if the beads are released from rest, what is the speed vc of c at the instant the beads collide? This is a topic that many people are looking for. star-trek-voyager.net is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, star-trek-voyager.net would like to introduce to you A 0.400-kg blue bead slides on a frictionless, curved wire, starting from rest at point A in the Fig. Following along are instructions in the video below:
Take a moment to pause. The video and attempt the question before listening on as as with many physics problems were going to be able to solve this one breaking it up into three different parts in part 1 of the question. The blue bead will slide from point a to point b.
And because its sliding along a frictionless wire energy conservation can be used then once the blue bead slides to point b. Its going to collide elastically with the green bead. And because its an elastic collision both kinetic energy and momentum will be conserved finally after the collision.
The green bead is going to slide up the frictionless wire. And again we can use energy conservation make sure you pause the video to consider all three parts before moving on so for part 1. Again the blue bead will slide from point a to point b.
We can write out the energy conservation formula. Now the blue bead starts from rest. So the initial speed of it will be zero.
And that will eliminate this term right here similarly after the blue bead slides down to point b. Its height at that point will equal zero. And as a result this term will cancel out the remaining terms both contain mass.
So if we divided them both by mass that would eliminate mass from the equation. So we can simplify the equation. Two that will then multiply both sides by two we can take the square root.
And this will help us isolate. The vb term. We can now plug in the known value of g.
And also the height of the bead at. Position a which was stated in the question as being 15 meters and if we simplify that on our calculator.
We should calculate approximately five point four two meters per second and that will be the speed of the blue bead once it travels down the wire to point b. In part two. Were going to have the elastic collision between the blue bead and the green bead.
Which is initially at rest. Now because the collision is elastic. We know that both kinetic energy and momentum are conserved.
Now it does turn out that theres a special shortcut in this situation. And the reason. The shortcut applies is for the following reasons.
Whenever you have in a a stick head on collision and object to which in this case is the green bead is initially at rest. Then the following equation can be used to calculate the final speed of object two after the collision so in this equation. We have the final speed of object.
Two we have the mass of object. One labeled m1 the mass of object. Two labeled m2 and then we have the initial speed of object.
One which we calculated as five point four two so if we simply plug in the mass of the blue bead. The mass of the green bead and the initial speed of the blue bead. Were going to easily be able to calculate the final speed of the green bead after the collision.
So lets go ahead. And do that after plugging in the known values you should obtain. Approximately four point three four meters per second.
And that will represent again the final speed of object. Two which is the green bead.
So here we have the green bead. And its now moving at four point three four meters per second. And its going to be propelled up the ramp.
So well move on to part three now as before in part one were going to use energy conservation to determine how high up this wire the green bead will travel lets not forget that at this point. This is right after the collision. The initial speed of the green bead is four point three four meters per second keeping that in mind lets write out the energy conservation formula again notice in the picture that we have labeled the top of the wire.
As point c. We know that once the green bead gets up to that point it will stop and so its final speed at point c. Will equal zero.
Thats going to eliminate this term from the equation down here. At point b. Before the bead travels up the wire.
We can see that the height is zero. And since the height is zero at that point that will drop out this term as before when the remaining terms. We have the mass and that can be divided out so the equation simplifies and then if we divide both sides by g.
Were going to be able to isolate the height at point c. And now all we have to do is plug in the speed at point b. Which was determined previously is four point three four and then the known value of g.
And when we compute that on our calculator. We get hc to equal zero point nine six meters. And that represents the height that the green bead will travel up the wire after it collided with the blue bead as always thank you for watching this video.
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