Physics 11 question?

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

Step 1: Define the forces acting on the cart.
Fw = The force from the mass falling off the desk.
Fw = m2g = .5 * 9.8 m/s^2 = 4.9N

Fn = Normal force of the cart. Since the desk is assumed to be horizontal, Fn = weight of cart = m1g = 1 * 9.8 = 9.8N

Ff = Frictional force on the cart (the last item asked for).
Ff = μFn = .15 * 9.8 = 1.47N directed opposite of Fw.

Note that for Fn and Ff, the mass falling off the desk is ignored, because it pulls the cart horizontally, thus it is not pushing against the desk (and thus does not contribute to friction).

Step 2: Find the net force.

Net force = Fw - Ff = 4.9 - 1.47 = 3.43 N

Net force ignores Fn, because Fn is directed into the ground and cancelled by the force the ground exerts back on the cart.

Step 3: Given the net force, find acceleration.
Acceleration of cart = net force / mass = 3.43 N / 1 kg = 3.43 m/s^2