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11. Which of the following is the unit vector representation ofthe vector <-3,-1,3 > ? [Hint: get the magnitude of thevector and divide each component with th...

Question

11. Which of the following is the unit vector representation ofthe vector <-3,-1,3 > ? [Hint: get the magnitude of thevector and divide each component with the magnitude]12. A pillow is thrown with an initial velocity of 8 m/s. Solvefor the total time of flight (meaning: the time it reaches themaximum height plus the time it comes back down to its originalposition)13. Vector A = 20 m, East and vector B = 30 m, East. Determinethe cross product of vector A and B.14. What must be the angle be

11. Which of the following is the unit vector representation of the vector <-3,-1,3 > ? [Hint: get the magnitude of the vector and divide each component with the magnitude] 12. A pillow is thrown with an initial velocity of 8 m/s. Solve for the total time of flight (meaning: the time it reaches the maximum height plus the time it comes back down to its original position) 13. Vector A = 20 m, East and vector B = 30 m, East. Determine the cross product of vector A and B. 14. What must be the angle between two vectors A = 2i + 2j and A = -3i - 3j? 15. An object with a velocity 10 m/s finishes one lap around a circular path at a rate of 2 m/s2 . What is the radius of the circular path? 16. If a projectile can reach a range of 8 meters in 12 seconds, how long can it reach its maximum height? Assume that the trajectory is symmetric. 17. A car accelerates from rest to 8 m/s in 20 seconds.The car continues at this constant speed for another 20 seconds. Determine the total distance travelled by the car. 18. If a 10-N force pushes a box to the right and the box is displaced 3 meters, calculate the word done by the force. 19. A 49-N rock is suspended 8 meters from the floor. What is the gravitational potential energy of the rock? 20. The net work done on an object is 50 J. If the initial kinetic energy of the object is 22 J, what is the final kinetic energy? 21. Wade pulled a 100-kg box across the floor for 20 meters. Lebron also pulled a 100-kg box across the floor for 20 meters. Wade did it in 14 seconds, Lebron finished in 4 seconds. Which of the two has greater power?



Answers

A skateboarder with his board can be modeled as a particle of mass $76.0 \mathrm{kg},$ located at his center of mass. As shown in Figure $\mathrm{P} 8.37$ of Chapter $8,$ the skateboarder starts from rest in a crouching position at one lip of a cylinder of radius 6.80 $\mathrm{m}$ with its axis horizontal. On his descent, the skateboarder moves without friction and maintains his crouch so that his center of mass moves through one ouarter of a circle of radius 630 $\mathrm{m}$ (a) Find his speed at the bottom of the half-pipe (point $\mathbb{B} )$ . (b) Find his angular momentum about the center of curvature. (c) Immediately after passing point ( $\mathbb{B}$ , he stands up and raises his arms, lifting his center of gravity from 0.500 $\mathrm{m}$ to 0.950 $\mathrm{m}$ above the concrete (point @). Explain why his angular momentum is constant in this maneuver, whereas his linear momentum and his mechanical energy are not constant. (d) Find his speed immediately after he
stands up, when his center of mass is moving in a quarter circle of radius 5.85 $\mathrm{m}$ . (c) How much chemical energy in the skateboarder's legs was converted into mechanical energy as he stood up? Next, the skateboarder glides upward with his center of mass moving in a quarter circle
of radius 5.85 $\mathrm{m}$ . His body is horizontal when he passes point $\mathbb{Q}$ , the far lip of the half-pipe. (f) Find his speed at this location. At last he goes ballistic, twisting around while his center of mass moves vertically. (g) How high above point $\mathbb{O}$ does he rise? (h) Over what time interval is he airborne before he touches down, facing downward and again in a crouch, 2.34 $\mathrm{m}$ below the level of point $\mathbb{Q}$ ? (i) Compare the solution to this problem with the solution to Problem 8.37 . Which is more accurate? Why? Caution: Do not try this stunt yourself without the required skill and protective equipment, or in a drainage channel
to which you do not have legal access.

Quality fiction this selfish. We have initial kinetic energy getting converted into the energy stored in the spring. So we have K. It was M V. Over X squared equals five times one point 2/0 1.0.1 squared equals 7.2 times 10 to the to Newton per medal.

