Work and Power: Lever Efficiency Problem

[NDiggity]

Homework Statement

A person uses a rope to pull a 1000kg. boat 50.0m along a wharf. The rope makes an angle of 45 degrees with the horizontal. If a force of 40.0N is used to move the boat, how much work is done?

Homework Equations

W=fd
Here is my problem. My physics class has 5 days left and we have 3 units to get through so were basically doing a unit in a day and a half. So my teacher is giving a very brief overview of the units and then gives us work sheets. So I am still a little confused. Is the question just giving me extra information to trick me? My question is, if the direction of movement is horizontal like in this question, do you use the horizontal force to find work then? Do you only use the tension in the rope if it is given to find the force needed to move the box horizontally.

The Attempt at a Solution

I'm not too sure. I thought maybe it was 40(50)=2000J since 40N is needed to move the boat 50m.

 

[neutrino]

You are close but not close enough. Remember that the rope makes an angle with the horizontal.

 

[NDiggity]

is it 40(50)cos45? I'm obviously still a little confused with this unit since we had to learn the whole thing in a day.

 

[neutrino]

is it 40(50)cos45?

That is correct.

The work done by a constant force is F.d, the dot product of the force and displacement. In the problem at hand, the displacement is purely horizontal, while the force has both horizontal and vertical components.

Here's a site that you might find helpful, http://hyperphysics.phy-astr.gsu.edu/hbase/wcon.html

 

[esalihm]

correct

 

[NDiggity]

Thank you very much for the help! I have one more question.

A force of 2250N is exerted on a lever system to raise a 1200N rock 1.32m. If the efficiency of the lever is 58.7%, how far did the effort force move?

So I used the efficiency equation: Efficiency=work with no machine/work with machine

I plugged in the variables to get:
58.7=1200(1.32)/2250d

I isolated d and got .012m. This seems too small. What did I do wrong?