Can the Magnet and Picture Move on the Fridge?

[physicsnerd7]

Trick Question?? Please help!

Homework Statement

John hangs a picture of his lovely family on the fridge with a magnet. The magnet applies a force of 15 N. If the magnet and the picture have a mass of 500 g. The coefficient of static friction is 0.40 and the coefficient of kinetic friction is 0.35. Calculate the acceleration of the magnet and picture. Include and FBD with your answer.

Homework Equations

F_s = μs Fn
F_g = mg
F_k = μk Fn

The Attempt at a Solution

Fs = (0.40) (15N)
= 6.0 N

Fg = (0.5 kg) (9.80 N/kg)
= 4.9 N

Fk = (0.35) (15N)
= 5.25 N

Since the magnet doesn't overcome the Fs then it won't move right? but my teacher says you can solve this. How??

 

[nasu]

Have you done the FBD?

 

[Panphobia]

Did your teacher give you the answer to this question? Your teacher says you can solve it because you can, if the magnet doesn't overcome the static friction, it still has an acceleration, can you think any acceleration an object has if it is stationary?

 

[physicsnerd7]

yes i drew the FBD. i have Fs pointing up, Fn pointing right, Fg pointing down, and F_{applied from the magnet} pointing left. Would the acceleration then be 0 N/kg because it stays stationary? he doesn't give us the answer. :(

 

[nasu]

The magnet does not overcome (or not) friction.
The two forces are not along the same direction. An FBD may clarify this. What is the direction of the 15N force?

Edit
I wrote the above while you were posting.
Is this the FBD for the magnet?
The Fn and F_magnet are acting on the same object? An FBD should include only forces on one object (free body).
What is Fn in this case?

 

[physicsnerd7]

It is to the left because I have my picture with the magnet on the right and it is going on the fridge which is to the left.

 

[physicsnerd7]

This is my work with the FBD

 

[nasu]

OK, F_magnet is the attraction from the fridge on the magnet, right?
It looks OK.
And the acceleration is zero because the weight is less than the maximum static friction.

 

[physicsnerd7]

Wait so a magnet attracts the object so would the action force would be on the fridge pulling left and the reaction force would be the fridge pulling on the magnet to the right.

 

[nasu]

You said the magnet is on the right side.
So the magnet pull the fridge towards right and the fridge pulls the magnet to the left.
But only one of these goes in the FBD, the force on the magnet, from the fridge.
These are the forces describing the magnetic interaction.
Then you have another pair describing the elastic deformation of the two bodies in contact. The ones usually called normal forces.

A more familiar situation is the case when you have a body on a horizontal surface and you have gravity and normal force acting on the vertical.
In this problem the role of gravity is played by magnetism and the gravity acts tangential to the surface.

 

[physicsnerd7]

So how would I change my FBD then?

 

[nasu]

I did not say you should change it.
It looks OK. Just tried to make sure you understand the forces on the FBD.

 

[physicsnerd7]

oh okay sorry. Ya I get the forces acting on the magnet and the picture but when I tried to solve for acceleration I get a 0 acceleration because it hasn't yet overcome static friction. Would this statement be correct?

 

[nasu]

With the given data, it looks OK.

 

[physicsnerd7]

okay thank you very much!