A 530 kg roller coaster starts from rest at point A and rolls freely (no friction) to point B where the brakes are applied and it slides along horizontally with a frictional force of 520 N. How far does the coaster slide past point B before coming to rest?
To find the distance the roller coaster slides past point B before coming to rest, we need to determine the work done on the roller coaster by the frictional force.
The work-energy principle states that the work done on an object equals the change in its kinetic energy. In this case, the initial kinetic energy of the roller coaster is zero because it starts from rest. Therefore, the work done by the frictional force will equal the initial kinetic energy.
The work done by a force is calculated using the equation:
Work = force * distance * cosine(theta)
Given:
Mass of the roller coaster (m) = 530 kg
Frictional force (f) = 520 N
Since the frictional force acts horizontally, the angle (theta) between the force and displacement is 0 degrees. Therefore, the cosine of theta is 1.
Using the equation mentioned above, we can rearrange it to find the distance (d):
Work = force * distance * 1
Work = force * distance
Rearranging the equation gives:
Distance = Work / Force
Substituting the given values into the equation:
Distance = (520 N) / (530 kg)
Calculating this gives:
Distance = 0.981 m
Therefore, the coaster slides past point B before coming to rest for approximately 0.981 meters.