How can I find the mechanical energy lost due to friction?

[johny_doe]

Find the mechanical energy lost due to friction:

Starting from rest a 5.0kg block slides 2.5m down a rough 30.0 degree incline in 2.0s.


I know that the PE is 61.3 J. I keep on getting about -57 J when I try to find the mechanical energy lost due to friction but the answer is actually -45 J. Does anyone know what I am doing wrong. This is how I was trying to find it:

W = KEf - PEi
= .5mv^2-mgy
= .5(5.0kg)(2.5m/2.0s)^2 - (5.0kg)(9.8)(sin30*2.5m)

 

[Fermat]

Forget the PE.

You are asked to find the energy lost due friction. So you have to find the friction, that's all.

The block is sliding down a plane. What are the forces acting on it ?
Use Newton's 3rd law to devlop an eqn of motion.
You can find out the unknowns in this eqn by using the data about motion already given.

 

[verty]

Your velocity calculation is wrong. You are calculating the average velocity, but you want the final velocity for the kinetic energy.

So instead of s/t, you'd want 2s/t (from S = t(u+v)/2). I get 45.6J.

The other method is to determine the acceleration of the block, then the frictional force, then the work. I don't exactly understand Fermat's suggestion. Actually, I think he was suggest this approach, that you use the acceleration to find the frictional force.

 

[Fermat]

I'll clarify my approach.

...The block is sliding down a plane. What are the forces acting on it ?

There are two forces. The slope component of the mass, Fm say, acting down the plane and the friction force, Fr say, acting up the plane. The net force on the body is Fnet = Fm - Fr.

...Use Newton's 3rd law to devlop an eqn of motion...

i.e F= ma
or
Fnet = ma

...You can find out the unknowns in this eqn by using the data about motion already given.

You can do this bit now, yes ?