Calculating Work Done by Gravitational Force: Undergrad Homework Help

[janthony]

I thought I knew how to solve this, but I'm stuck

a block slides down an incline. As it moves from point A to point B, which are 5.0 m apart, a force F acts on the block, with magnitude 2.4 N and directed down the incline. The magnitude of the frictional force acting on the block is 10 N. If the kinetic energy of the block increases by 45 J between A and B, how much work is done on the block by the gravitational force as the block moves from A to B?

I used the equation W'=delta ke+gravitational force

W'=2.4-10=-7.6 J
then I subtracted ke to get gravitational force=-52.6 J

then -mg=-52.6/5=-10.52

i then set 45=mgh, solved for h and got h=4.27756654

and then divided -52.6 by h to get -12.2967. This is wrong, and I'm stuck.

 

[gneill]

Watch your units. Work is not force, so in your equation for w', you can't just equate Joules (energy) with Newtons (force).

The question is asking you to calculate the work done by gravity, so why not cast everything into the form of work done? Work done by a force f acting over distance d is given by f.d, where the period represents the vector dot product. Luckily, almost all our given forces act directly along the line of motion, they just become f*d, the usual product.

Can you write an equation that expresses the gain in kinetic energy as the net work done by all the forces acting?

 

[janthony]

alright. so, W=F*d.

So, the work of kinetic energy is 45J.

I calculated the work of F and friction to be 12J and 50J, respectively.

so, not I have the equation:

(45+12+50) + Work done by gravity=F*d.

And now I'm stuck.

 

[gneill]

alright. so, W=F*d.

So, the work of kinetic energy is 45J.

I calculated the work of F and friction to be 12J and 50J, respectively.

so, not I have the equation:

(45+12+50) + Work done by gravity=F*d.

And now I'm stuck.

Pay attention to the directions that forces are operating. The force F is doing work in the direction of motion, so it can be called positive, and it serves to add kinetic energy to the block. The force of friction is working against the direction of motion, so it's robbing energy from the block's motion; it'll be a negative contribution. The work done by gravity will also be adding to the downslope motion of the block.

So, if +45J is the net change in kinetic energy (the sum of all the individual contributions to the change), write the equation: 45J = ?...