if the system is a basket,
the basket is tied to a rope and it is stopped by a fixed clamp when it is falling down, I know there is initial KE but how come initial work is negative. Isnt force and displacement are in the same direction, so work should be positive?
In order to understand why the initial work is negative in this scenario, let's break it down step by step and consider the forces and displacements involved.
1. Initially, the basket is at rest. Therefore, its initial kinetic energy (KE) is zero.
2. When the basket starts to fall down, gravity acts as the only force on it. This force is directed downwards while the displacement is also downwards. So we have force and displacement in the same direction.
3. However, it is important to consider the reference point for calculating work. Work is defined as the dot product of force and displacement. The dot product considers the angle between the force and displacement vectors. If the angle between them is 0° (i.e., if they are in the same direction), the work will be positive. But if the angle is 180° (i.e., if they are in opposite directions), the work will be negative.
4. In this case, the basket is tied to a rope and stopped by a fixed clamp. The clamp exerts an upward force on the basket to stop its fall. As a result, the force and displacement vectors are in opposite directions (180° apart), making the angle between them 180°.
5. Due to this 180° angle, the work done by the upward force of the clamp is negative. This negative work reduces the gravitational potential energy of the basket, resulting in a change from potential energy to kinetic energy. This is why the initial work is negative.
In conclusion, although the force and displacement are in the same direction, the presence of an opposite force (from the clamp) causes the work to be negative. Understanding the relationship between forces, displacements, and the angle between them is crucial to determining the sign (positive or negative) of the work done on an object in any given situation.