What is the Mechanical energy of a 500-kg roller-coaster car moving with a speed of 3 m/s at the top of a hill that is 30 m high?
To find the mechanical energy of the roller-coaster car at the top of the hill, we need to consider its potential energy and kinetic energy.
1. Potential Energy (PE):
Potential energy is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height.
Given:
Mass (m) = 500 kg
Height (h) = 30 m
Acceleration due to gravity (g) = 9.8 m/s^2
Plugging in the values, we have:
PE = mgh
= 500 kg * 9.8 m/s^2 * 30 m
2. Kinetic Energy (KE):
Kinetic energy is given by the formula KE = 1/2 mv^2, where m is the mass and v is the velocity or speed.
Given:
Mass (m) = 500 kg
Velocity (v) = 3 m/s
Plugging in the values, we have:
KE = 1/2 mv^2
= 1/2 * 500 kg * (3 m/s)^2
3. Total Mechanical Energy (ME):
The total mechanical energy is the sum of the potential and kinetic energy.
ME = PE + KE
Now, plug in the values we calculated earlier for PE and KE to find the total mechanical energy.