Tension Force problem involving friction

[chimbooze]

1. A horizontal rope pulls a 20kg wood sled across frictionless snow. A 5 kg wood box rides on the sled. The coefficient of static friction for wood on wood is 0.5. What is the largest tension force for which the box doesn't slip?

m = 5 kg box, 20 kg sled
mu = .5
T = ?

2.
F = ma
Ff= mu x n

3.
F = ma
a of box is zero since it is not moving

T - mu x (20 + 5) x (9.8) = 0

 

[Doc Al]

a of box is zero since it is not moving

No, both sled and box are accelerating. (They're being pulled by a rope.)

Hint: What is the maximum static friction between box and sled?

 

[chimbooze]

I partially get it. If Tension force is greater than the static friction force, then the box will move. So just find friction force.

Ff = mu x n
Ff = .5(9.8)(5)

But that isn't the right answer.

 

[Doc Al]

But that isn't the right answer.

That's just one step toward the answer. Now that you know the maximum friction force on the box, what is the maximum acceleration that the sled can have without the box slipping?

To get the final answer, you'll need to apply Newton's 2nd law twice.

 

[chimbooze]

So:

sum of F = ma
Ff = ma
.5(9.8)(5) = 5(a)

a = 4.9

Tension of rope: T = ma

T = (10 + 5)(4.9)
T = 73.5

Thanks a lot. I got it correct.

 

[Doc Al]

Excellent!