6th period AP Physics 1
Problem 10.61
At the top of a hill, a car with a mass of 1200 kg is moving at a speed of 20 m/s. The car then travels down the hill and reaches the bottom with a speed of 30 m/s. The height of the hill is 50 meters. Calculate the gravitational potential energy of the car at the top of the hill and the kinetic energy of the car at the bottom of the hill.
Given:
Mass of the car (m) = 1200 kg
Initial velocity (v1) = 20 m/s
Final velocity (v2) = 30 m/s
Height of the hill (h) = 50 m
To calculate the gravitational potential energy (PE) at the top of the hill, we can use the formula:
PE = mgh
where:
m = mass of the car
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the hill
Substituting the given values into the formula:
PE = (1200 kg)(9.8 m/s^2)(50 m)
PE = 588,000 J
Therefore, the gravitational potential energy of the car at the top of the hill is 588,000 J.
To calculate the kinetic energy (KE) of the car at the bottom of the hill, we can use the formula:
KE = (1/2)mv^2
where:
m = mass of the car
v = velocity of the car
Substituting the given values into the formula:
KE = (1/2)(1200 kg)(30 m/s)^2
KE = 540,000 J
Therefore, the kinetic energy of the car at the bottom of the hill is 540,000 J.