Work Done and Types of Energy

Work is defined as the product of force and the displacement of an object in the direction of the force. In this scenario, although a force of 500 N is applied, the object does not move, which means the displacement is zero. Since work is calculated as \( \text{Work} = \text{Force} \times \text{Displacement} \), and displacement is zero, the total work done on the object is also zero joules.

Work done is calculated using the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the direction of motion. Here, the force of 20 N is applied in the same direction as the movement of 4 m, making θ = 0 degrees, and cos(0) = 1. Thus, the work done is 20 N × 4 m × 1 = 80 J. The weight of the object does not affect the work done by the pulling force in this scenario.

Work is defined as the product of force and the distance moved in the direction of that force. In this scenario, although the boy applies a force of 400 N, the cupboard does not move at all. Since there is no displacement, no work is accomplished, regardless of the amount of force exerted. Thus, the correct conclusion is that work is not done because the cupboard remains stationary and does not move in the direction of the applied force.

Work done is defined as the product of the force applied to an object and the distance over which that force is applied, provided the force is in the direction of the movement. This relationship is expressed mathematically as W = F × d, where W represents work, F is the force, and d is the distance. This formula captures the essential concept that work is done when a force causes displacement.

When a spring is compressed, it stores energy due to its deformation, which is known as elastic potential energy. This energy is a result of the spring's ability to return to its original shape when the compressive force is removed. Unlike gravitational potential energy, which depends on an object's height, elastic potential energy specifically relates to the position of elastic materials like springs. Thus, when the spring is compressed by 5 cm, it accumulates elastic potential energy that can be released when the spring expands back to its equilibrium position.

When holding a heavy box stationary, the force exerted by the person is directed upward to counteract the weight of the box. However, since there is no movement in the direction of this force (the box remains at rest), the distance moved in that direction is zero. Work is defined as the product of force and the distance moved in the direction of that force. Therefore, if there is no movement, no work is done, regardless of the amount of force applied.

As an object is lifted higher above the ground, it gains gravitational potential energy due to the work done against the gravitational force. This energy is calculated using the formula PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height above the ground. As the height (h) increases, the potential energy increases proportionally, reflecting the object's increased ability to do work when it falls back to a lower position. Thus, lifting the object higher results in an increase in its gravitational potential energy.