Physics help?

Question

A 1.0 kg cart runs on a desk with a wire connecting it to a 0.5 kg mass that is going off the desk and pulls the cart along. The coefficient of friction is 0.15, what is the net force, acceleration, and force of friction on the whole apparatus?

Answer 1

Without friction, the force on the cart would be the same as the force pulling the 0.5 kg mass down from the edge. So that force would be:

F = ma
F = (0.5 kg)(9.8 m/s^2)
F = 4.9 N

But since we're considering friction, the force will be decrease a little bit. By how much? The Force of friction is a factor of the coefficient of friction and the force normal to the surface. In this case, since the cart is on a flat desk (assumed), then the normal force is found through our normal equation:

Fn = ma
Fn = (1.0 kg)(9.8 m/s^2)
Fn = 9.8 N

(If there were an incline to the desk, we'd have to account for that angle and break down the force into normal and tangential components and use that in this next step.)

To find our force caused by friction, we use this normal force and our coefficient of friction (this assumes that there isn't any friction between the wire and the desk - the only friction comes from the cart and the desk):

Ff = cf * Fn
Ff = (0.15)(9.8 N)
Ff = 1.425 N

Our net force on this cart is then the difference of the forces we found:

Net F = F - Ff
Net F = 4.9 N - 1.425 N
Net F = 3.475 N

Finally, the acceleration is found from our force formula:

F = ma
3.475 N = (1.0 kg)a
a = 3.475 m/s^2