A motorcycle has a constant speed of 24.0 m/s as it passes over the top of a hill whose radius of curvature is 103 m. The mass of the motorcycle and driver is 347 kg.
(a) Find the magnitude of the centripetal force that acts on the cycle.
(b) Find the magnitude of the normal force that acts on the cycle.
(a)
Fc=-mv²/r (upwards for crests, and downwards for valleys)
(b) Add the (negative) centripetal force to the weight, mg.
F=mg-Fc
Post your calculations/answers for verifications if necessary.
1940.5 N
1460.1 N
To find the magnitude of the centripetal force, we can use the equation:
Fc = m * (v^2 / r)
where Fc is the centripetal force, m is the mass of the motorcycle and driver, v is the velocity, and r is the radius of curvature.
(a) Let's calculate the magnitude of the centripetal force:
Fc = 347 kg * (24.0 m/s)^2 / 103 m
Using the calculator:
Fc ≈ 2034.16 N
So, the magnitude of the centripetal force acting on the motorcycle is approximately 2034.16 N.
To find the magnitude of the normal force, we need to consider the forces acting on the motorcycle at the top of the hill. At this point, there are two forces acting on the motorcycle: the gravitational force (mg) and the normal force (Fn).
(b) We know that the gravitational force is given by:
Fg = m * g
where g is the acceleration due to gravity.
Fg = 347 kg * 9.8 m/s^2
Using the calculator:
Fg ≈ 3406.6 N
Since the motorcycle is at the top of the hill, the normal force and gravitational force should add up to provide the necessary centripetal force. Therefore, the magnitude of the normal force can be calculated as:
Fn = Fc + Fg
Fn = 2034.16 N + 3406.6 N
Using the calculator:
Fn ≈ 5439.76 N
So, the magnitude of the normal force acting on the motorcycle is approximately 5439.76 N.