The loaded car of a roller coaster has mass M = 320 kg. It goes over the hig
a speed v of 21.4 m/s. The radius of curvature R of the hill is 62.3m
(a) What is the force (N) that the track must exert on the car? (positive is
(b) What must be the force (N) that the car exerts on a 61 kg passenger?
To answer these questions, we will be using the principles of centripetal force and Newton's second law of motion. The centripetal force is the force that acts towards the center of the circular motion and keeps an object moving along a curved path.
(a) To find the force exerted by the track on the car, we need to calculate the centripetal force acting on the car. The formula for centripetal force is given by:
F = (m v^2) / R
where F is the centripetal force, m is the mass of the car, v is the velocity of the car, and R is the radius of curvature.
Given:
m = 320 kg
v = 21.4 m/s
R = 62.3 m
Substituting these values into the formula, we get:
F = (320 kg * (21.4 m/s)^2) / 62.3 m
Calculating this, we find:
F ≈ 3668.6 N
Therefore, the force that the track must exert on the car is approximately 3668.6 N.
(b) To find the force exerted by the car on the passenger, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
F = m * a
In this case, the passenger is experiencing a centripetal force due to the circular motion of the roller coaster. So, the force exerted by the car on the passenger is equal to the centripetal force acting on the passenger.
Given:
m = 61 kg (mass of the passenger)
v = 21.4 m/s (velocity of the car)
R = 62.3 m (radius of curvature)
Substituting these values into the formula for centripetal force, we get:
F = (m v^2) / R
Calculating this, we find:
F = (61 kg * (21.4 m/s)^2) / 62.3 m
Calculating this, we find:
F ≈ 526.9 N
Therefore, the force that the car must exert on the passenger is approximately 526.9 N.