Question

A block with mass M = 5.00 kg rests on a frictionless table and is attached by a
horizontal spring (k = 130 N/m) to a wall. A second block, of mass m = 1.25 kg rests on top of M.
The blocks are displaced by 10 cm then released.
If the coefficient of static friction between the two blocks
is 0.3, does block m slip off block M? (Show your work)
YES / NO

Answer 1

F = - k x
= -130 (.1) = -13 N

if they do not slip m = 6.25 kg

a = 13/6.25 = 2.08 m/s^2

force required to accelerate small block = 1.25 *2.08 = 2.6 N

do we have that much?
weight = m g = 1.25 * 9.81
so max friction = .3*1.25*9.81 = 3.68 N
so
no slip :)

Answer 2

Thank you so much!

Answer 3

You are welcome :)

Answer 4

Just to clarify, when you conclude that the block m doesn't slip, which forces are you comparing? If the friction was smaller than the force required to accelerate the small block, would it then slip?

Answer 5

Yes, if the friction was less than the force required to accelerate the upper block, it would accelerate more slowly than the bottom one. In other words slip :)