3 boxes are stacked on top of each other, as shown. The middle block, block 2, i

Question

3 boxes are stacked on top of each other, as shown. The middle block, block 2, is pushed with a force F.

The masses are m1=1kg, m2=2kg, m3=1kg.

The coefficients of friction are:

uk= 0.1 for the kinetic friction between box 1 and the ground

us= 0.3 for the static friction between box 1 and box 2

us= 0.2 for the static friction between box 2 and box 3

Part a: If the boxes are sliding together, what is the frictional force between box 1 and the ground?

Part b: What is the largest possible frictional force between box 2 and box 3?

Part c: What is the largest possible frictional force between box 1 and box 2?

Part d: What is the largest possible acceleration such that box 3 remains in contact with box 2?

Part e: If the boxes move with constant velocity, what is the frictional force on box 3?

Explanation / Answer

a)

as they are moving together,

frictional force = co-efficient of kinetic friction between ground and 1*total weight

So,frictional force between the ground and mass 1 = 0.1*(1+2+1)*9.8 = 3.92 N

b)

largest frictional force = static friction co-efficient on this surface*normal force acting on the surface = 0.2*(mass of particle 3*9.8)

So, largest frictional force = 0.2*1*9.8 = 1.96 N

c)

largest frictional force = static friction co-efficient on this surface*normal force acting on the surface = 0.2*((mass of particle 3+masss of particle 2)*9.8)

So, largest force = 0.3*(2+1)*9.8 = 8.82 N

d)

largest possible acceleration such that box 3 remains in contact with box 2 is when maximum possible kinetic friction acts on it

So, friction = u*(m3)*9.8

So, a = friction/m3 = u*m3 = 0.2*9.8

So, largest acceleration = 0.2*9.8 = 1.96 m/s2

e)

If the body move with constant velocity, then, frictional force from the ground on 3 = 0 N <------answer

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