An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s–1 to 8 m s–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.
Solution and Explanation
Mass of the object, m= 100 kg,
Initial velocity, u= 5 ms-1
Final velocity, v= 8 ms-1
(i) Initial momentum =mu= 100 x 5=500 kg-ms-1
Final momentum = mv = 100 x 8 = 800 kg-ms-1
(ii) From Newton’s second law, Force exerted on the object = Rate of change of momentum
= Change in momentum
= Time Final momentum- Initial momentum
Time = \(\frac{800-500}{6}\) =\(\frac{300}{6}\)= 50N
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.