A body weighing 2 kg falls from a height of 5 meters. what work does gravity do? what is the power being developed?
Work characterizes the action of a force applied to the body to move it. Its value is determined by the formula A = F * S, where A is work, F is force, S is displacement (moreover, the direction of force and displacement of the body coincide here).
In our case, gravity is applied to the body – F = mg,
where m is the mass of the body, g is the acceleration of gravity (we will round it up to 10 m / s² for convenience), and it moves to the ground.
The work done by her in this case will be –
A = 2 kg * 10 m / s² * 5 m = 100 N * m or 100 J.
Power (designation – N) is defined as the work done in some time: N = A / t (unit of measurement – J / s or Watt).
In our case, time is the time the body falls to the ground. Let’s find it from a simple formula describing uniformly accelerated rectilinear motion without initial velocity (we have free fall) –
S = (gt²) / 2, where g is the acceleration of gravity. 5 m = 10 m / s² * t² / 2.
Hence, t² = 5 m * 2/10 m / s² = 1 s²; t = 1 s.
Therefore, the power developed when performing work by gravity (by moving the body (down, to the ground)) will be equal to: N = 100 J / 1 s = 100 J / s or 100 watts. Thus, we have found the desired values of the values of our task.
