Lesson: Collisions and Conservation of Momentum

In this lesson, we will learn how to apply the law of conservation of momentum to study collisions in one dimension and differentiate between elastic and inelastic collisions.

Sample Question Videos

  • 03:12

Worksheet: 25 Questions • 1 Video

Q1:

On a smooth plane inclined at 3 0 to the horizontal, 𝐴 𝐵 is a line segment parallel to a line of greatest slope of the plane. The point 𝐴 is at the top of the plane, and the distance between 𝐴 and 𝐵 is 7 m. A sphere of mass 45 g was left to roll down the plane from the point 𝐴 . At the same moment, another sphere of mass 165 g was projected up the line segment from point 𝐵 at 7 m/s. Given that, when the two spheres collided, they coalesced into one body, find the speed 𝑣 of this combined body and the maximum distance 𝑙 that the body will move up the plane after the collision stating the answer to the nearest two decimal places. Consider the acceleration due to gravity to be 𝑔 = 9 . 8 / m s .

Q2:

A railway carriage of mass 11 metric tons started moving down a plane from rest. The plane was inclined to the horizontal at an angle whose sine is 1 5 0 , and the resistance to the carriage’s motion was 16 kg-wt per tonne of the carriage’s mass. The carriage reached the bottom of the plane after covering a distance of 144 m, and then it collided with another carriage of the same mass that was at rest. Given that the two carriages coupled together as a result of the impact then came to rest 50 seconds later, determine the distance covered by the two carriages on the horizontal road. Consider the acceleration due to gravity to be 𝑔 = 9 . 8 / m s .

Q3:

A body of mass 5 kg was moving at 18 cm/s when it collided with another body of mass 1 kg moving at 27 cm/s in the opposite direction. The two bodies coalesced into one body. Then, this body collided with a third body of mass 12 kg which was at rest. As a result, this body coalesced into the other, forming one body from all three. Find the speed of this last compound body after the collision.

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