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$\bullet$ A stone with a mass of 0.100 $\mathrm{kg}$ rests on a frictionless, horizontal surface. A bullet of mass 2.50 $\mathrm{g}$ traveling horizontally at 500 $\mathrm{m} / \mathrm{s}$ strikes the stone and rebounds horizontally at right angles to its original direction with a speed of 300 $\mathrm{m} / \mathrm{s}$ . (a) Compute the magnitude and direction of the velocity of the stone after it is struck. (b) Is the collision perfectly elastic?

a) 14.6 $\mathrm{m} / \mathrm{s}$ at $31^{\circ}$ from the line of impactb) $(14.6 \mathrm{m} / \mathrm{s})-(300 \mathrm{m} / \mathrm{s}) \neq 500 \mathrm{m} / \mathrm{s}-0$

Physics 101 Mechanics

Chapter 8

Momentum

Physics Basics

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

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Yeah. Mm. So we are told that a bullet of mass 2.25 kg, that was to the right higher second and collides with the stone of 0.1 kg. So, after they collide the bullet Charles the left that 300 liters per second. Mhm. And we want to know the velocity and magnitude of the stolen. So initially the momentum of the system will be the mass times velocity of the bullet. 500 times 5000.25 12.5 kg tops second. So the final momentum will also have to equal 2.5 and then the final one, which will be the two momentum's combined because the initial momentum is 12.5 going to the right or make that positive. And we're told that after the collision the bullet travels to the left, which means that momentum will be negative. So that momentum of the bullet will be 0.25 times negative, 300 plus the momentum of the stone, which is the mass. 0.1 times the velocity, which we don't know. So we can calculate the momentum of the bullet after the collision. 2.25 times 300 B negative. Yeah. 7.50 point one time fee. We can move that to the other side by adding it to 12.5 2012.1 V. We saw for velocity we know the velocity will be 200 second to the right. So now it is asking is the collusion is elastic. So we can solve that by checking if kinetic energy is conserved. We know that the initial energy will be one has the squared which will be that of the bullet. Yeah five squared. We can calculate that and find out that the initial energy is 3102 150 jewels. Now we calculate the final energy using the final velocity is given to us and that we catch it. So the energy final will be the kinetic energy of the bullet. Plastic kinetic energy stone, which would be one half 2.25 times the velocity of 300 plus one half 3.1 times 200 square. Never got the squid. So. Mhm. The bullet has a final kinetic energy of 1001 to 5. And the stone okay, has a final correct energy of 2000, which gives us 3125 jewels. So yes, okay, this collusion is elastic.

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