What is the Coefficient of Static Friction for Two Tied Objects?

[oMovements]

Homework Statement

Two objects are made of identical material and are tied together with string. The first object has a mass of 5.0kg and the second object has a mass of 3.0kg. Students measure the maximum force of static friction as 31.4N to move both objects across a horizontal surface.
a) What is the coefficient of static friction?
b) What is the magnitude of the tension in the string if they pull on the first object?
c) A student pushes the 3.0kg object with a force of 15.0[down]. What are the magnitudes of the maximum force of static friction and the tension now?
d) Will your answers to (c) change if the student pushes down on the 5.0kg object instead? Explain.

Homework Equations

The Attempt at a Solution

a) μ_s=F_s / F_n
=31.4 / (8)(9.8)
μ_s= 0.40

b) To solve B) I came up with two equations, one for each object and equated them to solve for acceleration, and tension.

F_s-F_t=ma
31.4-F_t=5a
F_t=31.4-5a
F_t= 11.78N <-- I found this by finding the acceleration first, and subbing it into 31.4-5a

Ft=ma
31.4-5a=3a
31.4=8a
a=2.925m/s²

c)

d)

I know how to solve a) b) but I have no clue how to solve c). How would I go about doing it?

 

[haruspex]

b) To solve B) I came up with two equations, one for each object and equated them to solve for acceleration, and tension.

What acceleration? This is still the static case.

For c, what is the normal force from the surface on the 3kg block now? (Is the 15 in Newtons or kg-weight?)

 

[NascentOxygen]

b) To solve B) I came up with two equations, one for each object and equated them to solve for acceleration, and tension.

F_s-F_t=ma
31.4-F_t=5a
F_t=31.4-5a
F_t= 11.78N <-- I found this by finding the acceleration first, and subbing it into

It is probably best not to do it that roundabout way, because you are assuming that coefficient of kinetic friction is going to be equal to the coefficient of static friction and you know, in principle, this is almost never true.

All you need to consider is that the 3kg object (with μ_s=0.4) is being dragged by the string. Find the max tension in the string.

I know how to solve a) b) but I have no clue how to solve c). How would I go about doing it?

In part (c), someone is pushing down on the object, increasing the normal force between the object and the surface it sits on. You need to now find the increased tangential friction force.

 

[oMovements]

What acceleration? This is still the static case.

For c, what is the normal force from the surface on the 3kg block now? (Is the 15 in Newtons or kg-weight?)

15N. There is an acceleration because the it states "Students measure the maximum force of static friction as 21.4N to move both objects across a horizontal surface." and static friction can also cause an object to move if I remember correctly.

 

[oMovements]

It is probably best not to do it that roundabout way, because you are assuming that coefficient of kinetic friction is going to be equal to the coefficient of static friction and you know, in principle, this is almost never true.

All you need to consider is that the 3kg object (with μ_s=0.4) is being dragged by the string. Find the max tension in the string.In part (c), someone is pushing down on the object, increasing the normal force between the object and the surface it sits on. You need to now find the increased tangential friction force.

What other way can I solve the tension in the string without equating the 2 equations? I still got the correct answer using this method by the way.

I'm also still confused how to solve c)

 

[NascentOxygen]

With what force is the 3kg block in (c) pushing down onto the table?

 

[oMovements]

With what force is the 3kg block in (c) pushing down onto the table?

Force of 15N

 

[haruspex]

Force of 15N

What force was the 3kg block exerting on the table before the student pressed down on it? What do you think that force will increase by when the student presses down?

There is an acceleration because the it states "Students measure the maximum force of static friction as 21.4N to move both objects across a horizontal surface."

That's the force required to overcome static friction. Until it is overcome there is no acceleration.

and static friction can also cause an object to move if I remember correctly.

Yes, but it cannot cause the object to move relative to the surface. Friction always opposes relative motion of the surfaces in contact.

 

[NascentOxygen]

Force of 15N

Plus its weight!