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## Homework Statement

Imagine that a treasure chest of mass m=100kg falls to the ground from a jet flying at an altitude of 35 km.

(a) calculate the chest's initial potential energy according to formula V(z)=mgz

(b) caculate the chest's initial potential energy according to formula V(r)=-G(m1m2/r)

(c) Are answers different? Explain why this is.

(d) Caculate change in chest's ptoential energy during its fall according to formula V(z)=mgz

(e) Calculate change in chest's potential energy during its fall according to formula

V(r)=-G(m1m2/r)

(f) Are answers different? Explain why this is.

## Homework Equations

V(z)=mgz

V(r)=-G(m1m2/r)

r=35000m + re = 6,415,000m

re=center of earth to surface=6,380,000m

## The Attempt at a Solution

(a) I know this answer is 3.4x10^7 J

(b)V(chest)=[-3.99x10^14 Jm/kg(100Kg)]/6,415,000m = 3.41x10^7J (WRONG)

(c) The answers should not be the same because the formula used in A and B are for different things. The formula used in A is only for kinetic energy near the earths surface while the formula used in B should be used for items in space (Not very clear on this)

(d) V(chest)=mg(change in z)=-3.4x10^7J (is a negative number reasonable??)

(e) V(chest)=-GMm[(1/re)-(1/re+r)]=-3.4x10^5 J

(f) The answers should not be the same because the formula used in A and B are for different things. The formula used in A is only for kinetic energy near the earths surface while the formula used in B should be used for items in space (Not very clear on this).