A 3.56-kg rock is released from rest at a height of 15.2 m. Ignore air resistance and determine (a) the kinetic energy at 15.2 m, (b) the gravitational potential energy at 15.2 m, (c) the total mechanical energy at 15.2 m, (d) the kinetic energy at 0 m, (e) the gravitational potential energy at 0 m, and (f) the total mechanical energy at 0 m.
To answer these questions, we'll need to use the equations for kinetic energy (KE) and gravitational potential energy (PE), as well as the concept of mechanical energy.
(a) The kinetic energy at 15.2 m can be found using the equation:
KE = (1/2) * mass * velocity^2
Since the rock is released from rest, its initial velocity is 0 m/s. Therefore, the kinetic energy at 15.2 m is also 0.
(b) The gravitational potential energy at 15.2 m can be calculated using the equation:
PE = mass * gravity * height
Here, "gravity" represents the acceleration due to gravity, which is approximately 9.8 m/s^2. Therefore, the gravitational potential energy at 15.2 m is:
PE = 3.56 kg * 9.8 m/s^2 * 15.2 m = 523.328 J
(c) The total mechanical energy at 15.2 m is the sum of the kinetic energy and the gravitational potential energy. Since the kinetic energy is 0, the total mechanical energy at 15.2 m is 523.328 J.
(d) To determine the kinetic energy at 0 m, we need to calculate the velocity of the rock at that height. Recall that the rock is released from rest, so its final velocity can be found using the equation:
vf^2 = vi^2 + 2 * gravity * height
Since the initial velocity (vi) is 0, the equation simplifies to:
vf^2 = 2 * gravity * height
Solving for vf, we have:
vf = sqrt(2 * gravity * height) = sqrt(2 * 9.8 m/s^2 * 15.2 m) ≈ 17.56 m/s
Now, we can calculate the kinetic energy at 0 m using the same formula as in part (a):
KE = (1/2) * mass * velocity^2 = (1/2) * 3.56 kg * (17.56 m/s)^2 ≈ 539.439 J
Therefore, the kinetic energy at 0 m is approximately 539.439 J.
(e) The gravitational potential energy at 0 m is 0, because there is no height to have potential energy from gravity.
(f) The total mechanical energy at 0 m is the sum of the kinetic energy and the gravitational potential energy, which is:
Total mechanical energy = KE + PE = 539.439 J + 0 J = 539.439 J