Final answer:
To lift a box to the same height using a longer ramp does not change the work done but decreases the force needed. A 4 m ramp would require half the force, so 100 N would be needed.
Step-by-step explanation:
The question involves the concept of work and mechanical advantage provided by a ramp in physics. To determine the force needed to lift the box with a 4m ramp, we need to apply the work-energy principle which states that the work done on an object is equal to the change in its energy. Here, the work done to lift the box remains the same but is distributed over a longer distance when using a ramp.
Using the ramp, the same amount of energy is required to lift the box to the same height, but the force is applied over a longer distance. Hence, the force needed is inversely proportional to the length of the ramp. If 200 N is needed to lift the box 2 m high without the ramp, a 4 m ramp would halve the force required, so 100 N would be needed to push the box up the 4 m ramp.