Unformatted text preview: Quiz 5A DL Sec Grading: Name First three letters of your family name Last 6 digits of student ID: 1. Two occupants (Alice and Bob) of a stationary sled on a frictionless icy surface each threw a snowball simultaneously from the sled in different direction. The snowball A Alice threw had a mass of 0.3kg and speed of 15 m/s. The snowball B Bob threw had a mass of 0.5kg and speed of 10 m/s. The velocities of the two snowballs were perpendicular to each other. What is the resultant velocity (magnitude and direction with respect to the horizontal) of the sled with two occupants after the throw? Combined mass of the sled and the two occupants is 120kg. Show your work below. B v120kg
90 Sled A v120kg vector not to scale There is no external force on the system (sled+two occupants, snowball A, snowball B) therefore, the momentum of the system is conserved. Iext = F net,ext t = p = 0 pinitial = pfinal and as pinitial = 0, pfinal = 0 as well. Thus, the momentum of the sled with two occupants must be equal in magnitude and opposite in direction as the momentum of the snowballs A and B. x component: mAvA = m120kg v120kg, x Solve for v120kg, x v120kg, x ( x component of the resultant velocity of the sled with two occupants), = mAvA/ m120kg = ( 0.3kg)(15m/s)/120kg = 0.0375kgm/s y component: mBvB = m120kg v120kg, y Solve for v120kg, y v120kg, y ( y component of the resultant velocity of the sled with two occupants), = mBvB/ m120kg = ( 0.5kg)(10m/s)/120kg = 0.042kgm/s v120kg, x 0.0375kgm/s (pointing to left) Angle 48 degrees v120kg Solve for the magnitude of v120kg v120kg = { (v120kg, x)2 + (v120kg, x)2 } = { ( 0.0375kgm/s)2 + ( 0.042kgm/s)2 } v120kg = 0.056 m/s Find the angle of v120kg w.r.t. the horizontal Tan 1( 0.042/0.0375) = 48 degrees v120kg, y 0.042kgm/s (pointing down) Thus, the resultant velocity of the sled with two occupants after the throw points 48 degrees downward from the horizontal and its magnitude is 0.056m/s ( ~ 2inches/s). Torque : = rF = rFtangential , L = I , Angular Impulse : AngJext = ext t = L Question 1A (45%): (getting the magnitude of velocity) Q > Correct answer; a magnitude of v = 0.056m/s ( 10.0 ) A > Wrote only the horizontal component, misunderstanding the question, but otherwise all good ( 9.5 ) W > Minor Logic mistake (left in terms of momentum), but otherwise all good ( 9.0 ) E > Used p=mv like a one dimensional problem ( 7.5 ) T > Found p/v in x and y direction, but didn't finish or messed up ( 7.5 ) S > Used energy to solve the problem ( 6.5) R > Fundamental error (5.5) Question 1B (30%): (getting the direction) Q > Found the correct angle (48.228) ( 10.0 ) W > Wrong direction, but the angle calculation is good (ie said 42 degrees) ( 9.0 ) A > Correct direction with no angle given, but good work (ie used a momentum chart) ( 8.5 ) E > Correct direction with no/bad work ( 6.5 ) T > Opposite direction with no/bad work ( 6.5 ) S > Fundamental error ( 5.5 ) Momentum chart will look like this: You can fill out everything except to begin with. Then, it is clear that the final momentum of the sled with two occupants has to be such that it cancels the final momentum of snowball A and B, since the final momentum of the system must remain zero. + + = 0 p We do not need to know these to solve this problem. pinitial A 0 pfinal B Sled with two occupants Total 0 0 0 0 0 2. Consider a bike wheel with an axle clamped to the table as in your DL activity (See figure (1)). The wheel is initially rotating with a constant speed of15 revolutions/second. Then in the final state, the wheel is rotating with a constant speed of 5 revolutions/second in the same direction. (a) In figure (2) below, draw initial and final angular momentum vectors (Linitial and Lfinal) . No quantitative calculation necessary, just show the direction and relative magnitude of the two vectors. (b) Draw the direction of torque vector ( ) that was applied between the initial and final state. Label properly. Torque : = rF = rFtangential , L = I , Angular Impulse : AngJext = ext t = L (1) (2) Sideview Draw your vectors here axle
table Lfinal table axle Linitial
angular velocity vector points to the left toward the table. (a) Use Right Hand Rule to figure out the direction of Linitial and Lfinal (b) Recall AngJext = ext t = L, torque vector points in the same direction as the change in the angular momentum, i.e., L. Question 2 (25%) Q > All good; had all the correct vectors ( 10.0 ) W > Flipped everything, but otherwise all good ( 9.0 ) E > Wrong direction /magnitude of Li,Lf, but correct corresponding torque ( 8.5 ) A > Correct Li,Lf (magnitude and direction), but wrong torque ( 8.0 ) T > Correct magnitude of Li,Lf but wrong torque (based on their work) ( 6.5 ) R > Fundamental Error ( 5.5 ) Torque : = rF = rFtangential , L = I , Angular Impulse : AngJext = ext t = L ...
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 Spring '08
 Taylor
 Angular Momentum, Friction, Angular Impulse, resultant velocity

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