Question

A hammer of mass 200g is dropped from the top of a roof of the two storey building to the ground. Another hammer of equal mass fell from a coffee table to the ground. Given than the height of the two storey building and the coffee table are 10 m and 5 m respectively.
a. Show that a hummer dropped from two storey building roof does more work than a hammer falling from a coffee table.
b. Calculate the potential energy from the two heights.

Answer 1

Answer on Question #54734, Physics / Mechanics | Kinematics | Dynamics

A hammer of mass 200g is dropped from the top of a roof of the two storey building to the ground. Another hammer of equal mass fell from a coffee table to the ground. Given that the height of the two storey building and the coffee table are 10 m and 5 m respectively.

a. Show that a hammer dropped from two storey building roof does more work than a hammer falling from a coffee table.

b. Calculate the potential energy from the two heights.

Solution:

a. In order to accomplish work on an object there must be a force exerted on the object and it must move in the direction of the force.

$$\text{Work} = \text{Force} \times \text{distance moved in direction of force}$$

Energy can be defined as the capacity for doing work. It may exist in a variety of forms and may be transformed from one type of energy to another. However, these energy transformations are constrained by a fundamental principle, the Conservation of Energy principle.

In our case

$$\text{work} = \text{decreasing of potential energy}$$ $$W = mgh$$

The potential energy at a height $h$ is equal to the work which would be required to lift the object to that height.

For hammer dropped from two storey building

$$W_1 = (0.2 \, kg)(10 \, m/s^2)(10 \, m) = 20 \, \text{Joules}$$

For hammer dropped from a coffee table

$$W_2 = (0.2 \, kg)(10 \, m/s^2)(5 \, m) = 10 \, \text{Joules}$$ $$W_1 = W_2$$

b.

$$PE_1 = W_1 = mgh_1 = 20 \, \text{Joules}$$ $$PE_2 = W_2 = mgh_2 = 10 \, \text{Joules}$$