What Is the Angular Acceleration and Force Exerted on a Falling Fence?

[momiki]

Homework Statement

A man jumps at a fence. The fence hits the ground in 0.81 seconds, and the height of the fence is 1.24 meters. What is the angular acceleration of the fence? What is the force exerted by the man on the fence? The fence has a mass of 40 kg.

Homework Equations

F(torque) = m * r * ALPHA

...not sure if torque is even involved?

The Attempt at a Solution

Angular Acceleration:
ωi = 0rpm
ωf = 2pi*.25 / .81 = 1.939 rad/s^2
ALPHA = ωf - ωi / .81 = 1.939/.81 = 2.393 rad/s^2

Ft = m * r * ALPHA
= 40*1.24* 2.393
= 118.693 N

 

[haruspex]

ωi = 0rpm
ωf = 2pi*.25 / .81 = 1.939 rad/s^2

You have divided an angle by a time. What units will result from that?
I assume you are after finding the average angular acceleration of the fence, and in the step here you are trying to calculate the final angular velocity. What quantity have you actually calculated?

Ft = m * r * ALPHA
= 40*1.24* 2.393
= 118.693 N

A few problems there.
First, it's not clear whether the man locks onto the fence and comes down with it.
1. Suppose he doesn't - he just crashes into it and bounces off or stays upright.
The question asks for force, which it is impossible to determine. He collides with the fence at some speed, imparting momentum. We don't know how long the collision takes so it is impossible to say what force is involved. So assume the question really asks for the momentum. But there's still a difficulty - we can either assume he strikes the top of the fence, or restrict our calculation to arriving at the angular momentum he imparts.
2. Suppose he comes down with it. We're not told if he locks onto the top of the fence. Suppose he does. First, he collides with it at some speed imparting angular momentum (to the whole system: fence+man). Now you have to consider the moment of inertia of that system about the axis (bottom of fence), and the fact that gravity is assisting. But I'm still not sure how to answer the 'force' question. At least now you can compute the average torque he supplies during the whole incident, so I suppose you could divide by the fence height to get the force.

 

[momiki]

Thank you for the reply!

For the first part I copied it down wrong

ωi = 0rpm
ωf = 2pi*.25 / .81 = 1.939 rad/s

ALPHA(angularAcceleration) = ωf - ωi / Δt = 1.939/.81 = 2.394 m/s/s

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As for the specifics, the man does not come down with the fence. The only specification beyond that is that we must calculate the "component perpendicular to the fence", so I am guessing that using angular momentum is the way to go.

where angularMomentum = I * ω
and I can by modeled by a rod about one end, or (1/3)MR^2
=(1/3)(40)(1.24)^2
=20.501
plug back into angularMomentum = I * ω = 39.751N

which seems reasonable, but what then was the point of the question asking to calculate angularAcceleration?

 

[haruspex]

Thank you for the reply!

For the first part I copied it down wrong

ωi = 0rpm
ωf = 2pi*.25 / .81 = 1.939 rad/s

OK, you've corrected the units, but you have not corrected the other problem here. You have taken the total angle traveled and divided by the total time taken. That will give the average rotation rate, not the final rotation rate.

As for the specifics, the man does not come down with the fence. The only specification beyond that is that we must calculate the "component perpendicular to the fence", so I am guessing that using angular momentum is the way to go.

where angularMomentum = I * ω
and I can by modeled by a rod about one end, or (1/3)MR^2
=(1/3)(40)(1.24)^2
=20.501
plug back into angularMomentum = I * ω = 39.751N

Wrong units, and you're still ignoring action of gravity on the fence.

 

[momiki]

alright, in that case I don't see how the final rotation rate would help anyways considering that I want to find the force at the point of impact?

As for force of gravity, at the point of impact it would be downwards (from 90 degrees) and thus negligible, correct?

 

[haruspex]

alright, in that case I don't see how the final rotation rate would help anyways considering that I want to find the force at the point of impact?

The first thing asked in the OP is the acceleration. You wanted to calculate the final angular velocity in order to obtain the acceleration, but you have still not successfully calculated the final velocity, only the average velocity. See below.

As for force of gravity, at the point of impact it would be downwards (from 90 degrees) and thus negligible, correct?

The man sets the fence rotating from the vertical with some angular speed. But the speed will not stay constant. Gravity will accelerate the fence as it falls.
When the fence is at angle theta to the vertical, what torque does gravity apply? What angular acceleration will result?
(But it will be simpler to go straight to the energy equation. What PE will it have lost at that angle? So what will be its rate of rotation/)

 

[momiki]

(But it will be simpler to go straight to the energy equation. What PE will it have lost at that angle? So what will be its rate of rotation/)

how can PE be applied here? I know that PE = m*g*h, but the fence is technically resting on the ground, with a mass distributed through the height of the fence?

 

[haruspex]

how can PE be applied here? I know that PE = m*g*h, but the fence is technically resting on the ground, with a mass distributed through the height of the fence?

Initially it is standing. Its centre of mass is not on the ground then, but it is at the finish.

 

[momiki]

Would it be better, then, to calculate angular acceleration from the kinematic equation vi*t+1/2at^2 = d.

Then plug that acceleration into the torque equation

rF = I(ALPHA)

and use the inertia of a rod about one end, or I=(1/3)ML^2 for inertia. Not sure if the best way to model the fence is with that inertia?

 

[haruspex]

Would it be better, then, to calculate angular acceleration from the kinematic equation vi*t+1/2at^2 = d.

Then plug that acceleration into the torque equation

rF = I(ALPHA)

Use work conservation when you can (and you can here) because it does the first integration step for you. When the fence has rotated through an angle theta from the upright position, how far has its centre of mass descended?

and use the inertia of a rod about one end, or I=(1/3)ML^2 for inertia. Not sure if the best way to model the fence is with that inertia?

Yes, use that.