A 500 kg roller coaster starts from rest at point A (Fig. 6.29) and rolls freely (no friction) to point B where the brakes are applied and it slides along horizontally with a frictional force of 410 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 calculate the work done by the frictional force and equate it to the initial kinetic energy of the roller coaster.
First, let's calculate the initial kinetic energy of the roller coaster at point B.
The roller coaster starts from rest, so its initial velocity (v_initial) at point B is zero.
The formula for kinetic energy (KE) is given by KE = (1/2) * m * v^2, where m is the mass of the roller coaster and v is its velocity.
In this case, m = 500 kg and v = 0, therefore the initial kinetic energy (KE_initial) is:
KE_initial = (1/2) * 500 kg * (0 m/s)^2
= 0 J (Joules)
Next, we need to calculate the work done by the frictional force as the coaster slides along horizontally.
The work done (W_friction) is given by the formula W_friction = force x distance x cos(theta), where theta is the angle between the direction of the force and the direction of motion. In this case, theta is 180 degrees since the force and the motion are in opposite directions and cos(180 degrees) = -1.
The frictional force (force) is given as 410 N, and the distance the roller coaster slides (distance) is what we need to find.
We can rearrange the formula to solve for distance:
distance = W_friction / (force x cos(theta))
Since the coaster comes to rest, the work done by the frictional force is equal to the initial kinetic energy of the coaster.
Therefore, distance = KE_initial / (force x cos(theta))
Substituting the values:
distance = 0 J / (410 N * cos(180 degrees))
= 0 J / (410 N * (-1))
= 0 m
Hence, the roller coaster slides 0 meters past point B before coming to rest.