What Forces Act on a Box Moving Up a Frictional Ramp?

[freshcoast]

Homework Statement

A 25kg box of books is pushed up a ramp and into the back of a pickup truck. The box-ramp system has coefficients of friction (static = 0.6, kinetic = 0.45). The ramp is placed at the maximum angle possible with respect toe the horizontal before the stationary box would slip down the ramp. Under these conditions:

a)What is the magnitude of the maximum possible static friction force?
b)An external force parallel to the floor is now applied to the box. What minimum force must be applied tot he box to cause it to begin to move up the ramp?
c)What minimum force must be applied to cause it to continue to move up the ramp with constant speed?

Homework Equations

ƩF = ma

The Attempt at a Solution

For part a) I drew a free body diagram of the box and summed all the forces in the +I direction and made it equal to 0 since we are dealing with a static friction. And in the J direction I summed all the forces, made it equal to 0 since object is not moving up or down, and from there I was able to find the normal force and substituted that into the friction force to find the angle.

For part b) I drew a free body diagram, summed the forces in I and J directions but added a new unknown force in the I direction and used the coefficient of the kinetic friction force to get the minimum force needed for the box to begin to move. I also used the same angle found in part a) since the ramp is placed at the maximum possible angle before the box slips

Please check to see if I was able to do parts a) and b) correctly,

Now I am having trouble with part c, for the box to continue to move up with a constant speed, would that mean there would be no force to slow it down such as the friction force moving in the opposite direction?

Thanks again for your input

 

[haruspex]

It's a bit hard to read, but your a and b look ok. For c, just use Kinetic friction instead of static.

 

[ap123]

In part (b) it says the external force is parallel to the floor, but you have it parallel to the ramp.

 

[freshcoast]

thanks for the find on the horizontal force ! this is my new answer for part B) and my attempt at part c)

thanks for the helpful advice!

 

[haruspex]

In part (b) it says the external force is parallel to the floor, but you have it parallel to the ramp.

It's not at all clear to me whether that means it's horizontal or parallel to the ramp. if it means horizontal, why not say horizontal? As far as the block is concerned, the floor is the ramp. On balance, I feel the OP interpretation is the more likely.

 

[ap123]

For part (b), I think you have θ for F wrong - shouldn't θ be the angle between F and the plane (ie the positive x-axis )?
Also, in your calculations, you seem to have missed out the x-component of the weight and the y-component of F, ( if I'm reading your notes right ).
Anyway, the answer looks wrong here ( what is F when θ=0? )

Also, in part (c), you have F along the ramp again :(

edit : also see post #5

 

[ap123]

It's not at all clear to me whether that means it's horizontal or parallel to the ramp. if it means horizontal, why not say horizontal? As far as the block is concerned, the floor is the ramp. On balance, I feel the OP interpretation is the more likely.

I agree it's unclear.
It seems to me to be strange wording to refer to the ramp as the floor.

Does the OP have any way of checking?

 

[freshcoast]

Thanks guys for your input. The problem just states that for part b) that there is a force parallel to the floor so I agree that this is sort of strange and my professor needs talking to. But for now if we treat the floor as the ramp, would my solution for b) and c) be correct?. Edit: I am unable to post a revised picture of part b) through my phone but all I did differently is set F parallel to the ramp, and account the gravity force in the -I direction and drew the free body diagrams for both I and J components, made both summation equal to 0 and used it to find F in the +I direction

Edit: part 2.

 

[ap123]

Your calculations look ok for part (b)