Plzzzz help me i have 2 questions so plzzz read it care fully and help me which formula i have to use.?

Question

1. a ball of mass 0,440kg moving east ( +x direction) with a speed of 3,30m/s collides head on with a 0,220kg ball at rest. If the collision is perfectly elastic what will be the speed and direction of each ball after the collision?


2. A squash ball hits a wall at a 45 degree angle. What is the direction. a) of the change in momentum of the ball. b) of the force on the wall?

Answer 1

In all collision, there is conservation of momentum. In perfectly elastic collisions, there is also conservation of energy.

Momentum is mass times velocity (m * v) and kinetic energy is 1/2 m * v^2

Here, you have a 0.44 kg ball moving at 3.3 m/s, that means the momentum is 1.452 kg m/s. The kinetic energy is 1/2 m v^2, so this works out to be 2.3958 kg m^2/s^2 or joules.

After the collision, you should now have the 0.44 kg AND the 0.22 kg ball moving, and the total momentum of both balls should be 1.452 kg m/s and the total enery should be 2.2958 J.

Lets put "a" for the post-collision speed of the heavier ball, and "b" for the lighter one, so we have

1.452 = 0.44 * a + 0.22 * b
and
2.2958 = 1/2 0.44 a^2 + 1/2 0.22 b^2
which reduces to
2.2958 = .22 a^2 + .11 b^2

Two equations, two unknowns, you do so algebra to isolate a or b from one equation and plug its value in the other one, you end up with a quadratic equation with two solutions for "a", -13.98 and 0.78. Evidently, the -13.98 would have the ball going faster after the impact, and is not to be retained, so the 0.44 kg ball will still move east but at 0.78 m/s.
The other ball will also move east, but at 5.04 m/s.

Note the effect, as it is an interesting and important result in physics: the small ball is now moving FASTER than the heavier ball was moving before the collision.

As for the second question, the ball would bounce off at 45 degree from the wall, or at 90 degree from the initial trajectory, so the mumentum is now at a right angle to the origial one. The force on the wall is perpendicular (walls cannot exert force in any direction but at a right angle to their surface) but if you make a drawing of the wall/ball system, you will se that the momentum could have been divide into 2 component: one in the direction parallel to the wall, and one perperdicular to the wall. The momentum parallel to the wall remains, and the one perpendicular is reversed. Therefore the force in the wall is perpenticular to the wall, as this is the only thing needed to reverse the trajectory of the ball.

Answer 2

1. In a vacuum the ball will lose 1/2 of the original speed and induce an acceleration of 1.65m/s in to the second ball. The direction will remain constant. This is a desk top toy that is sold in novelty shops but only the balls of equal weight sell better.
2. The change in direction is 45 degrees providing that the ball has no spin. The loss of momentum will vary with the resistance of the two combine surfaces.

Answer 3

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Answer 4

F=MA??