Problem

a) If the gravitational potential energy of a 40.0-kg rock is 500. J relative to a value...

a) If the gravitational potential energy of a 40.0-kg rock is 500. J relative to a value of zero on the ground, how high is the rock above the ground?

b) If the rock were lifted to twice its original height, how would the value of its gravitational potential energy change?

Step-by-Step Solution

Solution 1

THINK:

Potential energyis the energy stored in the configuration of a system of objects that exerts forces on one another. The work done by gravitational force on an object that is lifted through a height to be

This work should be stored as potential energy in the system.

RESEARCH:

We elect to set the potential energy is stored in the rock to zero on the floor that is

At the instant rock of mass of m rises to a height h above the floor has only potential energy. Therefore the total energy of the system is

. . . . . . (1)

Hereis the acceleration due to gravity.

SIMPLIFY:

From equation (1), by solving for height of the rock above the ground is

. . . . . . (2)

CALCULATE:

According to the given information and the origin of the coordinate system we selected

Mass of the rock,

Potential energy of rock,

(a) Let the height of the block rises from floor be.

Therefore from equation (2), the height of the rock above the ground is

(b) When the rock is lifted to twice its height, that is

Then the gravitational potential energy at this height is

The initial potential energy of the system is

Therefore the change in gravitational potential energy of the system is

ROUND: keeping the answer into three significant figures

a)

b)

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