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Two inelastic spheres of masses 10 kg each move with velocities of 15 m/s and 5 m/s respectively in the same direction. The loss in kinetic energy when they collide
- a)500 Nm
- b)0 Nm
- c)250 Nm
- d)1000 Nm
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two inelastic spheres of masses 10 kg each move with velocities of 15 ...
- Momentum is conserved in all collisions.
- In elastic collision, kinetic energy is also conserved.
- In an inelastic collision, kinetic energy is not conserved. In a perfectly inelastic collision, objects stick together after the collision.
Conservation of momentum:
m1v1 + m2v2 = (m1 + m2) vf
Loss of kinetic energy:
Calculation:
Given:
m1 = m2 = 10 kg, v1 = 15 m/s, v2 = 5 m/s
Loss of kinetic energy:
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Community Answer
Two inelastic spheres of masses 10 kg each move with velocities of 15 ...
Explanation:
Given Data:
- Mass of each sphere, m = 10 kg
- Initial velocities, u1 = 15 m/s and u2 = 5 m/s
Loss in Kinetic Energy:
- The initial total kinetic energy of the system is given by:
KE_initial = (1/2) * m1 * u1^2 + (1/2) * m2 * u2^2
= (1/2) * 10 * 15^2 + (1/2) * 10 * 5^2
= 1125 + 125
= 1250 J
- After the collision, the final total kinetic energy of the system is given by:
KE_final = (1/2) * (m1 + m2) * V^2
where V is the common final velocity of both spheres.
- Since the collision is inelastic, kinetic energy is not conserved. The loss in kinetic energy is given by:
Loss in KE = KE_initial - KE_final
- From the law of conservation of momentum:
m1 * u1 + m2 * u2 = (m1 + m2) * V
10 * 15 + 10 * 5 = 20 * V
150 + 50 = 20V
V = 10 m/s
- Substituting the value of V in the equation for KE_final:
KE_final = (1/2) * 20 * 10^2
= 1000 J
- Therefore, the loss in kinetic energy is:
Loss in KE = 1250 - 1000
= 250 J
Therefore, the correct answer is option C, 250 Nm.
Given Data:
- Mass of each sphere, m = 10 kg
- Initial velocities, u1 = 15 m/s and u2 = 5 m/s
Loss in Kinetic Energy:
- The initial total kinetic energy of the system is given by:
KE_initial = (1/2) * m1 * u1^2 + (1/2) * m2 * u2^2
= (1/2) * 10 * 15^2 + (1/2) * 10 * 5^2
= 1125 + 125
= 1250 J
- After the collision, the final total kinetic energy of the system is given by:
KE_final = (1/2) * (m1 + m2) * V^2
where V is the common final velocity of both spheres.
- Since the collision is inelastic, kinetic energy is not conserved. The loss in kinetic energy is given by:
Loss in KE = KE_initial - KE_final
- From the law of conservation of momentum:
m1 * u1 + m2 * u2 = (m1 + m2) * V
10 * 15 + 10 * 5 = 20 * V
150 + 50 = 20V
V = 10 m/s
- Substituting the value of V in the equation for KE_final:
KE_final = (1/2) * 20 * 10^2
= 1000 J
- Therefore, the loss in kinetic energy is:
Loss in KE = 1250 - 1000
= 250 J
Therefore, the correct answer is option C, 250 Nm.
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