A particle of mass 10 kg is slowly lifted up to a height of 10 metre then calculate the workdone by external and gravity force ?
Work=mgh
To calculate the work done by the external force and gravity, we need to understand the concept of work and the relevant formulas.
Work is defined as the product of force and displacement in the direction of the force. Mathematically, it can be represented as:
Work = Force * Displacement * cos(θ)
Where:
- Force is the magnitude of the force applied
- Displacement is the magnitude of the displacement
- θ is the angle between the force and displacement vectors
In this case, the work done by the external force will be in lifting the particle against gravity, whereas the work done by gravity will be in resisting the particle's upward movement.
1. Work done by the external force:
When the particle is lifted, the external force applies an upward force equal to the weight of the particle (mg) to counteract gravity. The displacement will be vertical and upward, which makes the angle (θ) between force and displacement 0 degrees (cos(0) = 1).
The formula for work becomes:
Work = Force * Displacement * cos(θ)
= mg * h * cos(0)
= mgh
Given:
- mass (m) = 10 kg
- height (h) = 10 m
Using the formula, we can calculate the work done by the external force:
Work = 10 kg * 9.8 m/s^2 * 10 m
= 980 Joules (J)
Therefore, the work done by the external force is 980 J.
2. Work done by gravity:
The work done by gravity can be calculated using the same formula. In this case, the force of gravity is acting downwards, while the displacement is in the upward direction. Therefore, the angle (θ) between force and displacement is 180 degrees (cos(180) = -1).
The formula for work becomes:
Work = Force * Displacement * cos(θ)
= mg * h * cos(180)
= -mgh
Using the given values, we can calculate the work done by gravity as:
Work = 10 kg * 9.8 m/s^2 * 10 m
= -980 Joules (J) (Negative sign indicates that the work is done against the direction of displacement)
Therefore, the work done by gravity is -980 J.