What is the total mechanical energy of a 575 kg roller coaster that is at rest 50.0 m above the lowest point on the ride? The maximum possible speed of the roller coaster is 31.3 m/s. (do not include units in your answer)
If it is at rest 50 m high, the total is
m g h = 575 * 9.81 * 50 = 282,037 Joules
The speed does not matter because we counted the total while at rest.
However let's see ho much kinetic energy it has at the bottom
(1/2) m v^2 = .5*575*31.3^2 = 281,660 Joules
so to 3 significant figures no energy was lost to friction while accelerating down the rails.
To find the total mechanical energy of the roller coaster, we need to consider its potential energy at the highest point and its kinetic energy at the maximum speed.
1. Calculate the potential energy:
Potential energy (PE) = mass (m) × gravitational acceleration (g) × height (h)
Given:
mass (m) = 575 kg
gravitational acceleration (g) = 9.8 m/s²
height (h) = 50.0 m
PE = 575 kg × 9.8 m/s² × 50.0 m
2. Calculate the kinetic energy:
Kinetic energy (KE) = 0.5 × mass (m) × speed²
Given:
mass (m) = 575 kg
speed (v) = 31.3 m/s
KE = 0.5 × 575 kg × (31.3 m/s)²
3. Add the potential energy and kinetic energy to find the total mechanical energy:
Total mechanical energy (E) = potential energy (PE) + kinetic energy (KE)
E = PE + KE
Now you can plug the values into the equations and calculate:
Potential energy (PE) = 575 kg × 9.8 m/s² × 50.0 m
Kinetic energy (KE) = 0.5 × 575 kg × (31.3 m/s)²
Total mechanical energy (E) = PE + KE
Evaluate these expressions to find the solution. Remember not to include units in your answer.