A 1.0 kg book initially at rest falls from a height of 1.5 m to the floor. a. Se

Question

A 1.0 kg book initially at rest falls from a height of 1.5 m to the floor.

a. Set the origin of the coordinate system at the floor and calculate the initial gravitational potential energy. the final gravitational potential energy (just before the book hits the floor), and the change in the gravitational potential energy. Show your work.

b. Set the origin of the coordinate system at the starting point 1.5 above the floor and calculate the initial gravitational potential energy, the final gravitational potential energy (just before the book hits the floor), and the change in the gravitational potential energy. Show your work.

c. Does the gravitational potential energy at the initial and final points depend upon the location of the origin of the coordinate system?

d. Does the change in gravitational potential energy depend on the location of the origin of the coordinate system?

e. Use the conservation of mechanical energy and show symbolically that the final speed of the book depends on the change in gravitational potential energy, and hence is independent of your choice of coordinate system.

PEi PEf

PE

A 1.0 kg book initially at rest falls from a height of 1.5 m to the floor. a. Set the origin of the coordinate system at the floor and calculate the initial gravitational potential energy. the final gravitational potential energy (just before the book hits the floor), and the change in the gravitational potential energy. Show your work. b. Set the origin of the coordinate system at the starting point 1.5 above the floor and calculate the initial gravitational potential energy, the final gravitational potential energy (just before the book hits the floor), and the change in the gravitational potential energy. Show your work. c. Does the gravitational potential energy at the initial and final points depend upon the location of the origin of the coordinate system? d. Does the change in gravitational potential energy depend on the location of the origin of the coordinate system? e. Use the conservation of mechanical energy and show symbolically that the final speed of the book depends on the change in gravitational potential energy, and hence is independent of your choice of coordinate system.

Explanation / Answer

a)   PE = mgh
h - height from origin point
PEi = 1 x 9.81 x 1.5 = 14.72 J

PEf = mgh = 1 x 9.81 x 0 = 0

CHange in P.E. = PEf - PEi = - 14.72 J

b) PE = mgh
h - height from origin point
PEi = 1 x 9.81 x 0 = 0J

PEf = mgh = 1 x 9.81 x -1.5 = - 14.72

CHange in P.E. = PEf - PEi = - 14.72 - 0 =   - 14.72 J

c) YEs , it depends.

d) No, It doesn't .

e) using energy conservation,
P.Ei + K.E. i   = P.Ef + K.Ef
K.E.i   - K.E.f = P.E.f - P.E.i
K.E.i - K.E.f = change in P.E.
0 - 1v^2 /2   = -14.72
v = 5.42 m/s

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