Question

A large flat block of mass 7 m rests on a level, smooth tabletop (µk ≈ 0). On top of it is a much smaller block of mass m, with a coefficient of static friction between the two blocks of µs. If the small block is pulled horizontally with constant force F, we want both blocks to slide together across the table without slipping on each other.
What is the largest acceleration that the system can be given in terms of µs and g?
1. F − µs g/ 8
2. F /8 m
3. µs g /7
4. µs g
5. 7 µs g /8
6. 8 µs g

Answer 1

Answer:

3. µs g /7

Explanation:

The largest Force appear when the maximal friction Force is required.

Second Newton law for the small block:

$F_friction=u_s*N=u_s*(mg)$

$F-F_friction=ma$

$F-u_s*(mg)=ma$

Second Newton law for the Big Block:

$F_friction=7ma$

$u_s*(mg)=7ma$

$a=u_s*g/7$