A 50 g ball of clay traveling at speed v0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. (a) What is the speed of the brick after the collision?

Video transcript

Hey, everyone in this problem, a cricket ball with a mass of 176 g is moving to the right with an initial speed of the knot. It collides with and sticks to a 1.8 kg stationary cart. Assuming the track is frictionless. What is the velocity of the cart after the collision? And we're given a hint here to use the principle of conservation of momentum to solve the problem. Now, we're giving a little diagram and it has the cricket ball moving to the right towards the cart and then running into the cart. We have four answer choices. Option A 0.64 V naught. Option B 0.73 V naught. Option C 0.55 V naught and option D 0.89 be not. Now, we're gonna add a few things to this diagram. So we have our cricket ball. Let's go ahead and add the mass. And for the ball we're gonna use subscript B. So we have M B which is equal to g and the initial velocity V not of the ball is equal to V. Not now for our cart, the mass of the cart we're gonna use subscript C is 1.8 kilograms and its initial velocity is zero. OK. It's stationary. Now we have one mass given in grams, one mass given in kilograms. So let's go ahead and convert the mass of the cricket ball into our standard unit of kilograms. So the mass of the ball is equal to g. We're gonna multiply this and in every one kg we have 1000 g. OK. So we're multiplying by one kg divided by 1000 g, the unit of gram divides out. So what we're doing is essentially dividing by 1000 to go from grams to kilograms and we get 0.176 kg. All right. So we're giving a hint to use conservation of momentum. We have no net external forces acting on this system. So we can go ahead and use that conservation of the momentum recall tells us that the initial momentum P is equal to the final momentum P F. What makes up the initial momentum? Well, we have two things in our system, we have the ball and we have the cart. So we have the initial momentum of the ball. What's the initial momentum of the car? And that is going to equal the final momentum of the ball was the final momentum of the car. Momentum is equal to mass multiplied by velocity. So for each of these terms, we have the corresponding mass multiplied by the corresponding velocity. So we get M B multiplied by V not B plus MC multiplied by V. Not C is equal to M B multiplied by B or sorry, V F B plus MC multiplied by V F C. All right. So we're gonna substitute in the information we know and we're gonna try to solve for this final philosophy of the cart. Now, the initial velocity of the cart is zero. So the second term on the left hand side is gonna go to zero. On the right hand side, we have the final velocity of the ball and the final velocity of the car. We don't know either of those. OK. So how can we solve when we have two unknowns? Well, look at our problem, OK? We're told that when the ball collides with the cart, it sticks to it. OK? If they're stuck together and they're moving together. And so their velocity is gonna be the same. So the velocity of the final velocity of the ball is gonna equal the final velocity of the car. And we're just gonna call this V F, OK? That final velocity of that entire unit, OK. The ball and the cart together. So on the left-hand side, substituting in our values, we have the mass of the ball, 0.176 kg multiplied by its initial velocity V and that is equal to, on the right, if V F B and V F C are both equal and we're calling them V F, we can factor out V F. OK? And then we have the sum of the masses. So the mass of the ball, 0.176 kg plus the mass of the cart 1.8 kg. And all of that is multiplied by that final velocity V F. And so solving for V F, we're going to divide, we get V F is equal to 0.176 kg multiplied by V knot divided by 1.976 kg. And this is equal to 0. 89 V nine. And that's what we were looking for. We found that final velocity, OK? Which is the final velocity of both the cart and the ball. We found that in terms of the initial velocity of the ball V knot, the final velocity is equal to 0.89 V knott which corresponds with answer choice. D. Thanks everyone for watching. I hope this video helped see you in the next one.