How Is Work Calculated When Multiple Forces Act on a Sled?

[Heat]

Homework Statement

A farmer hitches her tractor to a sled loaded with firewood and pulls it a distance of 20m along level ground. The total weight of sled and load is 14700N. The tractor exerts a constant 5000N at an angle of 36.9 above the horizontal. There is a 3500N friction force opposing the sled's motion. Find the work done by each force acting on the sled and the total work done by all the forces.

The Attempt at a Solution

To start off,

I found the work done by each force.

I drew the figure as follows:

http://img254.imageshack.us/img254/3663/49497726xp3.jpg

my calculations

cos(angle) = x/5000

5000 cos 36.9 = 3998.42

(3998.42J)(20m) = 79968.47

and

3500cos180 = -3500

(-3500J) (20m) = -70000

79968.47-70000 = 9968.47

My answer: 9968.47
Book answer: 10000

Is my process wrong, if so where did I go wrong? Don't the gravity and normal force cancel out?

From my reading in the book, we suppose to only count the horizontal forces, which is what I did here.

 

[G01]

I agree with your answer, what is the answer in the book?

 

[Heat]

the answer in the book is 10,000.

Don't know if this is rounded off,etc...since physics books usually tend to teach that we must not round off and be exact upon things.

 

[Tlocc]

You are probably correct. My book actually does strange things such as G=9.8 instead of G=9.81. I'm pretty used to my answers being slightly off and I'm given full credit along with my classmates.

 

[G01]

the answer in the book is 10,000.

Your answer is more than close enough. The book is taking into account significant figures.