A block of mass 2.58 kg lies on a frictionless horizontal surface. The block is

Question

A block of mass 2.58 kg lies on a frictionless horizontal surface. The block is connected by a cord passing over a pulley to another block of mass 5.84 kg which hangs in the air, as shown on the following picture. Assume the cord to be light (massless and weightless) and unstretchable and the pulley to have no friction and no rotational inertia. The acceleration of gravity is 9.8 m/s^2. Calculate the acceleration of the first block. Answer in units of m/s^2. Calculate the tension in the cord. Answer in units of N.

Explanation / Answer

(a) Let the acceleration of the system is "a" m/s^2 and the tension in the rope is "T" Newton

=> By balancing the force on each mass:-

     mg - T = ma

=> 5.84g - T = 5.84a ------(i)
Here T = 2.58a ---------------(ii)

From Eqns (i) + (ii) :-
=> 5.84 x 9.8 = 8.42a
=> a = 6.8 m/s^2

(b) By putting this value in (ii) :-
=>T = 2.58 x 6.8 = 17.54 N

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