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Two objects of masses 2 kg and 3 kg are moving towards each other with velocities of 4 m/s and 2 m/s respectively. After the collision, the 2 kg object moves off with a velocity of 1 m/s in the opposite direction to its initial velocity. What is the velocity of the 3 kg object after the collision?
- a)1 m/s in the opposite direction as the initial velocity.
- b)4/3 m/s in the opposite direction as the initial velocity.
- c)4/3 m/s in the same direction as the initial velocity.
- d)1 m/s in the same direction as the initial velocity.
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two objects of masses 2 kg and 3 kg are moving towards each other with...
In a two-body collision, the law of conservation of momentum states that the total momentum of the system before the collision is equal to the total momentum of the system after the collision.
It is provided by the fact that there are no external forces acting on the system.
Let m1 and m2 be the masses of the two objects, and u1 and u2 be their initial velocities.
After the collision, let v1 and v2 be their final velocities.
Then, applying the law of conservation of momentum, we have:
m1u1 + m2u2 = m1v1 + m2v2
Substituting the given values, we get:
(2 kg) (4 m/s) + (3 kg) (-2 m/s) = (2 kg) (-1 m/s) + (3 kg) v2
Solving for v2, we get:
v2 = (2 kg) (4 m/s) + (3 kg) (-2 m/s) + (2 kg) (1 m/s) / (3 kg)
v2 = 4/3 m/s.
Therefore, the velocity of the 3 kg object after the collision is (a) 4/3 m/s.
It is provided by the fact that there are no external forces acting on the system.
Let m1 and m2 be the masses of the two objects, and u1 and u2 be their initial velocities.
After the collision, let v1 and v2 be their final velocities.
Then, applying the law of conservation of momentum, we have:
m1u1 + m2u2 = m1v1 + m2v2
Substituting the given values, we get:
(2 kg) (4 m/s) + (3 kg) (-2 m/s) = (2 kg) (-1 m/s) + (3 kg) v2
Solving for v2, we get:
v2 = (2 kg) (4 m/s) + (3 kg) (-2 m/s) + (2 kg) (1 m/s) / (3 kg)
v2 = 4/3 m/s.
Therefore, the velocity of the 3 kg object after the collision is (a) 4/3 m/s.
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Community Answer
Two objects of masses 2 kg and 3 kg are moving towards each other with...
Understanding the Collision
In this problem, we have two objects colliding: a 2 kg object moving at 4 m/s towards a 3 kg object moving at 2 m/s. The 2 kg object reverses direction after the collision, moving at 1 m/s.
Initial Conditions
- Mass of Object 1 (m1) = 2 kg
- Initial Velocity of Object 1 (u1) = 4 m/s (towards right)
- Mass of Object 2 (m2) = 3 kg
- Initial Velocity of Object 2 (u2) = -2 m/s (towards left)
Final Conditions
- Final Velocity of Object 1 (v1) = -1 m/s (moving left)
- Final Velocity of Object 2 (v2) = ? (what we need to find)
Applying Conservation of Momentum
The principle of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision.
Equation Setup
1. Before collision:
- Total momentum = (m1 * u1) + (m2 * u2)
- = (2 kg * 4 m/s) + (3 kg * -2 m/s)
- = 8 kg·m/s - 6 kg·m/s = 2 kg·m/s
2. After collision:
- Total momentum = (m1 * v1) + (m2 * v2)
- = (2 kg * -1 m/s) + (3 kg * v2)
- = -2 kg·m/s + 3 kg * v2
Setting the Equations Equal
- Before: 2 kg·m/s = After: -2 kg·m/s + 3 kg * v2
Now, solving for v2:
- 2 = -2 + 3v2
- 4 = 3v2
- v2 = 4/3 m/s
Direction of Velocity
Since the initial velocity of the 3 kg object is towards the left, and the final velocity (4/3 m/s) is positive, it indicates that the 3 kg object moves in the same direction as it initially was.
Conclusion
Thus, the correct answer is option C: 4/3 m/s in the same direction as the initial velocity.
In this problem, we have two objects colliding: a 2 kg object moving at 4 m/s towards a 3 kg object moving at 2 m/s. The 2 kg object reverses direction after the collision, moving at 1 m/s.
Initial Conditions
- Mass of Object 1 (m1) = 2 kg
- Initial Velocity of Object 1 (u1) = 4 m/s (towards right)
- Mass of Object 2 (m2) = 3 kg
- Initial Velocity of Object 2 (u2) = -2 m/s (towards left)
Final Conditions
- Final Velocity of Object 1 (v1) = -1 m/s (moving left)
- Final Velocity of Object 2 (v2) = ? (what we need to find)
Applying Conservation of Momentum
The principle of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision.
Equation Setup
1. Before collision:
- Total momentum = (m1 * u1) + (m2 * u2)
- = (2 kg * 4 m/s) + (3 kg * -2 m/s)
- = 8 kg·m/s - 6 kg·m/s = 2 kg·m/s
2. After collision:
- Total momentum = (m1 * v1) + (m2 * v2)
- = (2 kg * -1 m/s) + (3 kg * v2)
- = -2 kg·m/s + 3 kg * v2
Setting the Equations Equal
- Before: 2 kg·m/s = After: -2 kg·m/s + 3 kg * v2
Now, solving for v2:
- 2 = -2 + 3v2
- 4 = 3v2
- v2 = 4/3 m/s
Direction of Velocity
Since the initial velocity of the 3 kg object is towards the left, and the final velocity (4/3 m/s) is positive, it indicates that the 3 kg object moves in the same direction as it initially was.
Conclusion
Thus, the correct answer is option C: 4/3 m/s in the same direction as the initial velocity.
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Two objects of masses 2 kg and 3 kg are moving towards each other with velocities of 4 m/s and 2 m/s respectively. After the collision, the 2 kg object moves off with a velocity of 1 m/s in the opposite direction to its initial velocity. What is the velocity of the 3 kg object after the collision?a)1 m/s in the opposite direction as the initial velocity.b)4/3 m/s in the opposite direction as the initial velocity.c)4/3 m/s in the same direction as the initial velocity.d)1 m/s in the same direction as the initial velocity.Correct answer is option 'C'. Can you explain this answer?
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