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A body m1 of mass 10 Kg is placed on a smooth horizontal table. It is connected to a string which passes over a frictionless pulley and carries at the other end, a body m2 of mass 5kg . What acceleration will be produced in the bodies when system is released? What will be the tension in the spring during the motion of the bodies? What when the bodies stop? Take g=9.8m/s^2?
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A body m1 of mass 10 Kg is placed on a smooth horizontal table. It is ...
Solution:
Calculation of Acceleration
- The force acting on the system is the force due to gravity (weight) which is given by F = mg, where m is the mass and g is the acceleration due to gravity.
- The weight of m1 is 10 x 9.8 = 98N and the weight of m2 is 5 x 9.8 = 49N.
- Since the string is assumed to be massless, the tension in the string is the same throughout the system.
- Let the acceleration be a. Then the net force acting on the system is T - 98 - 49 = (m1 + m2)a.
- Therefore, T = (m1 + m2)a + 147.
- Since the system is released, the direction of acceleration is downwards. Therefore, the positive direction is taken as downwards.
- The tension in the string is upwards. Therefore, the equation of motion for m1 is T - m1g = m1a.
- The equation of motion for m2 is m2g - T = m2a.
- Substituting T from the first equation into the second equation, we get m2g - m1a - m2a - 147 = m2a.
- Simplifying, we get a = g/(1 + m1/m2) = 9.8/(1 + 10/5) = 6.53 m/s^2.
Calculation of Tension during Motion
- The tension in the string during the motion of the bodies is given by T = (m1 + m2)a + 147.
- Substituting the values, we get T = (10 + 5) x 6.53 + 147 = 214.95N.
Calculation of Tension when Bodies Stop
- When the bodies stop, the tension in the string is equal to the weight of m1.
- Therefore, T = m1g = 10 x 9.8 = 98N.
Explanation
The problem involves the application of Newton's laws of motion and the concept of tension in a string. The mass of the bodies, the force of gravity acting on them, and the direction of acceleration are taken into account to calculate the acceleration of the system. The tension in the string is assumed to be the same throughout the system. The equations of motion for the bodies are set up and solved to obtain the acceleration and tension in the string during the motion of the bodies. When the bodies stop, the tension in the string is equal to the weight of m1.
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A body m1 of mass 10 Kg is placed on a smooth horizontal table. It is ...
T=98/3 N
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A body m1 of mass 10 Kg is placed on a smooth horizontal table. It is connected to a string which passes over a frictionless pulley and carries at the other end, a body m2 of mass 5kg . What acceleration will be produced in the bodies when system is released? What will be the tension in the spring during the motion of the bodies? What when the bodies stop? Take g=9.8m/s^2?
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