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.