PHYS 211 Sample Final 2 1 A child runs and with a velocity that exactly equals the tangential velocity of a rotating playground merry go round see figure lands on its outer edge You may treat the merry go round as a horizontal disk that rotates freely about its central axis without friction Under these circumstances and defining to be angular velocity and L to be angular momentum A merry go round will increase B merry go round will be unchanged C merry go round will decrease D Lchild Lmerry go round about the merry go round s rotation axis will increase E Lchild Lmerry go round about the merry go round s rotation axis will decrease Page 1 PHYS 211 Sample Final 2 2 A ball of mass m is attached to a massless string of length L The other end of the string is attached to the ceiling The ball is released from the position shown and swings downward At what point is the tension T in the string a maximum and why A At the bottom because the ball s velocity is perpendicular to the force of gravity there B The specific point depends on the relative values of m and L C Just after the release because its speed is small and T does not have to provide much centripetal force D At the bottom because the speed is largest and T is anti parallel to the force of gravity there E When the string is 45 degrees from vertical because the force of gravity has equal radial and tangential components there Page 2 PHYS 211 Sample Final 2 3 A child standing on the ladder of an above ground pool throws three stones at the same time Assume the stones start at water level They follow the trajectories shown with stones 1 2 reaching the same height and stones 2 3 landing the same distance away from the child The stones enter the water in the following order first to last in terms of what time they splash into the pool A 1 then 2 then 3 B 3 then 2 then 1 C 1 then 2 and 3 together D 1 and 2 together then 3 E 3 then 1 and 2 together Page 3 PHYS 211 Sample Final 2 4 In a classic amusement park ride riders stand against the wall in a cylindrically shaped room Once the room gets spinning fast enough the floor drops from the bottom of the room and the riders remain stuck to the wall See figure At the instant shown where v is the tangential speed of the rider shown in the figure the free body diagram of the rider of mass m is given by A D B E C Page 4 PHYS 211 Sample Final 2 5 A 2 kg mass attached to a massless spring undergoes undamped simple harmonic motion with a position given by x t 2cos 3t where x is in m and t is in s What is the total mechanical energy in the system A 1 J B 6 J C 18 J D 36 J E 48 J 6 A system rotates under the influence of a time varying torque such that the angular momentum of the system along a fixed axis changes as a function of time according to the graph Assuming that the object s moment of inertia is constant during what time interval s is the magnitude of the object s angular acceleration along this axis the largest A From 0 to 4 s and from 20 s to 24 s B From 16 s to 20 s C From 13 s to 24 s D From 12 s to 16 s E Just before t 24 s Page 5 PHYS 211 Sample Final 2 7 A satellite of mass m is in circular orbit around a planet of mass M at a distance R from the center of that planet What is the magnitude of the angular momentum of the satellite with respect to the center of the planet A 0 B C D E 8 A spring mass system oscillates in simple harmonic motion with a displacement shown as a function of time in the graph What is the angular frequency of the oscillator A 4 3 rad s B 3 4 rad s C 2 3 rad s D 3 2 rad s E 4 rad s Page 6 PHYS 211 Sample Final 2 9 A frictionless pulley in the shape of a uniform disk has a mass M and a radius R A massless rope that is wound around the rim of the pulley is pulled horizontally with a constant force F What is the angular acceleration of the pulley A 2F MR B F 2MR C F MR D F 2MR2 E 2F MR2 10 A block of mass M is on a frictional inclined plane kinetic friction coefficient k friction force of magnitude Ff as shown in the figure Released from rest the block is observed to have slid down a distance x along the plane after a time t as seen by a photo taken by a high speed camera we do not know anything about the velocity of the block at that time only that it slid down a distance x Which of the following statements is false Take x to be positive down the plane A If k is large enough it is possible for the block to be at rest after sliding a distance x B After sliding a distance x the final kinetic energy is the gravitational potential energy lost by the mass plus the negative work done by friction C In sliding through distance x the normal force Fn does not do any work D The normal force Fn is equal in magnitude to the component of the force of gravity perpendicular to the plane E Given the description of the situation the block must have a non zero acceleration Page 7 PHYS 211 Sample Final 2 11 A cannonball has a mass of 5 kg and is traveling at 200 m s in the X direction It misses its target by 5 m passing it on the left at a Y coordinate What is its angular momentum with respect to the target A 0 kg m2 s B 1000 kg m2 s in the down Z direction C 5000 kg m2 s in the up Z direction D 5000 kg m2 s in the forward X direction E None of the above 12 A mass of 1 kg is held by two identical springs one on each side When the mass is at the midpoint between the two walls both springs are at their equilibrium positions i e neither stretched nor compressed The angular frequency of the motion is 2 rad s What is the spring constant of one of the springs A 0 25 N m B 0 5 N m C 1 N m D 2 N m E 4 N m Page 8 PHYS 211 Sample Final 2 13 The figure shows a top view of a door of width …