What Is the Maximum Angle a Pendulum Swings When a Car Stops Suddenly?

[meeklobraca]

Homework Statement

You have a 0.35m long pendulum attached to the roof inside your car. Your car is traveling as a speed of 1m/s when it hits a concrete wall and stops immeadiately. If the pendulum is free to swing, to what maximum angle to the vertical does the pendulum swing upon impact.

Homework Equations

I don't have the slightet idea where to start. I am guessing we need to get some trig involved here because to find the angle we need at least the distance the pendulum swung.

I think we have a Vi that is 0 and a Vf that is 1 but again, I am not sure how to use that to figure this out.

The Attempt at a Solution

 

[madmike159]

I don't know where to begin without a stopping distance. I would guess 90 degrees because it stops immeadiately, but that doesn't sound right.

 

[meeklobraca]

Well does it help that this question is in a conservation of energy work sheet?

 

[madmike159]

Do you have any other numbers (such as mass)?

 

[meeklobraca]

Nah nothing else. LIke what I've been trying to rack my head around is trying to figure out the distance between where the pendulum starts, and where it reaches max angle. From there you can use some trig to get the angle, but I have no idea how to get that distance with the values we have.

 

[madmike159]

I could do it with mass, but without it I don't know where to start. Some one else might be able to help.

 

[meeklobraca]

Im just saying this theoretically, but what if the mass was 5Kg. THen how would you solve it?

 

[meeklobraca]

Its a fairly complicated process in this one, but as it was explained to me is that you have a starting point and then the stopping point of the pendulum as the car hits the wall. THe starting point has Ek and the stopping point is Ep. So you have to use 1/2mv2 = mgh and solve for h. Take the difference of h off the total length of the pendulum and create a right angle triangle and solve for the angle.

 

[madmike159]

Yes but you would need mass for that, I thought you didn't have it.

 

[meeklobraca]

mass can cancel each other out since theyre on each end of the equation

 

[madmike159]

Yea I see now, I did this not long ago (clearly didn't rember it).
1/2v^2 = gh
h = 1/2v^2/g = 1/2*1/9.81 = 0.051
sin^-1(O/H)=sin^-1(0.051/0.35)= 8.38 degrees.
Is that what you got?

 

[meeklobraca]

You have to take the .051 off the overall length of 0.35 to get the resting side, then you have 0.35 on the other side. so you .3/.35 inv cos and you get 31 degrees which is the answer

 

[madmike159]

Woops. I thought 8.38 sounded small.