A box is pushed through 4 m across a floor offering 100 n resistance. How many work is done by the resisting force?

To determine the work done by the resisting force when a box is pushed across the floor, we can use the formula for work, which is defined as the product of force and distance moved in the direction of the force. However, in this case, we are interested in the work done by the resisting force, which acts in the opposite direction to the movement of the box.

Understanding Work Done by a Force

Work (W) is calculated using the formula:

W = F × d × cos(θ)

Where:

• W = work done (in joules)
• F = force applied (in newtons)
• d = distance moved (in meters)
• θ = angle between the force and the direction of motion (in degrees)

Applying the Formula to the Resisting Force

In this scenario, the resisting force is 100 N, and the box is pushed through a distance of 4 m. Since the resisting force acts directly opposite to the direction of movement, the angle θ is 180 degrees. The cosine of 180 degrees is -1, which indicates that the work done by the resisting force will be negative, reflecting that it opposes the motion.

Now, substituting the values into the formula:

W = F × d × cos(θ)

W = 100 N × 4 m × cos(180°)

W = 100 N × 4 m × (-1)

W = -400 J

Interpreting the Result

The negative sign indicates that the work done by the resisting force is -400 joules. This means that the resisting force is doing work against the motion of the box, effectively taking energy away from the system as the box is pushed across the floor.

Real-World Analogy

Think of it like trying to walk on a sandy beach. If you push against the sand (the resisting force), you exert energy, but the sand also pushes back against you, making it harder to move forward. In this case, the work done by the sand (resisting force) is negative because it opposes your movement.

In summary, when you push the box across the floor against a resistance of 100 N for a distance of 4 m, the work done by the resisting force is -400 joules, indicating energy is being expended to overcome that resistance. This concept is crucial in understanding how forces interact in various physical situations.