Forces, Acceleration Hard Stuff (HELP)

AI Thread Summary
The discussion revolves around solving a physics problem involving a trailer being pulled by a vehicle, focusing on the forces and acceleration involved. The user Kevin outlines the steps to derive the vertical component of the pulling force (Py) in relation to the trailer's loaded weight (Fg) and acceleration (a). Key equations are developed, including net forces in the y-component and net torques about the center of mass. The final expression for Py is derived as Py = (Fg/L)*(d - a*h/g). This comprehensive breakdown aims to assist others facing similar challenges in understanding forces and acceleration in this context.
klopez
Messages
21
Reaction score
0
[SOLVED] Forces, Acceleration...Hard Stuff (HELP!)

p12-69.gif



A trailer with loaded weight Fg is being pulled by a vehicle with a force P. The trailer is loaded such that its center of mass is located as shown. Neglect the force of rolling friction and let a represent the x component of the acceleration of the trailer.


(a) Find the vertical component of P in terms of the given parameters. (Use F_g for Fg, a, d, L, h, and g as appropriate in your equation.)




I have no idea on how to use come up with an expression that involves acceleration. In matter of fact I do not know where to start because this looks confusing. Can anyone give me advice?

Thanks,
Kevin
 

Attachments

  • p12-69.gif
    p12-69.gif
    11.2 KB · Views: 416
Physics news on Phys.org
What can you deduce about the total torque about any point on the trailer?
 
Here is how I found the correct answer:

First, break down force P into two components: Px and Py


Second, consider the center of mass to be your axis point.


Third, derive an equation for the the net forces in y-components, \sumFy, and let that equal to 0.

Py + n - Fg = 0 (1)


Fourth, derive an equation for the only force in the x-component.

Px = m*a

(and since the force of gravity on the whole truck is mg, than m = Fg/g)
So...

Px = (Fg/g)*a (2)


Fifth, derive an equation for the net torques, \sum\tau acting on the center of mass, which when summed, should equal 0.

Py*(L-d) + Px*h -n*d = 0 (3)

(Both Px and Py produce torque in the same direction so therefore they should be added and then subtracted by the normal force, which is producing torque in the opposite direction.)



Now using equation (3), rearrange the equation so that you have it in terms of n.

n = [(Px*h) + Py*(L-d)]*(1/d)

Since you know Px from equation (2), then you can plug that into the equation above.

n = [(Fg*a*h/g) + Py*(L-d)]*(1/d)

Simplified a bit further...

n = [(Fg*a*h) + Py*g*(L-d)]/(d*g)

Now using the n above, rearrange equation (1) in terms of Py, and then plug in your derived expression for n, and you have the following:

Py = Fg - [(Fg*a*h) + Py*g*(L-d)]/(d*g)

Simplify a bit so you have your Py on one side...

Py*d*g + Py*g*(L-d) = Fg*d*g - Fg*a*h

When you pull out Pyg and divide L on both sides...

Py*g = Fg*(d*g - a*h)/L

Divide g by both sides and your left with your answer...


Py = (Fg/L)*(d - a*h/g)



I hope this helps others who were stuck on this problem.

Kevin
 
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Struggling to make relation between elastic force and height'
Hello guys this is what I tried so far. I used the UTS to calculate the force it needs when the rope tears. My idea was to make a relationship/ function that would give me the force depending on height. Yeah i couldnt find a way to solve it. I also thought about how I could use hooks law (how it was given to me in my script) with the thought of instead of having two part of a rope id have one singular rope from the middle to the top where I could find the difference in height. But the...
Back
Top