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Exam 2 practice problems solutions

Exam 2 practice problems solutions - Exam#2 practice...

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Exam #2 practice problems solutions Physics 203 1. You are trying to find a short cut across a calm river ( 20.0 m wide) without getting wet. Someone left their kayak on the bank but the paddle is nowhere to be found. So, you put the kayak in the water pointed at the opposite bank of the river. You then get a running start and jump onto the kayak. You and the kayak glide at a nearly constant rate until you reach the opposite side. However, you were having so much fun doing all this that you lost track of time as you were crossing the river. You realize, thanks to taking physics over the summer at Rutgers, that you can actually predict how long it took to cross the river. You estimate that you have a mass of 70.0 kg , the kayak has a mass of 20.0 kg , and that you were running at about 3.00 ms when you jumped onto the kayak. Predict how long it took to cross the river. Since you and the kayak moved across the river at constant velocity I can use kinematics to determine the time it took. 0 0 xx t v = But, I need to know the speed of you and the kayak. To do this I’ll use conservation of momentum and treat you jumping into the kayak as a collision. ( ) 0 y yk k mv m m v += + ( )( ) ( )( ) ( ) ( ) 0 0 20.0 90.0 8.57 70.0 3.00 0 yy kk xx m m t mm m kg ts kg m s −+ = = +  +  +  ⇒= = + 2. You are playing pool and need to hit a very specific shot. You need the cue ball (mass 0.17 kg ) to hit the 3-ball (mass 0.16 kg ) so that the following happens: 1) After it hits the 3-ball the cue ball needs to be traveling very slowly (you guess 0.1 ) at a 90 degree angle counterclockwise from its original direction of travel so it stops at a specific place on the table. 2) The 3-ball needs to be traveling at a 20 degree angle clockwise from the cue ball’s original direction of travel. What speed must you give the cue ball in order to pull off this shot? I’ll choose the two billiard balls to be the system. Since the net external force 1 ,,, , i f ci ni c f pp p p p p = ⇒+= +  on the system is zero the momentum of the system is a conserved quantity. The subscript ‘c’ refers to the cue ball. The subscript ‘n’ refers to the numbered ball. This vector equation splits into two equations, one for each of its two components. ,, , , 0 0 cos 0 0 sin cix nix cf x nf x ciy niy cf y nf y c ci n n f c cf n nf ppp p p θ + + +=+ I’ll solve for , nf v in the second equation and substitute it into the first equation. 1 Well, this may sound a bit odd since friction definitely plays a role when playing pool, but during the time the collision happens (a very very short time) it’s effect is extremely small. x y , p , cf p , p
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( ) ( ) , , , ,, sin cos cot 0.1 cot 20 0. 5 sin 27 c cf nf n n ci c f cn mv v m m v v ms mm θ θθ ⇒=  = = = °=   3. You are ice skating on a frozen lake and headed towards your friend at 2.00 . You hold your arm out to the side, and your friend digs into the ice with his skates so he won’t move. Your friend grabs your outstretched arm as you are passing him causing you to turn rapidly around him.
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Exam 2 practice problems solutions - Exam#2 practice...

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