Question

Find the magnitude of the accelerations of the two masses. [Hints: (1) Pick a coordinate system, and use positive and negative signs consistently to indicate the directions of the forces and accelerations. (2) The two accelerations of the two masses have to be equal in magnitude but of opposite signs, since one side eats up rope at the same rate at which the other side pays it out. (3) You need to apply Newton’s second law twice, once to each mass, and then solve the two equations for the unknowns: the acceleration, a, and the tension in the rope, T.]

Answer 1

The expression for the magnitude of the accelerations is
`a=(g(M-m))/(M+m)`

Step-by-step explanation:

According the Newton´s second law:

`Mg - T=Ma,for-mass-M\\T-mg=ma,for-mass-m`

Clearing T for second equation:

T = ma + mg

Replacing in the first equation:

Mg - ma - mg = Ma

Ma + ma = Mg - mg

a(M + m) = g(M - m)

`a=(g(M-m))/(M+m)`