An egg is released from rest from the roof of a building and falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origin at the ground. Do the values the two students assign to the following quantities match each other: initial gravitational potential energy, final gravitational potential energy, change in gravitational potential energy, and kinetic energy of the egg just before it strikes the ground? Explain.

Short Answer

Expert verified

Theinitial and final gravitational potential energies are different, but the change in gravitational potential energy and the kinetic energy of the egg is the same

Step by step solution

01

Concept/Significance of Work done

The work done on a particle by a constant gravitational force can be represented as a change in the gravitational potential energy is given by,

Wgrav=ΔUgrav=Ugrav,1-Ugrav,2=mgy1-mgy2......(1)

Here, assume that m is the mass of the egg y1and y2are the initial and final height of the building, g is the acceleration due to gravity, and localid="1668142626159" Wgrav, is the change in the gravitational potential energy.

02

Determine whether the values the two students assigned to the following quantities match each other 

The student on the roof will assign a coordinate of to the initial position of the egg and a final position of -h, here is the height of the roof when measured from the ground.

On the other hand, the student on the ground will assign a coordinate of to the initial position and a coordinate of to the final position.

Case 1:

When the person is on the roof.

Substitute -hfory1 , and 0fory2 in equation (1).

Wgrav=mgy1-mgy2=-mgh-0=-mgh

Case 2:

When the person is on the ground.

Substitute 0 for y1, and hfor y2in equation (1), and we get,

Wgrav=mgy1-mgy2=0-mgh=-mgh

Therefore, in both the cases the initial and final gravitational potential energies are different, but the change in gravitational potential energy and the kinetic energy of the egg just before it strikes the ground are the same.

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