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A trailer with loaded weightF(g) is bein...

A trailer with loaded weight`F_(g)` is being pulled by a vehicle with a force `P`, as in figure. The trailer is loaded such that its centre 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. (b) If a` =2.00 ms^(-2)` and `h = 1.50 m`, what must be the value of `d` in order that `P = 0` (no vertical load on the vehicle)?

Text Solution

Verified by Experts

a. If the acceleration is a we have `P_(x)=ma` and `P_(y)+n-F_(g)=0`
Taking the origin at the centre of gravity, the torque equation gives
`P_(y)(L-d)+P_(x)h-nd=0`
Solving these equations, we find `P_(Y)=(F_(g))/L(d-(ah)/g)`
b. If `P_(y)=0,` then
`d=(ah)/g=((2.00ms^(-2))(1.50m))/(10ms^(-2))=0.30m`
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