Two bodies of masses 10 kg and 20 kg respectively kept on a smooth, horizontal surface are tied to the ends of a light string. A horizontal force F = 600 N is applied to (i) A, (ii) B along the direction of string. What is the tension in the string in each case?
(a)
Given: the mass of the body A is 10 kg and the mass of the body B is 20 kg and the horizontal force of 600 N is applied to body A.
The free body diagram of the forces on the bodies are shown below.
The total mass of the system is,
m = 10 kg + 20 kg = 30 kg
Let F be the force on the body A and a be the acceleration of the system.
From Newton’s second law of motion, the force is,
F = m a
Substitute the values in the above expression.
600 N = ( 30 kg ) a a = 20 m / s 2
From the figure, the equation of motion for mass B is,
T = m B a
Substitute the values in the above expression.
T = 20 × 20 = 400 N
Thus, the tension in the string is 400 N.
(b)
Given: the mass of the body A is 10 kg and the mass of the body B is 20 kg . A horizontal force of 600 N is applied to body A.
The free body diagram of the forces on the bodies are shown below.
The total mass of the system is,
m = 10 kg + 20 kg = 30 kg
Let F be the force on the body B and a be the acceleration of the system.
From Newton’s second law of motion, the force is,
F = m a
Substitute the values in the above expression.
600 N = ( 30 kg ) a a = 20 m / s 2
From the figure, the equation of motion for mass B is,
T = m A a
Substitute the values in the above expression.
T = 10 × 20 = 200 N
Thus, the tension in the string is 200 N.
(a)
Given: the mass of the body A is
The free body diagram of the forces on the bodies are shown below.
The total mass of the system is,
Let
From Newton’s second law of motion, the force is,
Substitute the values in the above expression.
From the figure, the equation of motion for mass B is,
Substitute the values in the above expression.
Thus, the tension in the string is 400 N.
(b)
Given: the mass of the body A is
The free body diagram of the forces on the bodies are shown below.
The total mass of the system is,
Let
From Newton’s second law of motion, the force is,
Substitute the values in the above expression.
From the figure, the equation of motion for mass B is,
Substitute the values in the above expression.
Thus, the tension in the string is 200 N.
