Classic Mechanics Problem – Newton’s three laws of motion

Physics Tutorial

Classic Mechanics Problem - Newton's three laws of motion

Intro

Newton’s three laws of motion is the most frequent topic that you’ll definitely be tested in high school or college mechanics physics courses. The first law is the law of inertia, which means objects will stay in the current motion (static or dynamic) unless an unbalanced force F applied. Second law is the formula F = ma, which the acceleration produced when there is a force acted on a mass object. Third law states for every actions there is an equal but opposite direction of reaction force.

Sample Problem

Question source

From MIT University open course ware(see the URL attached):

Two objects, object A with mass M and B with mass 2M, are acted by a force C. Both objects start at rest and move a distance D along the horizontal frictionless surface.

Questions:
1. Which object move to a distance D with smallest time?
2. When they reach distance D, which object has larger kinetic energy?
3. How about we add a kinetic friction to question 2? Will the answer change?

Solution

1. Object A, because with the same force it has smaller mass, following Newton’s second law.

2. They have same KE. They have same force and same distance, therefore creating same change in amount of energy. (Kinetic Energy Theorem: F * D = KEf – KEi).

3. Object A. Smaller mass leads to smaller Normal force with smaller friction and larger net force. Net force is directly proportional to KE so it is A has higher KE.



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