Finding the acceleration of a refrigerator

[physics411]

Homework Statement

The coefficient of kinetic friction between a refrigerator and the floor is 0.20. The mass of the refrigerator is 100.0 kg, and the coefficient of static friction is 0.25. Determine the acceleration when you apply the minimum force needed to get the refrigerator to move.

The answer is 0.49 m/s^2.

Homework Equations

Sum of the forces: Fx = max = Fa + (-Fs)

Fy = 0 = Fn = mg

F = ma

The Attempt at a Solution

Okay, so I have worked at this problem for quite some time now. I know for a fact that the normal force applied on this object is 980 from solving it through the sum of the forces in the y-component formula.

I know that Fs can be written as Us times Fn. If I use static friction, Fs = 245 N. With kinetic, its 196 N.

I tried solving for acceleration using either forces (divide F by m) but was not able to get the right answer.

Perhaps someone here can assist me?

Thanks in advance.

 

[PietKuip]

Remember that there is friction when it moves.

 

[billy_joule]

Perhaps someone here can assist me?

It would help if you showed your working.
Your first step should almost always be to draw a free body diagram.

Do you know what static and kinetic friction mean?

What is the minimum push force required to move the refrigerator? ie which type of friction must be overcome?
Once the fridge is moving, what is the opposing frictional force? So what is the net force on the fridge that causes the acceleration?

 

[physics411]

It would help if you showed your working.
Your first step should almost always be to draw a free body diagram.

Do you know what static and kinetic friction mean?

What is the minimum push force required to move the refrigerator? ie which type of friction must be overcome?
Once the fridge is moving, what is the opposing frictional force? So what is the net force on the fridge that causes the acceleration?

Yes, I do know what static and kinetic friction mean.

The type of friction that must be overcome is the force of static friction, as the refrigerator is stationary initially, no?

So I already found that which is 245 N. Because Fa = Fs (as I stated before).

Fs = Us * Fn
= (0.25)(100*9.8)
= 245 N

So this is the force that has to be overcome.

When the fridge is moving:

Fk = Uk*Fn
= (0.20)(100*9.8)
= 196 N

Fnet = 245 - 196 / 100
= 0.49 m/s^2 !

Okay so thank you for helping me find the acceleration, but I am confused about one thing, why do we include Fs and Fk when finding the net force? When the object is moving, isn't the Fs out of the question then? and Why do we subtract them!

 

[PietKuip]

It is excellent that you still ask when you found the correct number.

Why subtract - because the forces are in opposite directions. You are still pushing, working against the friction.

 

[physics411]

It is excellent that you still ask when you found the correct number.

Why subtract - because the forces are in opposite directions. You are still pushing, working against the friction.

Ohh I understand how it all works now! Thanks for your time and help

 

[billy_joule]

Okay so thank you for helping me find the acceleration, but I am confused about one thing, why do we include Fs and Fk when finding the net force? When the object is moving, isn't the Fs out of the question then? and Why do we subtract them!

The force required to move the fridge needs to overcome the static friction. Once the fridge is moving you are still applying the same push force but now the opposing friction (now kinetic) force is less. You are right that F_{static friction} is out of the question when the object is moving but the push force when moving is determined by F_{static friction} in the first place.

The net force on the fridge is the sum of all forces:
∑F = ma
∑F = F_push + F_{kinetic friction} = ma

F_push and F_friction are in opposite directions so depending on what you chose as the positive x direction one of them will be negative.