Frictionless inclined plane problem

[Chester8990]

Homework Statement

A 2.5 kg block is placed on a movable 40° ramp weighing 120 N. The friction
coefficients between the ramp and the block are μk = 0.15 and μs = 0.35. With what
force does the ramp need to be pushed to keep the block

a) sliding at a constant speed up the ramp

b) sliding at a constant speed down the ramp

c) what range of forces keeps the block stationary on the ramp

Homework Equations

The only equations i can think of is F=ma, F_f= μk*mg

The Attempt at a Solution

I tried resolving the forces into components parallel to the acceleration's direction,
so for a general free body diagram of all the situations

ƩF_a=ma= F_gxcos(40)+F_fcos(40)

ƩF_y=ma*sin(40)=N-F_gy

Where signs can be changed according to actual situation

That's where i got stuck, I actually have the solution to this problem, but i didn't understand how the answer came about. Can anybody please offer some help? If you want i can also put the solution here

 

[anathema]

, but i don't think it will be very helpful, as the solution is just the answer to the questions, and not the reasoning behind it.

Hello, thank you for your post. It seems like you are on the right track with your equations. To answer the first part of the question, you can set up the equation F=ma for the block, where the force F is the pushing force on the ramp and the acceleration a is the constant speed up the ramp. You can then substitute the values given in the problem, such as the mass of the block and the friction coefficient, to solve for the force needed to keep the block sliding at a constant speed up the ramp.

For the second part of the question, you can use the same equation F=ma, but the acceleration a would now be the constant speed down the ramp. Again, you can substitute the values given in the problem to solve for the force needed.

To find the range of forces that keep the block stationary on the ramp, you can set up the equations ƩFa=0 and ƩFy=0, since the block is not moving. You can then solve for the range of forces by substituting the values given in the problem and using the friction coefficient μs.

I hope this helps clarify the reasoning behind the solution. If you have any further questions, please don't hesitate to ask.