Question

Two masses m₁ and m₂ are joined by a string and lie on a table with a smooth horizontal surface (Fig.). What will be the acceleration of the masses if a force F of 10⁵dyn directed parallel to the plane of the table is applied to mass m₁? What will be the tension in the string joining the bodies. The masses of m₁ and m₂ are 200 and 300g, respectively.

 

Find the value of F at which the string will break if this force is applied (a) to mass m₁, (b) to mass m₂. The string can withstand a maximum load of 1kg-wt. The friction between the bodies and the table may be neglected. In the calculations, take g to be 10m/sec²

Answer 1

Answer: a = 200cm/sec² ; f = 6 x 10⁴ dynes; F_max ≅ 1.7 x 10⁶ and 2.5 X 10⁶dynes. 

Explanation:

To determine the tension it is necessary to write the equations for Newton's second law for each of the bodies separately. Both masses move with the same acceleration a. Forces F and f (Fig. 203) act on mx; only force f acts on m₂ . The equations for Newton's second law for masses ml and m₂ take the form