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.

Someone pulling a block, to the right, up a 30 degree slope with a rope that is 30 degrees above the angle of the slope.

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 77 \(\rm{kg}\), 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.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.