Linear momentum and its conservation
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State the principle of conservation of momentum.
In a closed system, the total momentum remains constant if no external forces act on the system. Mathematically, this means the total momentum before an event (like a collision) equals the total momentum after the event.
Describe an elastic collision in terms of kinetic energy and relative speed.
In an elastic collision, total kinetic energy is conserved, meaning the total KE before the collision is equal to the total KE after the collision. Additionally, the relative speed of approach is equal to the relative speed of separation.
What is the difference between an elastic and an inelastic collision in terms of kinetic energy?
In an elastic collision, kinetic energy is conserved. In an inelastic collision, kinetic energy is NOT conserved; some kinetic energy is transformed into other forms of energy, such as heat or sound.
Two objects collide and stick together. Is this collision elastic or inelastic? Explain.
This is an inelastic collision. When objects stick together after a collision, kinetic energy is always lost (converted to other forms), so the total kinetic energy is not conserved.
A 2kg object moving at 3m/s collides head-on with a stationary 1kg object. If they stick together, what is their velocity after the collision?
Using conservation of momentum: (2kg)(3m/s) + (1kg)(0m/s) = (2kg + 1kg)v. Therefore, 6 = 3v, and v = 2 m/s. The combined object moves at 2 m/s in the original direction of the 2kg object.
Explain why momentum is always conserved in a closed system, even if kinetic energy is not.
Momentum conservation is a fundamental law based on Newton's laws of motion and the absence of external forces. Kinetic energy, however, can be transformed into other forms of energy during interactions, leading to a change in KE but not momentum.
Two objects of equal mass collide elastically head-on. Object A is initially moving and object B is stationary. What happens to their velocities after the collision?
In an elastic collision between objects of equal mass, the objects exchange velocities. Object A will come to rest, and Object B will move with the initial velocity of Object A.
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