# Two blocks held by a rope on an incline

## Homework Statement

A block with mass m1 = 9.4 kg is on an incline with an angle θ = 31.0° with respect to the horizontal.

Now a new block is attached to the first block. The new block is made of a different material and has a coefficient of static friction μ = 0.9. What minimum mass is needed to keep the system from accelerating?

## Homework Equations

Ft,1 = Ft,2
Fg,1 = m1*g
Fg,2 = m2*g
Fn,1= Fg,1*cos 31
Fn,2 = Fg,2*cos 31
Ff,s,2 = Fn*.9

## The Attempt at a Solution

Ft,1 = Ft,2
Fg,1 = m1*g = 92.12N
Fg,2 = m2*g = m2*9.8
Fn,1= Fg,1*cos 31
Fn,2 = Fg,2*cos 31
Ff,s,2 = Fn*.9

I'm not really sure what to do after this. I have some free-body diagrams set up, but since I can't post them here, I can't show them.

I had a value for the coefficient of static friction, but that was for a system with a spring (.292), so I don't think that'll work here. I also have one for kinetic friction (.212), but that might not apply here. After that, I'm stuck.

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PhanthomJay
Homework Helper
Gold Member
Please clarify this question, you are missing information.

CWatters
Homework Helper
Gold Member
Is the first block frictionless?

## Homework Statement

A block with mass m1 = 9.4 kg is on an incline with an angle θ = 31.0° with respect to the horizontal.

Now a new block is attached to the first block. The new block is made of a different material and has a coefficient of static friction μ = 0.9. What minimum mass is needed to keep the system from accelerating?

## Homework Equations

Ft,1 = Ft,2
Fg,1 = m1*g
Fg,2 = m2*g
Fn,1= Fg,1*cos 31
Fn,2 = Fg,2*cos 31
Ff,s,2 = Fn*.9

## The Attempt at a Solution

Ft,1 = Ft,2
Fg,1 = m1*g = 92.12N
Fg,2 = m2*g = m2*9.8
Fn,1= Fg,1*cos 31
Fn,2 = Fg,2*cos 31
Ff,s,2 = Fn*.9

I'm not really sure what to do after this. I have some free-body diagrams set up, but since I can't post them here, I can't show them.

I had a value for the coefficient of static friction, but that was for a system with a spring (.292), so I don't think that'll work here. I also have one for kinetic friction (.212), but that might not apply here. After that, I'm stuck.
The coefficients of friction are for the first block.

PhanthomJay
Homework Helper
Gold Member
Where's the rope? Please state the problem as written and provide a sketch if possible.

CWatters
Homework Helper
Gold Member
I'm sure this is a straightforward question but the way you have explained it is confusing...

For example..

Now a new block is attached to the first block. The new block is made of a different material and has a coefficient of static friction μ = 0.9. What minimum mass is needed to keep the system from accelerating?
is inconsistent with...

The coefficients of friction are for the first block.

CWatters
Homework Helper
Gold Member
If we take your original post at face value....

The first block is frictionless so it's simple to calculate the force down the slope due to gravity.

The second block has friction so you can write two equations, 1) for the force down the slope due to gravity and 2) for the friction force acting up the slope.

If the combination is static then the sum of all three forces equate to zero. Solve for the mass of the second block.