- #1

mirs08

## Homework Statement

A 5000 kg car rests on a 32° slanted ramp attached to a trailer. Only a cable running from the trailer to the car prevents the car from rolling off the ramp (the car's transmission is in neutral and its brakes are off). Find the tension in the cable and the force that the ramp exerts on the tires

**please keep in mind that I have been using Ft instead of T as indicated in the picture as our prof encourages us to do so, so we don't get confused between T for temperature and T for tension in future problems

## Homework Equations

F

_{g}

_{x}= mgsinΘ

F

_{g}

_{y}= -mgcosΘ

Θ+β+90° = 180°

β = 90°-Θ (1)

α + β= 90° ∴ 90°- β (2)

α = 90° - (90°- θ) = Θ

## The Attempt at a Solution

Our prof used a rotated coordinate system, putting +y in the n direction, and +x downwards and parallel to the surface of the incline (i.e. directly opposite/antiparallel to F

_{T}). He also used a bunch of different angles/triangle rules, letting Θ = the angle of the incline, and α = the angle that the -y-axis makes with w, creating a triangle. β = the angle opposite to α.

I don't really understand how to use the rotated coordinate system, so I started off by separating the forces into their x and y components based on how they are oriented in the picture, assuming that F

_{g}has no horizontal component and both the tension force and the normal force have both horizontal and vertical components. I also assumed that the net force of the system is zero since the car is still, so forces should be in equilibrium.

x-direction:

Fg = 0

F

_{T}

_{x}

n

_{x}

y-direction:

Fg = -mg = -49000 N

F

_{T}

_{y}

n

_{y}

ΣF

_{x}+ ΣF

_{y}= 0I'm assuming I will need to know the triangle rules to find the x and y components of the normal force, and I think this is where I'm struggling, so this might just be basic geometry skills that I am lacking. I'm guessing that the normal force is slightly reduced (not exactly equal and opposite to the weight of the car) since there is a pulling force from the cable, and the weight is shared between F

_{T}and n. Is there a different way to do this without having to break it up into two different triangles, or could someone please explain how I should start breaking it down?