To calculate the work done by the person on the box, we use the formula for work:
\[ \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \]
where:
- Work is in joules (J),
- Force is in newtons (N),
- Distance is in meters (m),
- \(\theta\) is the angle between the force and the direction of movement.
In this case, the force applied is 400 N and the distance over which the force is applied is 4 m. Assuming the force is applied in the same direction as the movement of the box (which means \(\theta = 0\) degrees and \(\cos(0) = 1\)), we can simplify the formula to:
\[ \text{Work} = \text{Force} \times \text{Distance} \]
Calculating the work done:
\[ \text{Work} = 400 , \text{N} \times 4 , \text{m} = 1600 , \text{J} \]
The sliding of the box after the person stops pushing does not contribute to the work done by the person.
Therefore, the amount of work done by the person pushing the box is 1,600 joules.