A body of mass 10kg is raised through a height of 15m from the ground where it was initially at rest when it was at that height it has velocity of 20m/s. find the work done.
work done=gain in Potentail energy+Kinetic energy
= mgh+1/2 mv^2=10*9.8*15+1/2 * 10*20^2 joules
To find the work done, we can use the formula:
Work = Force × Distance × Cos(θ)
In this case, the force is equal to the weight of the body, which is given by:
Force = mass × acceleration due to gravity
The distance is the height through which the body is raised, which is 15m.
The angle θ is the angle between the force and the direction of displacement. In this case, as the body is moving vertically upwards, the angle θ is 0 degrees, and thus the Cos(θ) is equal to 1.
Using these values, we can calculate the work done as follows:
Mass = 10 kg
Acceleration due to gravity = 9.8 m/s²
Distance = 15 m
Cos(θ) = 1
Force = mass × acceleration due to gravity = 10 kg × 9.8 m/s² = 98 N
Work = Force × Distance × Cos(θ) = 98 N × 15 m × 1 = 1470 Joules
Therefore, the work done in raising the body through a height of 15m is 1470 Joules.