A 10 kg mass on a horizontal friction-free table is accelerated by a string attached to 12 kg mass hanging vertically from a pulley. a) What's the force due to gravity on the 12 kg hanging mass? b) What's the acceleration of the masses?
a) F = mg = 12(9.8) = 117.6 N
b) F = (m1+m2)a => a = 117.6/(10+12) = 5.3 m/s^2
For b), you can use free body diagram: T = m1*a and m2g-T = m2*a. Adding two equations leads to
F = (m1+m2)a.