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 = ?...

 

[rwisz]

I can understand why you may be feeling stuck in this problem. It can be frustrating when our calculations don't match up with our expectations. However, it's important to remember that science is all about trial and error, and it's okay to make mistakes as long as we learn from them.

First, let's review the equation you used to calculate the work done by the gravitational force, W=ΔKE+ΔPE. In this problem, we are only concerned with the work done by the gravitational force, so we can simplify the equation to W=ΔPE. This means that the work done by the gravitational force is equal to the change in potential energy of the block.

Next, let's review the given information. We know that the block is moving from point A to point B, which are 5.0 m apart. We also know that the force F acting on the block has a magnitude of 2.4 N and is directed down the incline. The frictional force acting on the block has a magnitude of 10 N. And finally, we are given the change in kinetic energy of the block, which is 45 J.

To calculate the work done by the gravitational force, we need to find the change in potential energy of the block. This can be calculated using the formula ΔPE=mgh, where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s^2), and h is the change in height. In this case, h is the vertical distance between point A and point B, which is equal to the height of the incline.

Now, let's review your calculations. You correctly used the equation W=ΔKE+ΔPE, but your calculation for the work done by the gravitational force is incorrect. The correct calculation is W=ΔPE=mgh. Additionally, your calculation for h is incorrect. The correct calculation is h=5sin(θ), where θ is the angle of the incline.

To solve this problem, we need to first find the mass of the block. This can be calculated using the formula F=ma, where F is the net force acting on the block and a is the acceleration of the block. In this case, the net force is the difference between the force F and the frictional force, so F-Ff=ma. Substituting the given values, we get (