1 of 5 2009/10/30 8:27 AM PY105 Assignment 10 (1031274) 0/20 Tue Nov 17 2009 10:15 PM EST Question Points 1 2 3 4 5 6 7 0/2 0/6 0/2 0/2 0/2 0/5 0/1 Total 0/20 Description This assignment is worth 20 points. Each part is worth 1 point. Assume the numbers given in each problem are accurate to three significant figures. WebAssign expects your answers to be accurate within 1%. If you don't round off until the end, and then round off to three significant figures, you should be fine. Occasionally there are errors in WebAssign. If you are convinced your answer is correct and WebAssign is grading you incorrectly please check with Professor Duffy. 1. 0/2 pointsduffy_ep_ch11_p54 [1225029] A solid sphere rolls without slipping when it is released from rest at the top of a ramp that is inclined at 38.0 degrees with respect to the horizontal, but, if the angle exceeds 38.0 degrees, the sphere slips as it rolls. Use g = 10.0 m/s 2. (a)calculate the magnitude of the sphere's acceleration, when the angle of the incline is 38.0 degrees. 4.4 m/s 2. (b)calculate the coefficient of static friction between the sphere and the incline. 0.223 2. 0/6 pointsduffy_ep_ch11_p56 [1224915] A bowling ball of mass M and radius R = 20.0 cm is released with an initial translational velocity of v i = 15.0 m/s to the right and an initial angular velocity of zero. The bowling ball can be treated as a uniform solid sphere. The coefficient of kinetic friction between the ball and the surface is 0.150. The force of kinetic friction causes a linear acceleration, as well as a torque that causes the ball to spin. The ball rolls while slipping along the horizontal surface for some time, and then rolls without slipping at constant velocity after that. Use g = 10 m/s 2.
2 of 5 2009/10/30 8:27 AM (a) Which free-body diagram above shows all the forces acting on the ball while it is sliding? FBD 1 FBD 2 FBD 3 FBD 4 FBD 5 (b) What is the magnitude of the acceleration of the ball while it is sliding? 1.5 m/s 2 (c) What is the magnitude of the angular acceleration of the ball while it is sliding? 18.8 rad/s 2 (d) How far does the ball travel while it is sliding? 10.7 m (e) What is the constant speed of the ball when the ball rolls without slipping? 13.9 m/s (f) Which free-body diagram above shows all the forces acting on the ball after it starts rolling without slipping, moving at a constant velocity? FBD 1 FBD 2
3 of 5 2009/10/30 8:27 AM FBD 3 FBD 4 FBD 5 3. 0/2 pointsduffy_ep_ch11_p57 [1032403] The figure below shows the side view of a meter stick that can rotate without friction about an axis passing through the left end. Pennies (of negligible mass in comparison to the mass of the meter stick) have been placed on the meter stick at regular intervals. Initially, you hold it so that the stick is at rest in a horizontal position. When you let go, the meter stick rotates about the axis. Some of the pennies remain in contact with the meter stick while some lose contact with it. Use g = 9.8 m/s 2. (a) Determine the angular acceleration of the meter stick about the axis through the left end, immediately after you release the meter stick from rest. 14.7 rad/s 2 (b) Determine the linear acceleration, immediately after you release the meter stick from rest, of the point on the meter stick that is a distance of 85.0 cm from the axis. Note that the linear acceleration of the penny at that point on the meter stick is at most g. 12.5 m/s 2 4. 0/2 pointsduffy_ep_ch11_p36 [498324] A pulley has a mass M, a radius R, and is in the form of a uniform solid disk. The pulley can rotate without friction about a horizontal axis through its center. As shown in the diagram, the string wrapped around the outside edge of the pulley is subjected to an 8.00 N force in case 1, while in case 2 a block with a weight of 8.00 N hangs down from the string. Use g = 9.8 m/s 2. If M = 2.60 kg and R = 80.0 cm, calculate the magnitude of the angular acceleration of the pulley in (a) case 1. (b) case 2. 7.69 rad/s 2 4.73 rad/s 2 5. 0/2 pointsduffy_ep_ch11_p53 [1225038]
4 of 5 2009/10/30 8:27 AM For this problem, use M = 4.00 kg, R = 28.0 cm, and g = 10.0 m/s 2. A spool consists of two disks, each of radius R and mass M, connected by a cylindrical axle of radius R/2 and mass M. When an upward force of tension, of magnitude F T, is exerted on a string wrapped around the axle, the spool will roll without slipping as long as F T is not too large. (a) Calculate the spool s rotational inertia about an axis through its center. 0.353 kg m 2 (b) If the coefficient of static friction between the spool and the horizontal surface it is on is 0.900, what is the maximum value F T can be for the spool to roll without slipping? 85.5 N 6. 0/5 pointsduffy_ep_ch11_p32 [1224149] A beetle with a mass of 20.0 g is initially at rest on the outer edge of a horizontal turntable that is also initially at rest. The turntable, which is free to rotate with no friction about an axis through its center, has a mass of 75.0 g and can be treated as a uniform disk. The beetle then starts to walk around the edge of the turntable, traveling at an angular velocity of 0.0400 rad/s clockwise with respect to the turntable. (a) What does the turntable do while the beetle is walking? The turntable remains at rest. at the same angular velocity (same magnitude and direction) as the beetle. clockwise, with a larger angular speed than the beetle's. clockwise, with a smaller angular speed than the beetle's. counter-clockwise, but with the same angular speed as counter-clockwise, with a larger angular speed than counter-clockwise, with a smaller angular speed than
5 of 5 2009/10/30 8:27 AM (b) With respect to you, motionless as you watch the beetle and turntable, what is the angular velocity of the beetle? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise. 0.0316 rad/s (c) What is the angular velocity of the turntable (with respect to you)? Use a positive sign if the answer is clockwise, and a negative sign if the answer is counter-clockwise. -0.00842 rad/s (d) If a mark is placed on the turntable at the beetle s starting point, how long does it take the beetle to reach the mark again? 157 s (e) Upon reaching the mark, the beetle stops. What does the turntable do? also comes to rest. keeps rotating at the same angular velocity. slows down, but does not come to rest. speeds up. reverses direction, but keeps the same angular speed. 's angular velocity changes to the original angular velocity of the beetle. 7. 0/1 pointsduffy_ep_ch11_p34 [1225040] A particular horizontal turntable can be modeled as a uniform disk with a mass of 200 g and a radius of 20.0 cm that rotates without friction about a vertical axis passing through its center. The angular speed of the turntable is 3.00 rad/s. A ball of clay, with a mass of 40.0 g, is dropped from a height of 25.0 cm above the turntable. It hits the turntable at a distance of 15.0 cm from the middle, and sticks where it hits. Assuming the turntable is firmly supported by its axle so it remains horizontal at all times, find the final angular speed of the turntable-clay system. 2.45 rad/s Assignment Details