For this problem. On the topic of angular momentum. We are showing a ballistics card on an incline in the figure. An incline makes an angle theater with the horizontal. The cart has a mass big M. And a moment of inertia for each of the two wheels is little M. R. Squared over two. We went to first find the acceleration of the cut along the incline, then the amount delta X. By which the ball overshoots the card and finally the distance deed at the ball travels along the incline. Now we'll consider motion starting from rest over distance X. Along the incline and by the conservation of energy we have the translational kinetic energy plus the rotational kinetic energy plus the gravitational potential energy. Initially less work than against resistant forces. Down to E. Must equal the final translation of kinetic energy plus the final rotational kinetic energy plus the final potential energy. And so we know initially the cart has gravitational potential energy which is M. G. X. Sign theater. There's no work then Against Resistant Forces or Delta E. zero. And finally it has translational kinetic energy. A half I am V squared plus rotational kinetic energy Which is two times seven M. Little M R squared times omega squared which is the over our squared. And so from here we can see that two I am G X. Sine Theta is equal to big M plus two little M. Multiply by V squared. Now we know that the acceleration is constant. So we can use the equation re squared is equal to the I squared plus to A X. And this is equal to zero blessed to A X. Since the cards down from start and rest. And so we can see from our equation above that to M. G. X. Sign theater is equal to um Plus two Little M. Times to A X. Which means by rearranging we can find the acceleration of the card. A. And it's big M. Times G times Sine theta divided by Big M. Blessed two Times Little M. As required. We'll do part C. Next. And in part C we want to show the distance that the ball travels along the incline. Now suppose the boil is fired from a cart at rest, It moves with acceleration. G. Sign theater which is A. X. Down the incline and minus G. Co sign theater, which is a Y perpendicular to the incline. So for its range along the lamp, along the lamp, we have why am minus why I. Is the Y. I times t -1g. Co signed data, T squared. And so if we rearrange this equation, we get the time T and T. is equal to two V. Y. I. Since the y displacement is zero over G times the co sign of theater. Similarly along the X direction x minus X. I. Is the X. I plus a half A. X. Times T squared. So the X direction is along the incline. So this distance is D. And this is zero plus a half A. X. Is G. Sine theta times T squared and T. We get from above. This is for the why I squared over G squared Coulson squared data. So simplifying, we get this distance that the bowl or that the this is that the ball measured along the incline is equal to two V. Y. I squared sign theater divided by G. Call science squared data as required. Next, we'll do part B of the problem. And here we want to find the amount delta X. That the ball will overshoot the cut. So in the same time the cart moves a distance x minus X. I. Which is the exciting times, T plus a half A X T squared. And so the distance of the cart moves will call it D C zero plus half into G signed data, times M over big M. Blessed to times little M times T squared which is for V Y I squared over G squared. Cosine squared of theater. So the distance that the cart moves simplifies to V. Y. I squared. Sign data times big. M over G. Into the M Plus two times little M times Call science squared theater. So the ball overshoots the cart by a distance delta X. And data X is equal to d minus D C. Which is to be Y I squared scientific to divided by G cole sine squared theta minus two V Y I squared scientific data times M over G. Call science squared data into em Plus two times little m. And so this becomes two V Y I squared sign of data times M plus four V Y I squared. Sign off data times little M minus to be Y I squared sine of data times big M. All divided by G Cool science squared theater into big M plus two little M. And so we get delta X to be for times little M times V Y I squared sign of theater divided by big M plus two times little M into G Cool science squared theater.

Hi, everyone. This is the problem based on well, a stick part. Here it is, given our card. Last of all off. More thing. So here and is the mask off the board Capital Emmys Mosque off Sakhar having a moment off, Energia Twice off. Moment off in reserve the veal. That is a Marie script. In the first part, we have to fire the acceleration off the card in the horizontal direction. Toby M plus to him G sign theater. Toby proved in second part. Show that yeah, over suit dot card. And but who am upon am plus to him in tow? Sign off. Theater upon causes square tittle, Be right upon the here. Be by Is the velocity or court initial velocity off? All in the vertical direction. See part show that the distance traveled along the climb. Mm. By the bar is mhm toe Levite respect by a jeep. Sign off theater upon courses square the duties that distance a longer inclined plane. Let us here. Okay. All right. Yeah. Considered This is Toby XX is And this is Toby by axis. Yeah, first part. Considered Muslims starting from rest for dispense X over dispense X Hello and climate A plane contribution off energy. Right. Translate. Three kind of technology. Oh, vocational kind of technology. Gravitational potential. Energy initiative. Changing energy. Kate. Prostrated care reticent? No. Finally, Jiro plus zero m g x sent it. Er plus you half MV squared bliss there a modest script more so he can write to N g X. Sign up data. Yeah. Yeah, I am. Presto him into the script. Here. I have to make a correction. This is this morning. Small damage mass of the weed, the people right. Acceleration is constant, so we can apply the square. It's goingto be a square has to a x initial velocity zero. This is too. I am here. I have to make a correction. This is capital, um, to m g X Sign off theater upon M plus to wear Jiro plus tau X So acceleration you will get. And I'm mg Sign off Phaedra. And plus to him, she's the answer off a part. Mhm. Right. First people psalter C part. Let the ball is fired from a card and addressed it Moves build acceleration. Geese are not eaten down to the inclined plane. Okay? And minus G costs opted out perpendicular and client played for the reach along the ramp. You may also called Dreamed wise cult. Oh, being white, I not take plus half cheap because off the time to do you script that is zero. So these curto toe by upon G corset hands of distance Privett X minus Excise Pepto e x I t yeah. In tow to be by cheap, caustic chi squared on solving it d You will get to be white, I exclaimed, Sign off theater upon g causes square theater for see Pardon. Sorry. Be part X minus X I was scared. Toe v x, I t X t square. This is far. Motion off the card. Uh huh. D card. You will get zero plus. How? Jeez, I knocked it up in tow. AM upon I am plus to him into toe be by eye upon g corsetry square. So on solving it it is to be square. Sign up data upon uh huh de Paris. I am blessed to him. Question Square theater. So the wall bill over suit by that distance, do you minus dizzy? Oh, substituting the well unsolved ing it you will get for em diverted by. Right? That's so thanks for watching it

