Find the mass of object knowing the applied force and coefficient of friction

[liz777]

Homework Statement

If a force of 45 Newtons is needed to overcome friction and the coefficient of friction=0.26, what is the mass of the object?

The Attempt at a Solution

So would I need to find the frictional force first? But then I can't use the equation: (frictional force=coefficient of friction x weight) since I don't have the mass. I also thought about using the equation F=MA but then I don't have the acceleration, the friction, or the net force! Any help, I'm really stuck?

 

[Doc Al]

So would I need to find the frictional force first?

They give you the friction force. The way to interpret the given information is that the 45 N force is just enough to overcome friction, thus that force equals the friction.

But then I can't use the equation: (frictional force=coefficient of friction x weight) since I don't have the mass.

Sure you can use that equation. Remember that you're asked to find the mass.

 

[liz777]

Ok, so what you're saying is that the applied force equals the friction, in this case. I thought it wouldn't move though if that was true? I'm just confused on this concept.

But anyway, using that information, frictional force=coefficient of friction x weight
45=0.26m(9.8)
45=2.55m
m=17.65kg
Is that right?

 

[Assasinof6]

Yes.
You are given two values, and you need to solve for one of them using an equation with four variables, three of which are known (the other being g).

 

[rwisz]

To find the mass of the object, you can use the equation F=μN, where F is the frictional force, μ is the coefficient of friction, and N is the normal force (equal to the weight of the object). Since you know the applied force of 45 Newtons, you can set F=45 and solve for N. Then, use the equation N=mg, where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2). You can now solve for the mass (m) by dividing both sides by g. The final equation will be m=45/(0.26 x 9.8), which gives the mass of the object as approximately 17.3 kg. This is assuming that the applied force is equal to the maximum frictional force that can be overcome, and there is no net force acting on the object.