Basic Mechanics Focus Homework

Problem $1(4$ pts$)[$Done in class on Friday $10/07/2022,$ but it still needs to be fully done and turned in for credit$]$

The static coefficient of friction between the sides of a box and your hand is known to be $=0\mathrm{.}45.$ The box has a mass of $5$ kg and you are pressing inward with $100$ N of force on each side. You are holding the box in the air and are asked to determine the following:

a$)$ Draw a simple diagram showing each of the forces, including friction, acting on the box.

b$)$ Now that you have the direction of friction on the diagram, what is the value of friction in this case?

c$)$ How much weight could be added to the box before it slides out of your hands?

Problem $2(4$ pts$)$

You are asked to compare the ground pressure $($i$.$e$.$ the pressure exerted on the ground$)$ by a vehicle that has a mass of $1200$ kg with the ground pressure of an average person that has a mass of $80$ kg $.$ You can assume that the pressure is equally split between all four points of contact for the vehicle and both feet for the person. Several cases are asked for below.

a$)$ For the vehicle, the contact area for each tire is known to be $22$ in ${?}^2,$ what is the ground pressure in psi $(1$ pt$)$

b$)$ For the same vehicle, you are wanting to drive on snow and heard that adding tracks to your vehicle allows you drive on top. Further, you look up the tracks below and find that the contact area for each track is $675i{n}^2.$ There are four tracks. What is the ground pressure in psi? $(1$ pt$)$

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c$)$ Lastly, calculate the ground pressure in psi for the $80$ kg person. State your assumptions for the amount of contact area. $(2$ pts$)$