Question

Two blocks with rough surfaces are stacked on top of a slippery horizontal surface. The top block has a mass of m, and the bottom block a mass of 2m. A rope of negligible mass is attached to the bottom block and the other end is hung over a pulley with negligible friction and mass, where it is attached to a hanging block of mass 3m. The friction force between the two blocks keeps the top block from sliding off the bottom block, and the hanging block is released as the system begins at rest. Find the contact forces, the friction force, the tension force, and the distance the hanging weight drops in a time t. Your answers should all be in terms of m, g, and t.

Answer 1

Contact and tension force: 3mg

Friction force: mg

Distance the hanging block would drop in a time t:
`gt^2/2`

Step-by-step explanation:

The gravity force on the hanging block would be:

`F_h = m_hg = 3mg`

Which is the contact force that directly affect the 2 stacked-block system, which would have an acceleration of:

`a = (F_h)/(m_t + m_b) = (3mg)/(m + 2m) = g m/s^2`

So the friction force that pulls the top block must be

`F_f = am_t = gm`

Since the pulley has negligible mass and radius, the tension force would be the same as contact force, which is 3mg

Now that the system moves with an acceleration of g, then after t (seconds), the hanging block would have dropped by a distance of

`h = gt^2/2`