Newton's 3rd law, tension, friction

[teammatt3]

Homework Statement

Homework Equations

F=m*a
F_s <= N*u_s
F_k = N * u_k

The Attempt at a Solution

b) T-f_s = 120
T-.2 * 9.8 * (15 + 20 + 25) = 120 => T = 237.6 Newtons

c) (F_s)_{2 on 1} = (F_s)_{1 on 2} = 15 * 9.8* .6 = 88.2 Newtons

d) (15 + 20) * 9.8 * .6 = 205.8 Newtons

e) This is where I'm falling apart. Since we are applying a larger tension force than the static friction of both top boxes, then the boxes must slide off. Right?

f) My professor said they slide off at the same time, but I'm not sure how to show it, or why. I thought the top one would fly off first, since the static friction force is smallest.

Any help is appreciated!

 

[Doc Al]

e) This is where I'm falling apart. Since we are applying a larger tension force than the static friction of both top boxes, then the boxes must slide off. Right?

Ask yourself: In order to accelerate m1 (or m1 & m2) what force is required? Is static friction sufficient to provide that force?

f) My professor said they slide off at the same time, but I'm not sure how to show it, or why. I thought the top one would fly off first, since the static friction force is smallest.

Figure out the maximum acceleration that each box can have without sliding. (Consider the available static friction.)

 

[teammatt3]

Thank you! That helped.

The accelerations where the boxes start to slide are:

m1: 88.2 = 15 * a => a = 5.88
m2: 205.8 = (15+20) * a => a = 5.88

So they both slide at the same time. And in part e, since the acceleration is less than 5.88, they don't slide off.

 

[Doc Al]

Good!