🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning Texas A&M University ### Problem 54 Easy Difficulty # A system consists of two particles. At$t=0$one particle is at the origin; the other, which has a mass of 0.50$\mathrm{kg}$, is on the$y$-axis at$y=6.0 \mathrm{m}$. At$t=0$the center of mass of the system is on the$y$-axis at$y=2.4 \mathrm{m} .$The velocity of the center of mass is given by$\left(0.75 \mathrm{m} / \mathrm{s}^{3}\right) t^{2} \hat{\mathrm{i}}$, (a) Find the total mass of the system. (b) Find the acceleration of the center of mass at any time$t$. (c) Find the net external force acting on the system at$t=3.0 \mathrm{s} .$### Answer ## (a)$M=1.25 \mathrm{kg}$(b)$\overrightarrow{\mathrm{a}}_{\mathrm{cm}}=1.5 \mathrm{tm} / \mathrm{s}^{3}$i(c)$\sum \overrightarrow{\mathrm{F}}_{\text { ext }}=5.625\$ iN

#### Topics

Moment, Impulse, and Collisions

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##### Christina K.

Rutgers, The State University of New Jersey

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##### Marshall S.

University of Washington

##### Aspen F.

University of Sheffield

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### Video Transcript

{'transcript': "So we have two particles particle one and particle too at a cost zero were given that the first particle is at origin. So this means X one equals Jiro. Why? When it goes on Judah and we're not given the mass of the particle one and the particle toe is that x x two is a castillo and white were consumed six point zero meters and the muscle a particle to is given, which is point five kg we have used as a unity and we are also given the center ofthe month his position except Demeter, which is the but just wasn't dramas. When xx is Ichiro and y axis, we have to ban formula. We're also given that violent city Listen to mass we CME we have one seven five square metre per second scoop make a perfect cube which we should have killed here. Toto, make the so to make a dimension correct. We have this well, a citadel center mass in X direction. So we have to find out the muscular system. We have to also find the exploration was in dramas and we also have to find this force in the whole system. So first letters approach the first part. We We need to find them out of the whole system. So we have. And probably massive system must be close to someone. The march of the practical one. Plus my sabbatical. We can use the formula. We have X e m. It goes to and one next. One plus and two X two over. And one close. Em too. This is a formal over center of mass, so we can calculate the master. But we are given that axiom is zero and also the older position Sergeant. So this becomes your questions. We cannot use this formula to find the marshal system. We can use the second room that we have similar from the CIA. It goes to anyone. Why one plus and too, why two over and when? Plus m too, and were given that way or sent off. Mars is two point four meter. So that's put two point four. We have someone. We This is M one. This is we have Why one impulsive Jiro. So this because of Jiro, we have I'd do it goes to. And two we have the point five two point five kg and white noise six meters. So this over and when plus m too. So we can get through it and won. Plus, I am too putting the value of him too. We have point five into six. This is a multiplication symbol. Close one and do point four. So this gives and when, plus him do if course too. One point two five Canty. So that's the matter. The system And when pressed him too. Now when we will find out the exhibition center of Mass, we know that SCM the exceptional center of mass, is a cause to Devi cm over dt. So this is a different shell off But the city of the center of mass and we have given that this is point seven five three square so we can different shit. So this is differentiation is we have a king the V c M and putting it point seven five key square and the differentiation of the square Just duty and we might be glad out time here. So this is just one point five. We have the left here and the dimensions are meter or second. Q. Remember that this exploration the center of mass is time dependent. We have one point five meters per second. You a different time. We have different exploration. So if we want to find out the solution a Tequesta Generals, we place it was zero. And this is a question two at the most one second, we have one point five meters per second squared equals who do we have to make? A per second squared. And so when I know now we need to find our next force in the whole system. Forcing the whole system is it goes to master the whole system, which is anyone close him too, multiplied by exploration, which we have already finally. So this is It wants to one point two five multiplied by one point five team. This's also time dependent. We can put the really of time to find out the force a different time. Intervals remember that the velocity of the center of mass was in x direction. So the exploration is also in extraction and also the force of the fortune. The system is also own extraction. I hope you have understand. So thank you"}

Texas A&M University

#### Topics

Moment, Impulse, and Collisions

##### Christina K.

Rutgers, The State University of New Jersey

LB
##### Marshall S.

University of Washington

##### Aspen F.

University of Sheffield

Lectures

Join Bootcamp