(II) A 95-kg fullback is running at 3.0 m/s to the east and is...

Question

(II) A 95-kg fullback is running at 3.0 m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculate the average force exerted on the tackler.

Accepted Answer

Hey, everyone in this problem, a 100 kg basketball player is moving westward at a speed of 3.5 m per second. Suddenly co he comes to a halt in 1.5 seconds due to a head on collision with the defender approaching directly eastward. We're asked to determine the average force applied to the defender. We're given four answer choices. Option A 2.3 multiplied by 10 to the exponent to Newton's Due East. Option B, we have the same magnitude but due West option C 5.3 multiplied by 10 to the exponent to Newton's due East. And option D has the same magnitude as option C but due West. So let's start, we're gonna draw out what we have going on. So we have our basketball player, we're gonna draw them as a circle. We know that they have a mass which we're gonna call MB of 100 kg and they are moving westward, which we're gonna draw to the left at a speed of 3.5 m per second. And we have to make a decision about direction. So we're gonna take the typical approach where to the right is the positive direction, that's the eastward direction. And so the initial velocity of this basketball player will be negative because it's moving in the opposite direction, that westward direction. So it's negative 3.5 m per second, right? And they're running towards a defender. So we have our defender will draw as a circle as well. And we don't know the mass of the defender. We don't know how fast they're moving, but we do know that they're moving eastward. So they're moving towards that um Basketballer. All right. So that's what we have going on. We're looking for the average force applied to the defender. Uh We have some information about speed here of our basketball player. We have some information about mass. So we can think about the momentum, the change in momentum happening during this collision. We know that that's related to impulse and remember that we can relate impulse to the average force as well. So let's write down the relationship between these two things. So we have that our impulse J is equal to our average force a average multiplied by the time it's exerted over. So delta T and that's just equal to the change of momentum. And we know that the impulse is equal to both of these things. So these two have to be equal to each other. OK. So we're gonna use the second part of this equation and because we want f average in there, we're gonna use delta P that change in momentum to actually do the calculation. So what we have is that, that average force F average that we're looking for multiplied by delta T is gonna be equal to the final momentum minus the initial momentum. Now, momentum recall is given by mass multiplied by velocity. So we have F average multiplied by delta T is equal to the mass of the basketball player multiplied by their final velocity minus the mass of the basketball player multiplied by the initial velocity. Right? Let's keep going. And we are actually gonna add another subscript on the next line to make this very clear. On the right hand side, we're looking at the change of momentum of the basketball player. That means that this average force that we're looking at is the force that's applied to the basketball player. All right. So we're gonna call this F average B just to be very, very clear. And so we have F average B delta T we know is 1.5 seconds. This is gonna be equal to, we can factor out that mask mass of the basketball player. So we get 100 kg multiplied by the final velocity. While he comes to a halt, that final velocity is 0 m per second minus the initial velocity, which we said was negative 3.5 m per second. And when we're talking about momentum, momentum is a vector just like velocity. So we have to include the negative when we put our velocity in there to get the correct answer at the end. So make sure you have the right signs when you're doing these calculations. OK. Let's go ahead and simplify. We have f average basketball player multiplied by 1.5 seconds is gonna be equal to 350 kg meters per second. And we can divide both sides by 1.5 seconds and we get that f average acting on a basketball player, it's gonna be equal to 233.33 repeated news. Now again, this is the force applied to the basketball player. We want the force applied to the defender. And so the force applied to the basketball player is gonna be the force applied by the defender. OK? And because we have this action reaction pair of forces in the force applied to the defender is going to be equal in magnitude but opposite in direction to this force applied to the basketball player. And so the average force applied to the defender which we'll call F average D is just gonna be negative 233.33. New is we have to pay attention to whether we're looking for the force applied by the defender or to the defender. In this case, it's to the defender. So we're taking the negative of that force we found, you know, the negative is gonna indicate the direction. Remember initially, we chose the eastward direction to be positive. So the negative indicates that we're going in the westward direction. We can write this as two 133.33 repeated Newtons West. So that is that average force that we were looking for that is applied to the defender. If we compare this to the answer choices we found or we were given, sorry, we can see that the correct answer is going to be option B 2.3 multiplied by 10 to the exponent to Newton's Due West. Thanks everyone for watching. I hope this video helped see you in the next one.

(II) A 95-kg fullback is running at 3.0 m/s to the east and is stopped in 0.75 s by a head-on tackle by a tackler running due west. Calculate the average force exerted on the tackler.

Key Concepts

Momentum

Impulse

Newton's Second Law of Motion

Watch next