How Do You Calculate the Force Needed to Pull a Box Up a Ramp at Constant Speed?

[swimchica93]

What formula do I use to find the force that is used to pull on a box, going a constant speed.

I have mu-k, the degree of the ramp, and the weight of the box.

 

[ehild]

First draw a free-body diagram and than take into account that he resultant force is 0.

ehild

 

[swimchica93]

I drew a free body diagram, now Ijust don't know what to do with it.

 

[ehild]

You have got four forces:

gravity (G=mg) pointing vertically downward;
normal force F_n, normal to the ramp;
friction, F_f=mu *Fn parallel to the ramp and opposite to the velocity of the box
pull Fp, parallel with the slope.

Decompose each forces into components parallel and perpendicular to the ramp. Both the parallel and normal components have to cancel. The normal component of G is opposite to Fn, G-Fn=0, from that you get Fn, and the force of friction. Do you pull the box up or down the ramp?

ehild

 

[swimchica93]

The box goes up the ramp.

So, there isn't a formula to use? I know that the box weights 500kg, and the angle of the ramp is 50 degrees and the mu-k is .10. Then it has to be at a constant speed.

I tried:

F-mg(sin(theta))=0 is that kind of what you are talking about? The problem was I couldn't add friction.

 

[milagro]

the pulling force along the surface will be

F=coeff of friction*mg*sin(angle of surface with horizontal)

 

[ehild]

Well, the normal component of G is mgcos(theta). Do you know why?
So the normal force is Fn=mgcos(theta).
The magnitude of friction is mu*Fn. As the box moves uphill, the friction points downhill.

F(pull)-mgsin(theta)-mu*mgcos(theta)=0. Calculate F(pull).

ehild