How Do You Calculate Work and Force for a Displaced Mail Bag?

[melodrameric]

Hi there, I'm new here, and I desperately need help with this work/energy business. Here's my problem:

A mail bag with a mass of 140 kg is suspended by a vertical rope of length 8.00 m.
a) What horizontal force is necessary to hold the bag in a position displaced sideways a distance 3.00 m from its initial position?
b) How much work is done by the worker in moving the bag to this position?

I know that the angle from the vertical will be 22 degrees, and that the tension in the rope will be 1272 N (or am I wrong?), but I don't know where to go from there.

By the way, this is for a Mastering Physics problem, and I've already found out that 476.5 N [1272*cos(68)]is a wrong answer.

Thank you!

 

[Fermat]

You got the tension wrong, that's all. It looks like your method is OK.

 

[quicknote]

Hi there,

It seems like you have a good understanding of the problem and have identified the necessary information. To solve this problem, we can use the concepts of work and kinetic energy.

To answer part a), we can use the formula for work, which is W = Fd, where W is work, F is force, and d is displacement. In this case, the displacement is 3.00 m and the force needed is what we are trying to find. We also need to consider the angle of the rope, which is 22 degrees from the vertical. This means that the horizontal component of the tension force (1272 N) will be what contributes to the displacement. So we can use the formula F = Tcosθ, where F is the horizontal force, T is the tension force, and θ is the angle from the vertical. Plugging in the values, we get F = 1272cos(22) = 1208.5 N.

For part b), we need to calculate the work done by the worker in moving the bag to the new position. We can use the same formula, W = Fd, where F is the same as we calculated in part a) and d is the displacement of 3.00 m. So the work done is W = 1208.5 * 3.00 = 3625.5 Joules.

I hope this helps and good luck with your Mastering Physics problem! Remember to always check your units and use the correct formulas. Let us know if you have any further questions.