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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.

Q1:

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.

Q2:

Two spheres, 𝐴 and 𝐡, 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 𝐡 rebounded at 10 cm/s . Find the velocity of sphere 𝐴 after the collision given that its initial direction is the positive direction.

Q3:

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 𝐼 the second sphere exerted on the first one and the speed 𝑣 of the second sphere after impact.

  • A𝐼=βˆ’4.2β‹…Ns, 𝑣=9/ms
  • B𝐼=4.2β‹…Ns, 𝑣=βˆ’9/ms
  • C𝐼=1.4β‹…Ns, 𝑣=1/ms
  • D𝐼=4.2β‹…Ns, 𝑣=9/ms
  • E𝐼=βˆ’1.4β‹…Ns, 𝑣=βˆ’1/ms

Q4:

Two spheres of masses 2π‘š and 5π‘š 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.

Q5:

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.

Q6:

A car 𝐴 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, 𝐡, of mass 1.5 metric tons which was at rest. Directly after the impact, the velocity of car 𝐡 relative to car 𝐴 was 6 m/s. Find the actual speeds of both cars π‘£οŒ  and π‘£οŒ‘.

  • A𝑣=12.75/ms, 𝑣=18.75/ms
  • B𝑣=12.75/ms, 𝑣=6.75/ms
  • C𝑣=17.25/ms, 𝑣=11.25/ms
  • D𝑣=17.25/ms, 𝑣=23.25/ms

Q7:

A ball of mass 3 kg, moving in a straight line at 32 cm/s, collided with another ball of mass 2.5 kg that was at rest. Given that the two balls coalesced into one body, determine the speed of this new body.

Q8:

A builder is hammering nails into a wall. The hammer has a mass of 3.3 kg, and each nail has a mass of 308 g. Given that the hammer hits each stationary nail at a speed of 8.2 m/s, use the principle of conservation of momentum to find the speed of the hammer and nail directly after the impact.

Q9:

A bullet of mass 188 g was fired at 797 m/s into a wooden target of mass 3 kg which was at rest. The bullet embedded into the target, and they started to move together. Find the speed of the bullet and target after the impact, given that the total momentum of the system did not change.

Q10:

Two spheres are moving along a straight line. One has a mass of π‘š and is moving at speed 𝑣, 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 π‘š and 𝑣.

  • Aπ‘š=5g, 𝑣=108/cms
  • Bπ‘š=45g, 𝑣=12/cms
  • Cπ‘š=20g, 𝑣=27/cms
  • Dπ‘š=30g, 𝑣=18/cms

This lesson includes 75 additional questions and 387 additional question variations for subscribers.

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