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In this lesson, we will learn how to use the principle of conservation of momentum to solve problems involving elastic collisions.

Q1:

A sphere of mass 299 g was moving horizontally in a straight line at 51 cm/s. It collided with another sphere of mass 390 g that was at rest. As a result of the impact, the first sphere came to rest. Determine the speed of the second sphere after the impact.

Q2:

A sphere of mass 159 g was moving horizontally in a straight line at 66 cm/s. It collided with another sphere of mass 220 g that was at rest. As a result of the impact, the first sphere came to rest. Determine the speed of the second sphere after the impact.

Q3:

A car π΄ of mass 2.5 tonnes was moving at 24 m/s in a straight line on a smooth horizontal plane. It collided with another car, π΅ , of mass 1.5 tonnes which was at rest. Directly after the impact, the velocity of car π΅ relative to car π΄ was 6 m/s. Find the actual speeds of both cars π£ π΄ and π£ π΅ .

Q4:

Two spheres, each of mass 160 g, were moving across a smooth horizontal table, along the same straight line in the same direction, at 15 m/s separated by some distance. The first sphere collided with a barrier that was perpendicular to the path of the two spheres. It rebounded and collided with the second sphere from which it rebounded at 14 m/s. Given that the barrier gave an impulse of magnitude 3.2 Nβ s to the first sphere, determine the velocity of the second sphere after the impact. Let the positive direction be the original direction of the motion of the two spheres.

Q5:

Two spheres, each of mass 100 g, were moving across a smooth horizontal table, along the same straight line in the same direction, at 15 m/s separated by some distance. The first sphere collided with a barrier that was perpendicular to the path of the two spheres. It rebounded and collided with the second sphere from which it rebounded at 11 m/s. Given that the barrier gave an impulse of magnitude 2.1 Nβ s to the first sphere, determine the velocity of the second sphere after the impact. Let the positive direction be the original direction of the motion of the two spheres.

Q6:

Two spheres, π΄ and π΅ , of equal mass, were projected towards each other along a horizontal straight line at 19 cm/s and 29 cm/s, respectively. As a result of the impact, sphere π΅ rebounded at 10 cm/s . Find the velocity of sphere π΄ after the collision given that its initial direction is the positive direction.

Q7:

Two smooth spheres, each of mass 250 g, are moving in the same direction in a straight line along a section of horizontal ground. The first sphere is moving at π£ = 2 / 1 m s , and the second at π£ = 4 / 2 m s . If the two spheres collided, and the magnitude of the impulse of the second sphere on the first was 3 . 3 Γ 1 0 4 dynes, find the speeds of the two spheres, π£ β² 1 and π£ β² 2 , just after the impact.

Q8:

Two spheres are moving in opposite directions along a horizontal line. The first sphere had a mass of 6 kg, and its speed was 75 cm/s when it collided with the second sphere which was moving at 80 cm/s. As a result of the impact, the first sphere rebounded at 15 cm/s along the same line in the opposite direction, and the second sphere came to rest. Find the loss in kinetic energy as a result of the impact.

Q9:

Two spheres, π΄ and π΅ , of masses 18 g and 99 g respectively, were moving horizontally in a straight line in the same direction. They collided when their speeds were 20 m/s and 10 m/s respectively. The spheres kept moving in the same direction after the collision, and the ratio of their speeds was 1 βΆ 2 . Given that sphere π΄ continued moving at a constant speed after the collision and sphere π΅ started to decelerate as a result of a constant force resisting its motion that equals 2 7 of its weight, find the distance between the two spheres 2 seconds after the collision.

Q10:

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.

Q11:

Two spheres of masses 200 g and 350 g were moving towards 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 πΌ the second sphere exerted on the first, and the speed π£ of the second sphere after impact.

Q12:

Two spheres were moving horizontally in opposite directions along the same straight line. They collided when the speed of the first sphere was 56 cm/s and that of the second was 30 cm/s. The first sphere rebounded at 40 cm/s, and the second one came to rest. Given that the mass of the first sphere was 3 kg, determine the mass of the second.

Q13:

Two spheres of masses 2 π and 5 π 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 sphereβs speed increased to 6 m/s, find the speed of the heavier one rounded to the nearest hundredth.

Q14:

Two spheres of masses 200 g and 520 g were moving in a straight line towards each other at 11 m/s and 8 m/s, respectively. They collided, and the first sphere rebounded at 2 m/s. Calculate the loss in kinetic energy as a result of the impact.

Q15:

Two spheres of masses 105 g and 260 g were moving horizontally in opposite directions along the same straight line at 1.22 m/s and 1.25 m/s, respectively. When they collided, the second sphere kept moving in the same direction at 0.4 m/s. Determine the magnitude of the impulse exerted on the first sphere by the second.

Q16:

Two spheres, of masses 2.4 and 0.8 kilograms, were moving horizontally in the same direction along the same straight line. The first sphere was moving at 4 m/s, and the second was moving at 19 m/s. Given that the two spheres collided and that the speed of the first one increased by 7 m/s, find the speed of the second just after the impact.

Q17:

Two spheres, of masses 4.8 and 0.8 kilograms, were moving horizontally in the same direction along the same straight line. The first sphere was moving at 14 m/s, and the second was moving at 18 m/s. Given that the two spheres collided and that the speed of the first one increased by 1 m/s, find the speed of the second just after the impact.

Q18:

Two spheres of masses 140 g and 238 g were moving horizontally along the same straight line in opposite directions at 1.49 m/s and 1.31 m/s, respectively. Given that, when the two spheres collided, the second sphere kept moving in the same direction at 0.21 m/s, find the speed of the first sphere.

Q19:

A ball of mass 480 g fell from the top of a tower of height 183 m. At the same moment, another ball of the same mass was projected vertically upwards from the base of the tower at 65.3 m/s. When the two balls collided, the second ball rebounded at 26.7 m/s. Find the time the first ball took to reach the ground after the collision stating your answer to the nearest two decimal places, if required. Consider the acceleration due to gravity to be π = 9 . 8 / m s 2 .

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