R² = E/(GMm)

H - h = ER²/(GMm)

note GM/R² = g = 9.81 m/s²

so H - h = E/(mg)

H = h + E/(mg) = 20 + 500/(2*9.81) = 45.5 m