- #1

Jkyou

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## Homework Statement

Two trucks tow a third one by means of inextensible ropes and a pulley attached to them (fig. 1). The accelerations of the two trucks are a1 and a2. What is the acceleration of the third truck that is being towed?

(fig.1) is in this link (I'm sorry, I don't know how to post images on websites):

http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_AS_2007_QP.pdf

m=mass of truck

a1,a2 respective accelerations

a=the shared acceleration (whole system)

T= Tension

## Homework Equations

F = ma

Free body diagrams

## The Attempt at a Solution

Although the problem didn't specify, I'm assuming the masses of the trucks are equal

Since the total acceleration of the two trucks must be the same,

2ma = ma1-ma2

Thus, a= (a1-a2)/2

Furthermore, ma =T - ma2 for the second truck, so

T = ma + ma2 -> T = m(a1+a2)/2

The force of the tension on the pulley and 3rd truck = 2T

And total force on the pulley, which pulls the third truck = ma

Thus ma = 2T -> a = a1+a2, but the answer key says it's a = (a1+a2)/2