How Much Force Does the Larger Trunk Exert on the Smaller Trunk?

[Sace Ver]

Homework Statement

Two trunks sit side by side on the floor. The larger trunk (52kg) is to the left of the smaller trunk (34 kg). A person pushes on the larger trunk horizontally toward the right. The coefficient of static friction between the trunks and floor is 0.35. Calculate the force the larger trunk exerts on the smaller trunk?

mass of larger trunk = 52kg
mass of smaller trunk = 34kg
u_k = 0.35

Homework Equations

u_f = F_f/F_N
Fnet = sum of all forces

The Attempt at a Solution

F_Smax = u_sF_N
F_Smax = (0.35)(86kg)(9.8N/kg)
F_Smax = 290N

F_N = mg
F_N = (52kg)(9.8N/kg)
F_N = 509.6N

Not quite sure if doing right steps or what to do next?[/B]

 

[Mister T]

Are you sure you've given us the problem? It seems something is missing.

 

[Sace Ver]

Are you sure you've given us the problem? It seems something is missing.

The magnitude of the maximum force the person can exert without moving either trunk is 290N! And that's basically it!

 

[Mister T]

The magnitude of the maximum force the person can exert without moving either trunk is 290N!

Agreed, but nowhere in the statement of the problem is it mentioned that the maximum force is being applied. Neither do they state that the trunks aren't moving.

Anyway, if you make those assumptions the next step is to look at the horizontal force applied to the 34 kg trunk. Or to the horizontal forces applied to the 52 kg trunk. Drawing the free body diagrams is a big help.

 

[Sace Ver]

Agreed, but nowhere in the statement of the problem is it mentioned that the maximum force is being applied. Neither do they state that the trunks aren't moving.

Anyway, if you make those assumptions the next step is to look at the horizontal force applied to the 34 kg trunk. Or to the horizontal forces applied to the 52 kg trunk. Drawing the free body diagrams is a big help.

I'm pretty sure the trunks are not moving meaning acceleration would be zero and so would Fnet? And I drew the FBD and just wondering would F_T and F_F cancel each other out?

 

[Mister T]

What are F_T and F_F?

 

[Sace Ver]

What are F_T and F_F?

I think I made an error on my FBD, because I have yet to find F_T but would F_F be 290N?
And I'm looking for F_T right? And I'm just wondering if F_T equals F_Smax?

 

[Mister T]

What I meant was, how are you defining F_T and F_F?

 

[Sace Ver]

What I meant was, how are you defining F_T and F_F?

I think I figured it out

F_smax = u_sF _N
F_smax = (0.35)(34kg)(9.8N/kg)
Fsmax = 120N

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[haruspex]

I think I figured it out

F_smax = u_sF _N
F_smax = (0.35)(34kg)(9.8N/kg)
Fsmax = 120N

Right, though as E=mc² noted you have to fill in two missing pieces of information to arrive at that: that the trunks are not moving, but if the force between the trunks were any greater they would be. In the question as given, the pusher could be just breathing heavily against the larger trunk.