# Sliding box question- finding applied force with friction

## Homework Statement

A 90 kg box is pushed by a horizontal force F at constant speed up a ramp inclined at 28°, as shown. Determine the magnitude of the applied force.
when the ramp is frictionless.
when the coefficient of kinetic friction is 0.18.

Ff= uk(Fn)

## The Attempt at a Solution

I think I have the answer to part 1 complete and correct: I tilted the axis and ended up multiplying sin28degrees(90kg)(9.8m/s^2) to give me 414N for the applied force.
Im not sure about the second part though, where I have friction involved. I tried finding my force of friction --> (0.16)(882N) = 141 N, then subtracting it from my initial applied force I found - so 414N - 141 N gives me 273 N. Not sure if this is correct though.. Help please!

gneill
Mentor

## Homework Statement

A 90 kg box is pushed by a horizontal force F at constant speed up a ramp inclined at 28°, as shown. Determine the magnitude of the applied force.
when the ramp is frictionless.
when the coefficient of kinetic friction is 0.18.

Ff= uk(Fn)

## The Attempt at a Solution

I think I have the answer to part 1 complete and correct: I tilted the axis and ended up multiplying sin28degrees(90kg)(9.8m/s^2) to give me 414N for the applied force.
Keep in mind that the applied force is horizontal. Only a component of that force will be directed along the slope. Draw a free body diagram and see if you can't work out how to decompose the applied force into components along the slope and normal to the slope.

Im not sure about the second part though, where I have friction involved. I tried finding my force of friction --> (0.16)(882N) = 141 N, then subtracting it from my initial applied force I found - so 414N - 141 N gives me 273 N. Not sure if this is correct though.. Help please!

Again, since the applied force is not parallel to the slope, but is horizontal, it's component normal to the slope will contribute to the net normal force that results in friction...

PhanthomJay
Homework Helper
Gold Member

## Homework Statement

A 90 kg box is pushed by a horizontal force F at constant speed up a ramp inclined at 28°, as shown. Determine the magnitude of the applied force.
when the ramp is frictionless.
when the coefficient of kinetic friction is 0.18.

Ff= uk(Fn)

## The Attempt at a Solution

I think I have the answer to part 1 complete and correct: I tilted the axis and ended up multiplying sin28degrees(90kg)(9.8m/s^2) to give me 414N for the applied force.
No, you are assuming that the applied force is parallel to the incline, when it is given that the applied force is horizontal.
Im not sure about the second part though, where I have friction involved. I tried finding my force of friction --> (0.16)(882N) = 141 N, then subtracting it from my initial applied force I found - so 414N - 141 N gives me 273 N. Not sure if this is correct though.. Help please!
Since the applied force is horizontal, it has a component perpendicular to the incline, which affects the value of the normal force.
But why in any case would the applied force be less than the no friction case? It would be harder to push , wouldn't it?

Okay I see what you guys mean about the force being parallel versus horizontal . So instead, I break the Fapplied into x and y components. Since my Fnet of x is 0 d/t no acceleration, my Fgx should be equal and opposite to Fax.. So 414N I think. Then I used cos28Fax to find the applied force, so 370N?

gneill
Mentor
Okay I see what you guys mean about the force being parallel versus horizontal . So instead, I break the Fapplied into x and y components. Since my Fnet of x is 0 d/t no acceleration, my Fgx should be equal and opposite to Fax.. So 414N I think. Then I used cos28Fax to find the applied force, so 370N?

You can't get a component of a force that's larger than the force itself (414 is larger than 370) So revisit your calculation of the applied force. If F is the applied horizontal force, what expression yields Fax (its component parallel to the slope)?