Please help me
A 2 kg rock is released from rest at a height of 29 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights;20m 15m 9m
PE= mgh at any height.
KE at any height= InitialPE-finalPE
Total mech energy = KE+ PE
To determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the given heights, we need to use the formulas for these quantities.
First, let's calculate the initial potential energy at a height of 29 m. The formula for gravitational potential energy is given by:
Potential Energy = mass * gravity * height
where
- mass = 2 kg (given)
- gravity = 9.8 m/s^2 (acceleration due to gravity)
- height = 29 m (given)
So, the initial potential energy can be calculated as:
Potential Energy = 2 kg * 9.8 m/s^2 * 29 m = 568.4 Joules
Since the rock is released from rest, its initial velocity is zero. Therefore, the initial kinetic energy is also zero.
Now, let's calculate the potential energy, kinetic energy, and total mechanical energy at each of the given heights (20 m, 15 m, and 9 m) step by step:
1. At a height of 20 m:
Potential Energy = 2 kg * 9.8 m/s^2 * 20 m = 392 Joules (rounded to 3 significant figures)
Kinetic Energy = 0 Joules (since the rock is not moving)
Total Mechanical Energy = Potential Energy + Kinetic Energy = 392 J + 0 J = 392 Joules
2. At a height of 15 m:
Potential Energy = 2 kg * 9.8 m/s^2 * 15 m = 294 Joules (rounded to 3 significant figures)
Kinetic Energy = 0 Joules (since the rock is not moving)
Total Mechanical Energy = Potential Energy + Kinetic Energy = 294 J + 0 J = 294 Joules
3. At a height of 9 m:
Potential Energy = 2 kg * 9.8 m/s^2 * 9 m = 176.4 Joules (rounded to 3 significant figures)
Kinetic Energy = 0 Joules (since the rock is not moving)
Total Mechanical Energy = Potential Energy + Kinetic Energy = 176.4 J + 0 J = 176.4 Joules
Therefore, the kinetic energy, gravitational potential energy, and total mechanical energy at each of the given heights are as follows:
At 20 m: Kinetic Energy = 0 J, Potential Energy = 392 J, Total Mechanical Energy = 392 J
At 15 m: Kinetic Energy = 0 J, Potential Energy = 294 J, Total Mechanical Energy = 294 J
At 9 m: Kinetic Energy = 0 J, Potential Energy = 176.4 J, Total Mechanical Energy = 176.4 J