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Final-key-Su03

# Final-key-Su03 - Physics 221 Final Exam Summer 2003 The...

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Physics 221. Final Exam Summer 2003 The following situation refers to the next two problems: A block of mass m = 3 kg is released from rest from a height h on frictionless incline. It reaches the bottom of the incline with speed v = 10 m/s. (See figure 1). m m m h h h Figure 2 Figure 3 Figure 1 101. Find the initial height of the block, h . a. h = 1 m b. h = 3 m c. h = 5 m d. h = 8 m e. h = 10 m 102 . A disk and a ring, both of mass m (identical to the block) and radius R are released from rest at height h from similar inclines that do exert friction, so the disk and the ring roll without slipping (see figures 2 and 3). The three objects are released simultaneously. Rank the objects from first to last to reach the bottom of the incline. a. disk, ring, box b. ring, box, disk c. ring, disk, box d. box, disk, ring e. They all reach the bottom at the same time. Page 1 of 13

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Physics 221. Final Exam Summer 2003 103 . The object shown in the figure below is made of 10 identical, uniform flat squares of side a . Find the x component of the position of the center of mass of the object. The origin is taken right at the center of the empty square. y a x a. CM 1 2 x a =− b. CM 1 3 x a c. CM x a d. CM 2 3 x a e. CM 3 2 x a 104 . A stone of mass m attached to a string is swirled around in vertical circles of radius R . Find an expression for the tension on the string at the bottom of the trajectory, when the speed of the stone is v . a. T m g = b. 2 v Tm R = c. 2 v g R    d. 2 v g R =+ e. 2 2 v g R Page 2 of 13
Physics 221. Final Exam Summer 2003 i The following situation refers to the next two problems: A stone 1 of mass m 1 = 1 kg is thrown from the ground at an angle θ with the horizontal. Two seconds later, the velocity of the stone is 1 ˆ 12 m/s v = G . Right at this moment, it hits another stone 2 of mass m 2 = 2 kg that was falling vertically at speed v 2 = 10 m/s —at the moment of the collision (see figure below). Immediately after the collision, the velocity of stone 2 is . 2 ˆ 8 m/s vi = G m 2 x y θ m 1 v 2 v 1 Right before the collision 105. Determine the throwing angle θ . a. θ = 14° b. θ = 25° c. θ = 33° d. θ = 59° e. θ = 68° s s s s s 106 . Determine the velocity of stone 1 immediately after the collision. a. () 1 ˆˆ 82 0 m / j =− G b. 1 m / j =− − G c. 1 42 m / j G d. 1 41 m / j G e. 1 m / j =+ G Page 3 of 13

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Physics 221. Final Exam Summer 2003 The following situation refers to the next two problems: A uniform disk of mass M = 20 kg and radius R = 1.2 m is set on a frictionless, horizontal surface and is free to rotate about its axis. Three forces of identical magnitude
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Final-key-Su03 - Physics 221 Final Exam Summer 2003 The...

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