Arctic Haul#
An environmental physicist working in the Arctic pulls their supplies up a steep (\(\theta = 30^\circ\) above the horizontal) snow-covered slope. The rope that they pull with is at an angle \(\theta = 30^\circ\) above the angle of the slope (see figure below). The coefficient of kinetic friction between the supplies and the slope is \(\mu_k = {{ params.uk }}\). They maintain a constant velocity up the hill.
Part 1#
Draw a force identification diagram for their supplies. Be sure to identify the tension \(\vec{T}\), the normal force \(\vec{n}\), the weight \(\vec{W}\), the force of friction \(\vec{f_k}\), and any other forces acting on the supplies. Do this by downloading the given diagram (right-click \(\to\) save image as), and uploading a photo of your annotated copy as a pdf, with the name “part1.pdf”.
Answer Section#
File upload box will be shown here.
Part 2#
Draw a free body diagram for their supplies. Be sure to label all of the forces identified in Part 1. (Hint: choose the x-axis to be parallel to the slope and the y-axis perpendicular to the slope). Upload a photo of your work as a pdf, with the name “part2.pdf”.
Answer Section#
File upload box will be shown here.
Part 3#
Write Newton’s 2nd law for the forces parallel to the slope.
Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:
For |
Use |
|---|---|
\(T\) |
T |
\(W\) |
W |
\(n\) |
n |
\(f_k\) |
f_k |
\(\theta\) |
theta |
Answer Section#
Part 4#
Write Newton’s 2nd law for the forces perpendicular to the slope.
Note that it may not be necessary to use every variable. Use the following table as a reference for each variable:
For |
Use |
|---|---|
\(T\) |
T |
\(W\) |
W |
\(n\) |
n |
\(f_k\) |
f_k |
\(\theta\) |
theta |
Answer Section#
Part 5#
If the mass of their supplies is 33 \(\rm{kg}\), solve your equations to find the normal force on the supplies. (Hint: you will need to eliminate the tension and express \(f_k\) in terms of the normal force).
Answer Section#
Please enter in a numeric value in \(\rm{N}\).
Part 6#
Find the magnitude of the kinetic force of friction on the supplies.
Answer Section#
Please enter in a numeric value in \(\rm{N}\).
Part 7#
Solve your equations to find the tension in the rope.
Answer Section#
Please enter in a numeric value in \(\rm{N}\).
Attribution#
Problem is licensed under the CC-BY-NC-SA 4.0 license.
