Solving Easy Work Problem: 10N x 3.5m and 805 N x 22m

[diciccod]

Hi, i haven't been at school this week so i only got the homework and no help.

I know this is an easy question so just tell me which way of doing it is right.

A person carries a carton of milk that is a weight of 10 N for a distance of 3.5m along a level surface. How much work is being done?

is it just 10N * 3.5m * cos(90)

or is it just 10N * 3.5m

I would think it would be the first one because it is an angle of 90 degrees between the displacement and the weight, but it doesn't make sense because it says no work is being done.

Also, one more problem a hor. force of 805 N is needed to drag a crate across a hor. floor with a constant speed. You drag the crate using a rope held at an angle of 32 degrees.
a. What force do you exert on the rope?
b. How much work do you do on the crate when moving it 22m
c. If you complete the job in 8.0s, what power is developed.

I really just need help on part of that problem.
THanks a lot :)

 

[chroot]

In the first problem, you are correct. No work is being done at all (against gravity). If the object does not change altitude, then gravity is quite simply not relevant.

In the real world, of course, you have to contend with friction. In this problem, however, I believe you are to neglect friction.

The reason no work is done can be easily understood. Imagine sliding a jug of milk along a perfectly smooth, enormous iced-over lake. In the absence of friction, the only effort you'd have to spend is applying a force to get the jug moving. Once moving, sending it a few feet away and sending it clear to the other side of the lake would be (energetically speaking) exactly the same.

No work is done against (or by) gravity unless something is changing altitude.

- Warren

 

[M98Ranger]

Hi there,

First of all, don't worry about not being in school this week and not getting help. I'm happy to assist you with your homework.

For the first problem, you are correct in thinking that the first equation is the correct way to solve it. However, the reason it says no work is being done is because the angle between the displacement and the weight is 90 degrees, which means the force is perpendicular to the displacement. This means that no work is being done because the force is not causing any displacement in the direction of the force. So in this case, the work done would be 0.

For the second problem, let's break it down into parts:

a. To find the force exerted on the rope, we can use the formula F = ma, where F is the force, m is the mass, and a is the acceleration. Since the crate is moving at a constant speed, there is no acceleration, so the formula becomes F = 0. Therefore, the force exerted on the rope is 0.

b. The work done in this scenario can be calculated using the equation W = Fd, where W is the work, F is the force, and d is the distance. Since we know the force is 805 N and the distance is 22m, the work done would be 17,710 J.

c. To find the power developed, we can use the formula P = W/t, where P is the power, W is the work, and t is the time. Since we know the work is 17,710 J and the time is 8.0 seconds, the power developed would be 2,213.75 watts.

I hope this helps! Let me know if you have any other questions. Good luck with your homework!