Three small children of mass 20kg, 24kg, and 16kg hold hands and are pulled acro

Question

Three small children of mass 20kg, 24kg, and 16kg hold hands and are pulled across a smooth frozen pond by a larger boy on skates, who pulls a horizontal rope held by the first child. The skater pulls on the rope with a force of 135N. Calculate each of the following: a) acceleration of the skater b)the force with which each pair of children must hold hands, to ensure that the chain is not broken. I am so confused by this. I know f=ma, but it doesn't state the skaters acceleration so how do I calculate it? And b) just baffles me completely.

Explanation / Answer

Ok, you understand that F = m*a applies to ANY body. Lets seperate the bodies, imagining them as masses connected by a series of ropes. Start with the back child, draw a force diagram, what forces act on that child? There is just the "rope" pulling the child, call it F1 (we'll number them 1-3, starting at the back). Applying F = m*a F = m*a F1 = m1*a (equation 1) Ok, now lets look at kid #2. You've got F1 acting backwards between child 1 and 2, and F2 acting forward between child 2 and 3. F2 - F1 = m2*a (equation 2) Note that a is the same for both equations, they all move together. Now child 3. There is F2 acting backwards, and F3 acting forwards F3 - F2 = m3*a (Eq. 3) You are given the force on the rope between child 3 and the skater, F3. This leaves F1, F2, and a as unknowns. That's 3 unknowns, and 3 equations, which can be solved!

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