Such an easy problem but I cannot get it

[SprucerMoose]

This problem is from an old exam and for some reason i cannot solve it. Perhaps i have no idea what I am doing?

Homework Statement

A light inextensible string passes over a smooth, light pully. A mass of 5kg is attached to one end of the string and a mass of M kg is attached to the other end.

The M kg mass accelerateds downwards at (7/5)m/s^2.

The value of M is?

The Attempt at a Solution

M's motion taken as positive direction

Net Force on M = (5 x -9.8) + (m x 9.8)

M = Force/Acceleration

M = [(5 x -9.8) + (m x 9.8)] / (7/5)

7M = -245 + 49M

-42M = -245

M = 5.83 Kg


I don't know if I have done something wrong, but the test says the result should be 6.67 Kg. Can someone please check my calculations and confirm if I'm incorrect or if this crappy test is?

 

[phyzguy]

You're wrong, the test is right. You have assumed that the tension in the string is equal to the weight of the 5kg mass, but in fact the 5kg mass is accelerating too, so the tension in the string is not equal to the weight of the 5 kg mass. Try setting the tension in the string to some unknown, T, and write two equations to solve for two unknowns, T and M.

 

[SprucerMoose]

You da man