Comparing Momentum and Kinetic Energy of Two Objects with Different Masses

AI Thread Summary
When two objects of different masses are accelerated by a constant force on a frictionless surface, the momentum and kinetic energy can be compared based on their mass and acceleration. In the first scenario, when object 1 (greater mass) is accelerated and then object 2 (less mass) is accelerated through the same distance, the momentum of object 1 (P1) is greater than that of object 2 (P2), leading to the conclusion that P1 > P2, and K1 < K2 since kinetic energy is proportional to the square of velocity. In the second scenario, with a force applied for a time interval Δt, object 1 will have a greater momentum than object 2 due to its larger mass, resulting in P1 > P2, while the kinetic energy comparison will again show K1 < K2 as object 2 accelerates faster due to its lower mass. The analysis confirms that greater mass leads to lower acceleration under the same force, affecting both momentum and kinetic energy. Understanding these principles is crucial in classical mechanics for analyzing motion and energy transfer.
DanicaK
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1)Two objects are at rest on a frictionless surface. Object 1 has a greater mass than object 2. When a constant force is applied to object1, it accelerates trough distance d. The force is removed from object 1 and is applied to object 2. At the moment when object 2 has accelerated trough the same distance d, which statements are true?
a)P1<p2 b)p1=p2 c)p1>p2 d)K1<K2 e)K1=K2 f) K1>K2

2) Two objects are at rest on a frictionless surface. Object 1 has a greater mass then object 2. When a force is applied to object 1, it accelerates for a time interval Δt, which statements are true?
a)P1<p2 b)p1=p2 c)p1>p2 d)K1<K2 e)K1=K2 f) K1>K2


I need explication too.
 
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You should try to answer the questions yourself first. You could probably just use intuition, but to be more rigorous, you can use the equations of classical mechanics. Have a go.
 
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