# 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”.

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”.

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

## 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

## Part 5#

If the mass of their supplies is 31 $$\rm{kg}$$, 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).

Please enter in a numeric value in $$\rm{N}$$.

## Part 6#

Find the magnitude of the kinetic force of friction on the supplies.

Please enter in a numeric value in $$\rm{N}$$.

## Part 7#

Solve your equations to find the tension in the rope.

Please enter in a numeric value in $$\rm{N}$$. 