Speed of a box at the bottom of a incline.

[Paulbird20]

Ok so I am having trouble calculating the speed of a box as it travels down a incline.

I was Given 22 degree angle and the coefficient of friction (kinetic) is .22. Height of 9.10m (from rest at the top).
I calculated acceleration while it travels down the slop and got 1.6721.
I next need to calculate the speed when it reaches the bottom of the incline.

I thought i would simply need to use 2*G*H ^(1/2) . It gives me 13.355 and it is wrong.
Any help would be greatly appreciated or any equations i can use.

Thanks from a new user.
Paul.

 

[mdk31]

Why not use the approximation of gravitational potential energy for objects close to Earth?

U[g]=mgh

But that doesn't just equal the kinetic energy at the bottom. You have to take into account the work done by nonconservative forces, namely, in this case, friction.

I don't know if that was any help or not.

 

[Paulbird20]

I don't know how to calculate the mass to be able to use that equation. Only equations i have in my notes are
2*G*H^(1/2) = V1
and
calculations of sum of all forces. I have a free body diagram drawn also i just don't know where to go from here. I was almost sure 13.355 was gunan be the speed but it is wrong.

 

[mdk31]

That equation is true if the block is frictionless but it is not frictionless in this case. Go back and re-read your notes or the book to better understand the U[g]=mgh gravitational potential energy equation.

The equation that you have comes from conservation of energy:

(mv^2)/2=mgh; rearrange that
v=(2gh)^1/2

But, as I said before, you cannot apply that equation here because the surface is not frictionless. Some energy is lost to friction.

Here's a hint: W[friction] =F[friction]*distance

Subtracting this value from your initial potential energy will give you the final kinetic energy at the bottom of the block.

 

[Paulbird20]

Ok so from what i have gathered reviewing my notes.

Fnormal= m*g*cos (angle)
and
FF(friction force) = coef K * Fn

I was trying to use these two equations to determine FF but i can't because of the mass in the first one. Is there another equation i can use to get FF?

 

[Paulbird20]

AH HA! i found my equation your hint helped thank you.

I took 2 * A* x1-x0 ^(1/2) and it gave me my final velocity Thank you.

 

[mdk31]

Ah, I see. You used a kinematics equation. Just remember, it may have worked in this case but those five major equations only work when the acceleration is a constant value.