How Much Work Is Done When Pulling a Sled 1 km with a 45-Degree Rope Angle?

[zackf]

Homework Statement

A loaded sled is pulled by means of a rope that makes an angle of 45 degrees with the horizontal. The mass of the sled is 60 kg, and the friction force is 20 N. How much work is done pulling the sled along a level road for a distance of 1 km?

Homework Equations

W=FxD

The Attempt at a Solution

 

[berkeman]

Welcome to the PF, Zack. An important rule here is that we do not do your work for you and just solve your problem. You must show your own work so far to get help. What does your free body diagram look like? What equations have you been using so far?

(As an aside, generally the term "Physician" like you used in your title means a medical doctor, not a physicist. I'm not sure exactly what you meant by the use of the word. No big deal -- I just wanted to be sure you understood the distinction if english is not your primary language.)

 

[m2003]

To calculate the work done, we need to use the equation W = F x d, where W is work, F is force, and d is distance. In this case, the force is the tension in the rope, which can be calculated using trigonometry as F = mgcosθ, where m is the mass of the sled, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle between the rope and the horizontal (45 degrees in this case). So, F = (60 kg)(9.8 m/s^2)cos(45 degrees) = 411.6 N.

Next, we need to calculate the distance the sled is pulled, which is 1 km or 1000 m. Now, we can plug in these values into the equation W = F x d:

W = (411.6 N)(1000 m) = 411600 J

Therefore, the work done in pulling the sled along a level road for a distance of 1 km is 411600 J. This means that 411600 Joules of energy were transferred from the person pulling the sled to the sled itself.