Forces on an Incline: Solving & Sliding

[MitsuShai]

Homework Statement

http://s324.photobucket.com/albums/k327/ProtoGirlEXE/?action=view&current=q1-1.jpg

Homework Equations

f=ma
f= uFn

The Attempt at a Solution

a) I found the forces acting on the block acting in the x and y directions to make two equations

then I solved for weight force with the forces in the y direction and that will equal the normal force

next I basically just plugged stuff in:
ma = - mgSin(25) - u(k)mgCos(25)
a = - g[Sin(25) + u(k)Cos(25)]

I got the acceleration to be 1.57 m/s^2 , is that correct?


b) friction= u(s)mgCos(25)
For the block to slide down the weight component must be greater then the max friction force,so
mgSin(25) > u(s)mgcos(25)
Tan(25) > u(s)
.446> .44
so the block will slide down

am I correct?

 

[collinsmark]

next I basically just plugged stuff in:
ma = - mgSin(25) - u(k)mgCos(25)
a = - g[Sin(25) + u(k)Cos(25)]

Your approach looks about right to me.

I got the acceleration to be 1.57 m/s^2 , is that correct?

But you should double check your math. Something didn't come out correctly when you plugged the numbers in.

b) friction= u(s)mgCos(25)
For the block to slide down the weight component must be greater then the max friction force,so
mgSin(25) > u(s)mgcos(25)
Tan(25) > u(s)
.446> .44
so the block will slide down

Part b) looks fine to me.

(btw, for next time, this type of problem probably belongs in the "Introductory Physics", homework and coursework subforum.)

 

[MitsuShai]

Your approach looks about right to me.

But you should double check your math. Something didn't come out correctly when you plugged the numbers in.

Part b) looks fine to me.

(btw, for next time, this type of problem probably belongs in the "Introductory Physics", homework and coursework subforum.)

I'm still getting 1.57 m/s^2 as my answer:
a= [(1.6*9.8*sin25)-(.32*14.211*cos25)]/1.6 = 1.57 m/s^2

 

[collinsmark]

I'm still getting 1.57 m/s^2 as my answer:
a= [(1.6*9.8*sin25)-(.32*14.211*cos25)]/1.6 = 1.57 m/s^2

Whoa, Where did that equation come from. I didn't see anything like that in your original post.

Go back to to original post. You had the right idea then.

 

[MitsuShai]

Whoa, Where did that equation come from. I didn't see anything like that in your original post.

Go back to to original post. You had the right idea then.

But it's the same thing, the original equation is a simplified version of the second one, but I'll try it and see if there's a difference in my answer.

 

[MitsuShai]

Hmmm, that's weird
I got 6.98 m/s^2 now

or actually -6.98m/s^2

I did it again with the second equation (I accidentally left the minus out in the front) and got -6.72 m/s^2, why is it different?

a = - g[Sin(25) + u(k)Cos(25)] = -6.98 m/s^2
a= [-Fwsin(25)-usFncos(25)]/1.6 = -6.72 m/s^2

 

[collinsmark]

Hmmm, that's weird
I got 6.98 m/s^2 now

or actually -6.98m/s^2

I did it again with the second equation (I accidentally left the minus out in the front) and got -6.72 m/s^2, why is it different?

a = - g[Sin(25) + u(k)Cos(25)] = -6.98 m/s^2

That looks good. There you go. .

a= [-Fwsin(25)-usFncos(25)]/1.6 = -6.72 m/s^2

Well, I'm not really sure what to think of that. It looks like you have the normal force F_n in the second term, but the normal force already has the cos25 built into it. So your equation is accounting for the cos25 twice. You also seem to have the static coefficient of friction μ_s, tacked on, but you should be using the kinetic coefficient, not the static. So it looks to me like there are a couple of things wrong with the equation.

 

[MitsuShai]

That looks good. There you go. .

Well, I'm not really sure what to think of that. It looks like you have the normal force F_n in the second term, but the normal force already has the cos25 built into it. So your equation is accounting for the cos25 twice. You also seem to have the static coefficient of friction μ_s, tacked on, but you should be using the kinetic coefficient, not the static. So it looks to me like there are a couple of things wrong with the equation.

oh that was a very dumb mistake
thanks for you help!