Calculating Kinetic Energy Change on a Ramp: KE and Friction Homework Solution"

[gansta344u]

Homework Statement

An 83.6 N box of clothes is pulled 20.1 m up
a 39.5◦ ramp by a force of 119 N that points
along the ramp.
The acceleration of gravity is 9.81 m/s2 .
If the coefficient of kinetic friction between
the box and ramp is 0.23, calculate the change
in the box’s kinetic energy. Answer in units J

Homework Equations

Ff=u(k)Fn
KE=1/2mv^2

The Attempt at a Solution

I am a little bit confused on this problem. I think i have to add up all the forces by multiplying the normal force and uk. Also then i think we have to find the x-value of the force acting on the angle but i can't seem to put it all together or find a formula which helps me put everything together . Please if possible i kinda need help in both the concept and the formula

 

[Delphi51]

Draw the weight vector straight down from the box.
Resolve that into a vector along the ramp plus another one straight into the ramp.
Use trigonometry to find these parallel and normal vectors.
Then you can find the force of friction.

You could then continue analyzing the forces, find the acceleration and then the final velocity.

Or you could work with energy formulas to find the KE.

 

[gansta344u]

`i don't think i quite understand the method of drawing so can u please try to explain it more if possible because i don't understand what to do. If possible can you show me a algebraic method

 

[Delphi51]

You must draw the diagram before you can do the algebra!
It works a little nicer if you put the box right at the top of the ramp.
Draw the weight vector as an arrow that begins on the box and goes straight down.
Starting at the same place on the box, draw an arrow that goes along the ramp. Then another arrow that begins at the end of that one and goes to the end of the weight vector. You have shown the weight vector as the sum of a force along the ramp and a force into the ramp.

Something like this:

Mark your angle on the ramp and also in the triangle of the forces.
Use trigonometry to find the normal and parallel forces.
Then you can calculate the force of friction with your formula.

 

[gansta344u]

i think u misinterpreted the question , It says pulled up so i think the box should be at the bottom and the weight cannot be the sum of the other forces b/c the weight is the hypotenuse but the force is greater then it which cannot be possible since the hypotnuse is the longest side

 

[Delphi51]

Nevertheless, you need to find those parallel and normal components of the weight before you can find the force of friction. I didn't say the box was at the top, just that drawing it at the top seems to make it easier to draw the two blue vectors.

 

[gansta344u]

i really still don't get this . First of all the weight cannot be the hypotenuse because it is weaker in value then the force applied which is 119N compared to the 83.6N weight so to me it seems impossible can u please try to explain a little bit more clearly on what I am supposed to do because i don't get the whole point of the diagram and what we are supposed to solve b/c it seems to me this is only have of it and if u can just let me know what angle or what line we are supposed to find. TO find a line or angle u do use arithmetic so if u can just let me knw what line or angle i have to find and i can do that. that is simple but right know all I am doing is guessing on how to slve i don't understand it so if u can again please explain anyone please explain!> i really don't get by what u are trying to say by parallel forces