Question

Two blocks of masses m1=12 kg and m2=15 kg resting on a fricyionless surface connected by a light inextensible cord. A horizontal force F of 33 N directed to the right is applied to the block with m1. Find (a) the acceleration of the masses and (b) the tension T in the cord between the two blocks.

I need the diagram and complete solution for the given problem above.

Answer 1

In above diagrams, T: Tension in cord, F: Exerted force, M₁ & M₂ are masses of 12 kg and 15kg respectively.

NOTE: Right hand side is positive direction and left hand side is negative direction in this solution.

Equation of motion from free body diagram of M₂:

$$(F-T)=M_1a$$

where "a" is the acceleration of the masses.

$$\implies 33-T=12a .....Eq[1]\\$$

equation of motion from free body diagram of M₁:

$$T=M_2 a\\$$

$$\implies T=15a.....Eq[2]$$

Using Eq[2] in Eq[1]:

$$\implies 33-15a=12a\\ \implies a=\cfrac{11}{9} m/sec^2$$

putting this value "a" in Eq[2], we get

$$T=\cfrac{55}{3} N$$

Acceleration of both masses is $\cfrac{11}{9}m/sec^2$ and Tension in cord is $\cfrac{55}{3} N$ .