Question

A 4 kg object is lifted from the floor and placed on a shelf that is 3 m above the floor. What was the work done in lifting the object?

Answer 1

To calculate the work done in lifting an object against gravity, you can use the formula:

\[
\text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta)
\]

In this case:
- The force is equal to the weight of the object, which can be calculated as:

\[
\text{Force} = \text{mass} \times g
\]

where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \).

- The distance is the height the object is lifted, which is \( 3 \, \text{m} \).
- Since the force is applied in the same direction as the displacement when lifting the object, \( \theta = 0^\circ \), and \( \cos(0)=1 \).

Now, substituting the values:

1. Calculate the force (weight of the object):
\[
\text{Force} = 4 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 39.24 \, \text{N}
\]

2. Calculate the work done:
\[
\text{Work} = 39.24 \, \text{N} \times 3 \, \text{m} \times \cos(0) = 39.24 \, \text{N} \times 3 \, \text{m} = 117.72 \, \text{J}
\]

Therefore, the work done in lifting the object is \( 117.72 \, \text{J} \).