Work done by pulling block over surface.

[cthionic]

Homework Statement

A 80-kg block is pulled across a rough surface a distance of 1.25 metres. How much work was done in moving it? The coefficient of static friction was 0.3 and kinetic friction was 0.2. Assume the velocities were very low.

Homework Equations

W = fd
??

The Attempt at a Solution

I don't know how to apply kinetic/static friction together. static is to get from 0 velocity to starting to move, but how uncertain how to combine the two together.
W = 80(0.3/0.2??) * 1.25 = 16 * 1.25 = 20. .. multiple choice options are 98 J, 148 j, 196 j or 392 j

 

[cepheid]

Welcome to PF!

At the beginning, when you're trying to overcome static friction, you increase the force with which you're pulling until you overcome it, and the block starts moving. However, during this time that you're increasing your pull to start the block moving, the block is still stationary. That means there is no displacement. That means no work is done. It's only once you've got it in motion that work starts being done.

Now, let's assume you're lazy and you want to pull using the minimum required effort. Once you overcome static friction, kinetic friction (which is lower) takes over. So for this brief moment of time at the beginning, you are pulling with a force larger than the frictional force. So there is a net force on the block, and it accelerates up to some speed. Let's assume that you don't let it accelerate too much before lessening your pull so that it is *equal* to the kinetic friction. At this point, there is 0 net force on the block, and Newton's 1st says that it continues along at the constant (and very low) speed that you allowed it to accelerate up to before you lessened your pull.

So, for most of the motion, you pull with a force equal to the kinetic friction, and maybe it's not such a bad approximation to assume that that is how hard you pull for the entire time. If I make that assumption, then I get one of the answers given in the answer choices.

 

[cthionic]

Thanks!

So I would take the weight of the block, 80, multiply that by gravity, 9.8, which would be the normal force. then, 9.8 * 80 * 0.2, which is 156.8, then multiplied by the distance, 1.25, and then i get 196 J. is this correct?

 

[cepheid]

Thanks!

So I would take the weight of the block, 80, multiply that by gravity, 9.8, which would be the normal force. then, 9.8 * 80 * 0.2, which is 156.8, then multiplied by the distance, 1.25, and then i get 196 J. is this correct?

The math is correct. The physics is correct IF the assumptions I outlined in my previous post hold. Do you buy that line of reasoning?

 

[cthionic]

I think so. If you kept pulling/pushing with the force you needed to get it started, you would be accelerating instead of keeping a constant low velocity, right?

 

[cepheid]

I think so. If you kept pulling/pushing with the force you needed to get it started, you would be accelerating instead of keeping a constant low velocity, right?

Yeah, that's right.