Problem 110GP

As part of a circus act, a person drives a motorcycle with constant speed v around the inside of a vertical track of radius r, as indicated in Figure. If the combined mass of the motorcycle and rider is m, find the normal force exerted on the motorcycle by the track at the points (a) A, (b) B, and (c) C.

FIGURE

Solution 110GP

a.)

Step 1 of 3

We have to find the normal force exerted on the motorcycle by the track at the point .

The normal force exerted on the motorcycle by the track at the point can be found by applying the Newton’s second law in the vertical direction for point

where,

= forces at the point in direction

centripetal force

Now,

where,

is normal force in N

is mass of the motor cycle and the rider in kg

acceleration due to gravity in m/s2

and

Where,

speed of the motor cycle in m/s

radius of vertical track in m

Thus,

+

=

Therefore, the normal force exerted on the motorcycle by the track at the point is

b.)