Tension / Forces Question 40S Physics. Test Tommorow

[Brodo17]

A car is stuck in a snow band, but the driver is very knowledgeable about physics. She ties a rope from her car to a tree 25.0m away and then pulls sideways on the rope at a midpoint. If she applies a force of 425N and draws the rope over a horizonatal distance of 1.5m, how much force is applied to the car?


Equations
F=ma




I drew out the problem and I believe that the rope will be exerting an equal for in both directions (half the force on the car, the other half on the tree) I made a triangle with the 1.5m up and then a hypotenuse which is equal to the length of half the rope (12.5m). I don't understand at all how to solve this though. If someone could guide me through it I would really appreaciate it. There might be something like this on my test tommorow!

 

[RoryP]

yep you have the right idea there, set up a triangle for forces, and a separate one for lengths.
try and work out some angles, some legnths and try resolving forces
that should lead you in the right direction (i hope)
based on an AS in mechanics and AS in physics i got an answer of 51 N
would be great if you could tell me if that's correct as I am revising similar things

 

[Brodo17]

The answer in the back of the book says 3.56 x 10^3 N...

 

[LowlyPion]

Won't the forces be at the same ratio as the displacements?

1.5/12.5 = 425/F

 

[RoryP]

yep that gets the right answer, i also just got that answer using resolving forces

 

[Brodo17]

Won't the forces be at the same ratio as the displacements?

1.5/12.5 = 425/F

Im just wondering what exactly that equation is and when it can be used. I've never seen that before.

 

[Oscar Wilde]

Ok I got the right answer. These are the steps you could follow.

1) Using trig, find the hypotenuse of the rope (of the half-triangle). One side is 1.5m (how far she pulls back) and the other is 12.5m ((Should get value of 12.58967 for the side of the triangle between the woman and tree))

2) Use law of sine to find the angle opposite of the 1.5m ((comes out to 6.84277 degrees))

3) Then substitute in your Force value on the triangle, and solve for the side between the woman and the tree (this side was previously 12.589 m in our other triangle). The trick is switching over to Force values after you find the angles.

Which yields 3567N, or 3.56E3 Newtons


LowlyPion's way seems a lot quicker and "cleaner" if you ask me.

 

[LowlyPion]

My observation just took the hypotenuse to be the 12.5 m. That the rope was just under slight tension when tied straight, and force increased with horizontal movement. The presumption being that the rope doesn't stretch, the car moves a little. Note it yields a number slightly lower. Something like 3542 N.

The book answer is apparently to keep the distance between the car and tree fixed which is the more correct way. The longer way is the right way.

 

[Brodo17]

Alright, thanks for the help everyone. I should be ok now.

 

[Brodo17]

PS. How do I make it say that the Thread is solved?