# Problem with Newton's second law

1. Oct 25, 2012

### Bohrok

1. The problem statement, all variables and given/known data

In the following figure, the boy has a mass of 40kg, and the platform he is sitting on has a mass of 15kg. If the force of the board on the boy is 180N;

a) Find the acceleration of the boy

b) Find the reading of the scale.

http://www.csupomona.edu/~jarmand/131/131chall5s12_files/image002.gif [Broken]

2. Relevant equations

F = ma

3. The attempt at a solution

I think I have the acceleration kind of worked out with ƩFy = 2T - mg = may where m is the total mass of the system (platform + boy) and T is the tension in the rope. Would the force of the tension be the same as the reading on the scale?

Mostly I've been unsure how to use that 180N. Then I started thinking that the downward force that the boy exerts on the chair has the same magnitude as the upward normal force that the chair exerts on the boy, giving ƩFy = T + Fn - mboyg = mboyay
Two equations with two unknowns T and a:
2T -55(9.8) = 55a
T + 180 - 40(9.8) = 40a
???

Last edited by a moderator: May 6, 2017
2. Oct 25, 2012

### haruspex

That all looks correct. Do you not know how to solve simultaneous equations? Just get one of the equations in the form T = (some function of other variables) and use this to substitute for T in the other equation.

3. Oct 25, 2012

### Bohrok

Oh I know how to solve simultaneous equations; I just wanted to see if my work seemed alright
Thanks!

If no one else chimes in, I'll take it that they agree

4. Oct 25, 2012

### SammyS

Staff Emeritus
Yes. That all looks fine to me. I got the same thing without first looking at your solution.

Last edited by a moderator: May 6, 2017