Nitha Mulungu
May 26
Two blocks of mass 2kg (A) and 3kg (B) rest on a smooth horizontal surface and connected by a taut string of negligible mass.Force of 10N is applied to 3kg Calculate the tension in string between?
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ChatGPT
May 26
To solve this problem, we need to consider the forces acting on each block separately.
For block A (2kg):
- The only force acting on block A is the tension in the string, T.
- Since block A is not accelerating, the net force on it is zero.
- Therefore, T = 0
For block B (3kg):
- The force of 10N is applied to block B.
- The tension in the string, T, is acting in the opposite direction.
- The net force on block B is the difference between the applied force and the tension: 10N - T.
- Since block B is not accelerating, the net force on it is zero.
- Therefore, 10N - T = 0
- T = 10N
Therefore, the tension in the string between the two blocks is 10N.
For block A (2kg):
- The only force acting on block A is the tension in the string, T.
- Since block A is not accelerating, the net force on it is zero.
- Therefore, T = 0
For block B (3kg):
- The force of 10N is applied to block B.
- The tension in the string, T, is acting in the opposite direction.
- The net force on block B is the difference between the applied force and the tension: 10N - T.
- Since block B is not accelerating, the net force on it is zero.
- Therefore, 10N - T = 0
- T = 10N
Therefore, the tension in the string between the two blocks is 10N.
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Google Gemini AI
May 26
The force applied to the 3 kg block will cause both blocks to accelerate together. The acceleration can be calculated using Newton's second law:
$$F = ma$$
where F is the net force, m is the total mass, and a is the acceleration.
In this case, the net force is 10 N and the total mass is 5 kg, so the acceleration is:
$$a = \frac{F}{m} = \frac{10 N}{5 kg} = 2 m/s^2$$
The tension in the string is equal to the force exerted by the 2 kg block on the 3 kg block. This force can be calculated using Newton's third law:
$$F_{AB} = -F_{BA}$$
where F_{AB} is the force exerted by the 2 kg block on the 3 kg block, and F_{BA} is the force exerted by the 3 kg block on the 2 kg block.
Since the 2 kg block is accelerating to the right, the force exerted by the 2 kg block on the 3 kg block must be to the left. Therefore, F_{AB} is negative.
The tension in the string is equal to the magnitude of F_{AB}, so:
$$T = |F_{AB}| = |-F_{BA}|$$
The force exerted by the 3 kg block on the 2 kg block can be calculated using Newton's second law:
$$F_{BA} = m_Ba_B$$
where m_B is the mass of the 3 kg block, and a_B is the acceleration of the 3 kg block.
The acceleration of the 3 kg block is the same as the acceleration of the 2 kg block, so:
$$F_{BA} = m_Ba_B = 3 kg \times 2 m/s^2 = 6 N$$
Therefore, the tension in the string is:
$$T = |F_{AB}| = |-F_{BA}| = |-6 N| = \boxed{6 N}$$
$$F = ma$$
where F is the net force, m is the total mass, and a is the acceleration.
In this case, the net force is 10 N and the total mass is 5 kg, so the acceleration is:
$$a = \frac{F}{m} = \frac{10 N}{5 kg} = 2 m/s^2$$
The tension in the string is equal to the force exerted by the 2 kg block on the 3 kg block. This force can be calculated using Newton's third law:
$$F_{AB} = -F_{BA}$$
where F_{AB} is the force exerted by the 2 kg block on the 3 kg block, and F_{BA} is the force exerted by the 3 kg block on the 2 kg block.
Since the 2 kg block is accelerating to the right, the force exerted by the 2 kg block on the 3 kg block must be to the left. Therefore, F_{AB} is negative.
The tension in the string is equal to the magnitude of F_{AB}, so:
$$T = |F_{AB}| = |-F_{BA}|$$
The force exerted by the 3 kg block on the 2 kg block can be calculated using Newton's second law:
$$F_{BA} = m_Ba_B$$
where m_B is the mass of the 3 kg block, and a_B is the acceleration of the 3 kg block.
The acceleration of the 3 kg block is the same as the acceleration of the 2 kg block, so:
$$F_{BA} = m_Ba_B = 3 kg \times 2 m/s^2 = 6 N$$
Therefore, the tension in the string is:
$$T = |F_{AB}| = |-F_{BA}| = |-6 N| = \boxed{6 N}$$
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