Hi this given problem barrel and rails are held on an inclined plane. So if they do the brand view of this inclined plane, these rails will be along these rails will be line along this inclined name like this. The cross section of the roar, metallic roar lighting over the rails is shown here. If the mass of yes, metallic roar is M its weight will be acting work equally downward. Mg. And the magnetic will in this region that is also vertically downward. Any form magnetic field. Every here angle of this inclined plane made with the horizontal that is given as to two components of this weight will be component portentous color to this inclined plane because if this angle is here to hear this angle will also be freed up. This component perpendicular to the plane will be MG cause it to another component. A long line klein plane that will be MG. Scientific under which this metallic bar will be having a tendency to slide. No. Now when this bar will be sliding down it will be intercepting the magnetic field lines. Yeah, this is the magnitude of magnetic will be as this bar metallic bar will be intercepting the magnetic field lines. Emotional well being used to close it close it stands due to which our current will pass to this metallic bar due to which a force will start acting on it. The direction of magnetic force is like this here this is the magnetic force acting on this metallic bar. So if this angle is theater, this angle will also be theater. Now we can resolve this magnetic force into two components. One component that is a long the inclined plane in upward direction. Yeah, this which will be F. Yeah. And another component for perpendicular to the inclined plane like this and that will be F. And this is FBI. Here magnetic force this component will be F. D. Sign. He got No. We want to find expression for terminal velocity naturally terminal velocity means the uniform velocity, uniform speed. If we talk about the magnitude, only uniform speed means and there is no acceleration and when there is no acceleration means no net course acting on the roll, metallic role in the direction of motion. So there are two forces acting along this inclined surface. Mg sine theta which is trying to pull this roll downward and because it up vertically, I'm sorry, a longer inclined plane upwards means these two forces should be equal in magnitude F because theater should be equal to MG scientist dr No. Making it a question # one. We should find an expression for FBI. For which most of all the EMF induced. Because here this E M F induced will be You do that component of magnetic field? As here, this is the magnetic field. So this roar will be intercepting perpendicular component of the magnetic field. A particular cool the direction of explosion is here this company to eat like this. Yeah, it's So if this is be this angle here will be tita the component of the magnetic field perpendicular to the direction of motion of the road. That will be because data this because it a component will be intercepted by the rod or particularly hence emotional EMF induced. Rose the ends of the Lord. That is a magnetic clear the cost to is being intercepted by the road perpendicular into its velocity terminal velocity into the length of this metal bar. Uh huh. Current passing through this metal bar using arms law will be given by I. Is equal to have induced by the resistance. We can say this is B. The L. Cause Pita divided by our And finally the force experienced by this model bar will be given by the magnetic force that is I L. P. For this is the current or this is I into the length of the metal bar into be magnetic field for I. This is B into we into L. Into cost. Peter divided by art into L. Into B. Again. So here it comes out to be the And that is costing this is big square into vi into the square into cost. Pita guided by our So finally this is the magnetic force F. B. We can say hands using this Expression putting this expression in equation number one or using Equation # one. Now which says F. Because he like was two MG sine theaters or here it will be F B for FB. This is the square. It will be into elsewhere into course. Teacher divided by art into casita and that is equal to MG sine theta. Oh! Here, it may also be given as these square into V into Ellis square into false square theater invited by our is equal to MG sine theta. So finally, we will be given by terminal velocity expression for terminal velocity achieved by this metal bar will be given by I am. We are into scientific data, divided by these squared into ellis Squire, into course is quite. Which is the answer for this. Given problem here. Thank you.


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