(II) A 0.280-kg croquet ball makes an elastic head-on collision with a second ball initially at rest. The second ball moves off with half the original speed of the first ball. $(a)$ What is the mass of the second ball? $(b)$ What fraction of the original kinetic energy $(\Delta KE/KE)$ gets transferred to the second ball?

Answer

A. 0.84 $\mathrm{kg}$
B. 0.75

Related Courses

Physics 101 Mechanics

Physics

Chapter 7

LINEAR MOMENTUM

Section 5

Elastic Collisions in One Dimension

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Video Transcript

So in this question, we have to a head on collision of two. Boss, we have bought a They'll have Bobby. So a boy, it was initially moving tours. What be that? Bobby was initially at rest. So after is a collision. So this was freedom is an A an M B. A baby is there after the collision. They're both moving. And we know that is This has amused beef. A prime Kansas hezonja's be beautiful. Well, those that vivid crime is half of a his happens a visual speed of the first floor. So are there were asked by what is mess off sustainable? What is envy? So let's first right out The Christian for us and relative Speed s owen over elastic Lee was the relative speed was that your objective was a pleasure is always equal and opposite oozing relative speed after his equation. So that tells us the a minus Phoebe, he caused elective off the a pride minor speak right, But Phoebe is zero. So this's just a select aside was right here so we can substitute that BP prime equals 1/2 off, eh? Because this becomes effective. Be a pride. Bite us went half off people and we carry a ranch. This equation so that we finally had to be a prime equals on the crime equals look, too 1/2 B A. Yes, because it's for your primal erectus science. And it's one coffee and minus V on the right and said Yes. So it's via probably construction for half A. And after this, we already know this's fear. Crime in San, we already know that BB Prime equals half be ache, so that's actually kind of nice. We know that after the collision, there will be moving equal into equal opposite directions. So but what we need to find we need to find and be, and we can find out by using the conservation of momentum because we focus official comment on window view. We know BB with off your privacy, your privates, and we know a So from that equation, we should be able to find empty because official momentum we have initial Mitchum is Evie a captor. Words we have observant momentum is from a via prime plus in beefy crime. But then we can also substitute sis to here. So this becomes and a time selective about half a close and be over one hospital. I said Nice. Also be ace cancel. So this finally leaves us sad. If we rearrange it, we get and a equals active it equals while half off and be minus m a so we can move this to here. Such here bake was beaten by a so and B equals three types of me so that we kept looking at the numbers on their point you eight children and we can't pinpoint it for so it's 0 to 0 clicker. So that is a mess off and be so this pause that so it is being cried. It is three times the mass of Sir initial ball. Great. So that's four part, eh? Who would be? It asks us to find what friendship's original kinetic energy is transferred to. The second book are So this is really just asking us to plan? What is when is it should've kinetic energy of the original communiqu attitudes conduct entry transferred is just a kinetic energy of B crime and sands that wish his can energy of a So this is equal to 1/2 off m b B B prime square over Well half off, eh? P a square in every s ratio. So MP is just equal to three and a Is this like someone half castles be a square Baby Prime is well half off his group. So it's 1/2 of a script. So this is Sarah 0.75 So 75% off the kinetic energy will be transferred. She was a heavier goal.

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