Two blocks are connected by a string that passes over a frictionless pulley, as

Question

Two blocks are connected by a string that passes over a frictionless pulley, as shown in the figure. The pulley has a mass of                 mp = 2.00 kg, and can be treated as a uniform solid disk that rotates about its center. Block A, with a mass                 mA = 1.00 kg, rests on a ramp measuring 3.0 m vertically and 4.0 m horizontally. Block B hangs vertically below the                pulley. Note that you can solve this exercise entirely using forces, torques, and the constant-acceleration equations, but see if you can apply energy ideas                instead. Use g = 10 m/s2. When the system is released from rest, block A accelerates up the slope and block B accelerates straight                down. When block B has fallen through a height h = 2.0 m, its speed is v = 2.00 m/s.                 

Explanation / Answer

The string is ideal ? it does not stretch and , mass-less and friction-less pulley means
the tension on either side of the string is the same = T
and the magnitude of the acceleration 'a' of both the masses will be same .
The equation for these conditions :
For Mass 14.3 kg: 14.3*9.8 N is 14.3*a = 14.3*9.8 - T --------------(a)
and for 98 N or 98/9.8 = 10 kg mass : 10* a = T - 98 --------------(b)
Adding equations (a) and (b) gives 24.3 a = 1.43*98 - 98 = 0.43*98
? a = 0.43*98/ 24.3 = 1.734 m/sec/sec and
T = from (b) = 17.34 + 98 = 115.342 N

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