Physics Question?

Question

Two identical masses are attached by a light string that passes over a small pulley. The table and the pulley are frictionless. Calculate the masses' acceleration and the tension on the string.

Please show/explain all work and show what formulas were used.

Assume no friction.

Answer 1

I assume one mass is one th etable and the other hangs vertically.

The mass on the table sees a horizontal force due to the string, T, and since it accelerates:

T = ma

The hanging mass sees two verticl forces, T pull it up, and mg pulling it down. This mass also accelrates with acceleration a so:

-ma = T -mg ("-" indicates downward direction)

But T=ma from above so

-ma = ma -mg --->2a = g ---> a = g/2

Then T = ma = mg/2