An object moving at a constant speed of 25 m/s is making a turn with a radius of curvature of 7 m (this is the radius of the "kissing circle"). The object's momentum has a magnitude of 78 kg·m/s. What is the magnitude of the rate of change of the momentum?

- 278.34 kg m/s^2

Explanation:

The rate of the change of momentum is the same as the force.

The force that an object feels when moviming in a circular motion is given by:

F = - mrω^2

Where ω is the angular speed and r is the radius of the circumference

Aditionally, the tangential velocity of the body is given as:

v = rω

The question tells us that

v = 25 m/s

r = 7m

mv = 78 kg m/s

Therefore:

m = (78 kg m/s) / (25 m/s) = 3.12 kg

ω = (25 m/s) / (7 m) = 3.57 (1/s)

Now, we can calculate the force or rate of change of momentum:

F = - (3.12 kg) (7 m) (3.57 (1/s)) ^2

F = - 278.34 kg m/s^2