Work done on an incline plane with friction

[Zsmitty3]

You slide a box of books at constant speed up a 30^\circ ramp, applying a force of 210N directed up the slope. The coefficient of sliding friction is 0.18.

1. How much work have you done when the box has risen 2m vertically?

2.What is the mass of the box?



I think I could solve this if I was given the mass of the books



The pushing force is given, but how do you find the force of the friction with no mass to find the normal force. Once I get the force of friction I would just add it to the pushing force (210) and multiply by distance to get the work done.

 

[Maiq]

If the box moves at a constant speed then what is its acceleration? Now your only unknown is mass.

 

[Zsmitty3]

I'm missing something here. 210 is the force given. The Normal Force I'm taking it as.

So 210=m*(9.8)*cos30

or 210/(9.8*cos30)=m

that's not giving me the correct answer for mass though.

 

[Zsmitty3]

I'm missing something here. 210 is the force given. The Normal Force I'm taking it as.

So 210=m*(9.8)*cos30

or 210/(9.8*cos30)=m

that's not giving me the correct answer for mass though.

Okay after I read this I realized it's not the normal force its the pushing force up the ramp. So 210= m*a*sin30

so 210/sin30=m because there is no acceleration. This comes out to 420 which is still wrong so what am I messing up?

 

[idllotsaroms]

I would find the sum of forces in the X and Y planes first by drawing a Free-body-diagram and splitting the mg force into its x and y components.
You could then use the ƩFy = may = Fnormal - mgcos30
Try to solve for Fnormal which you can plug into another Newton equation

I might be wrong though

 

[ap123]

I would find the sum of forces in the X and Y planes first by drawing a Free-body-diagram and splitting the mg force into its x and y components.
You could then use the ƩFy = may = Fnormal - mgcos30
Try to solve for Fnormal which you can plug into another Newton equation

Yes, so n = mgcosθ

If you write out an expression for the x-components and use this expression for n, then the mass will be the only unknown.

 

[EM_Guy]

You have 3 unknowns: m, the force of friction, and the normal force.

To solve the problem, you need three equations.

Draw a FBD. That should give you two of your equations.

Then, recall how the force of friction is related to the normal force. That is your third equation.

Then, all you need to do is algebra. Plug and chug.