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Lesson Worksheet: Collisions and Conservation of Momentum Mathematics
In this worksheet, we will practice applying the law of conservation of momentum to study collisions in one dimension and differentiating between elastic and inelastic collisions.
A sphere of mass 675 g was moving in a straight line on a smooth horizontal table at 31 cm/s. The sphere crashed into another smooth sphere of mass 837 g that was at rest on the table. If the first sphere came to rest as a result of impact, find the magnitude of the impulse between the two spheres.
Two spheres, and , of equal mass, were projected toward each other along a horizontal straight line at 19 cm/s and 29 cm/s, respectively. As a result of the impact, sphere rebounded at 10 cm/s . Find the velocity of sphere after the collision given that its initial direction is the positive direction.
Two spheres of masses 200 g and 350 g were moving toward each other along the same horizontal straight line. The first was moving at 14 m/s and the second at 3 m/s. The two spheres collided. As a result, the first sphere rebounded at 7 m/s in the opposite direction. Given that the positive direction is the direction of motion of the first sphere before the impact, determine the impulse the second sphere exerted on the first one and the speed of the second sphere after impact.
Two spheres of masses and were moving in the same direction along the same straight line on a smooth horizontal table. The lighter sphere was in front and was moving at 4 m/s, and the heavier sphere was behind and was moving at 6 m/s. Given that when the two spheres collided, the lighter sphere’s speed increased to 6 m/s, find the speed of the heavier one rounded to the nearest hundredth.
A car of mass 2.5 metric tons was moving at 24 m/s in a straight line on a smooth horizontal plane. It collided with another car, , of mass 1.5 metric tons which was at rest. Directly after the impact, the velocity of car relative to car was 6 m/s. Find the actual speeds of both cars and .
Two spheres are moving along a straight line. One has a mass of and is moving at speed , whereas the other one has a mass of 10 g and is moving at 36 cm/s. If the two spheres were moving in the same direction when they collided, they would coalesce into one body and move at 30 cm/s in the same direction. However, if they were moving in opposite directions, they would coalesce into one body which would move at 6 cm/s in the direction the first sphere had been traveling. Find and .