What limit must the force excede if we want to separate two bodies + friction

[mmoadi]

Homework Statement

On a leveled base is a plank with a mass M = 2 kg, on the plank is a weight with a mass m = 1 kg. What limit must the force exceed, when we pull the plank in a horizontal direction for the weight to slip from the plank? Ratio of friction between the plank and the base is k1 = 0.4 and ratio of friction between the weight and the plank is k2 = 0.3.

Homework Equations

N= mg
Fk= μkN

The Attempt at a Solution

M= 2 kg
m= 1 kg
μk1= 0.4
μk2= 0.3

For the plank and weight to start moving: F1= (M+m)gμk1= 11.76 N
For the weight to start moving on the plank: F2= mgμk2= 2.94 N

So if my logic works correctly I simply add the two forces and the force will be big enough for the weigh to start falling off the plank.

F= F1 + F2= 11.76N + 2.94 N= 14.7 N

And the answer would be: The force have to be bigger than 14.7 N for the weight to fall off the plank.

 

[caitlincui]

I think it's right.

 

[tomcue]

I would like to clarify that the force must exceed 14.7 N in order for the weight to slip from the plank. This is because the combined frictional forces between the plank and the base (F1) and between the weight and the plank (F2) must be overcome by a greater force (F) to initiate motion. In other words, the force applied to the plank must be greater than the total frictional force acting on the weight and the plank for the weight to slip off the plank. This is an important consideration when designing systems that involve movement or sliding of objects, as the force applied must be greater than the frictional forces to ensure proper functioning.