PHYS 2420 Problem Set 14 PDF

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PHYS 2420 Introductory Mechanics for physics majors (CRN 28672) Prof. Jorge Munoz Problem Set 14 (last one!) Assigned: 4/30/19, Due: 5/6/19 1. Warm up problems: (Exercises 12.1 and 12.2) a. A high-speed drill reaches 2000 rpm in 0.50 s. What is the drill’s angular acceleration and through how many revolutions does it turn during this first 0.50 s? (419 rad/s2, 8.3 revs) b. A skater holds her arms outstretched as she spins at 180 rpm. What is the speed of her hands if they are 140 cm apart? (13.2 m/s) 2. The three masses shown in the figure below are connected by massless, rigid rods. What are the coordinates of the center of mass? (Exercise 12.7) (x = 8.0 cm and y = 5.0 cm)

3. The three 200 g masses in the figure below are connected by massless, rigid rods. (a) What is the triangle’s moment of inertia about the axis through the center? (b) What is the triangle’s kinetic energy if it rotates about the axis at 5.0 rev/s? (Exercise 12.11) (0.032 kg m2 and 15.8 J)

4. The axle in the figure below is half the distance from the center to the rim. What is the net torque about the axle? (Exercise 12.21) (-14.7N m)

5. An object whose moment of inertia is 4.0 kg m2 experiences the torque shown in the figure below. What is the object’s angular velocity at t=3.0 s? Assume it starts from rest. (Exercise 12.25) (0.50 rad/s)

6. An 8.0-cm-diameter, 400 g solid sphere is released from rest at the top of a 2.1-m-long, 25° incline. It rolls, without slipping, to the bottom. (a) What is the sphere’s angular velocity at the bottom of the incline? (b) What fraction of its kinetic energy is rotational? (Exercise 12.35) (88 rad/s and 2/7) 7. A solid sphere of radius R is placed at a height of 30 cm on a 15° slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius R be released on the same slope in order to equal the sphere’s speed at the bottom? (Exercise 12.36) (42.9 cm) 8. A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter and stick. What is the turntable’s angular velocity, in rpm, just after this event? (Exercise 12.46) (50 rpm) 9. Flywheels are large, massive wheels used to store energy. They can be spun slowly, then the wheel’s energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 1.5 m diameter and a mass of 250 kg. Its maximum angular velocity is 1200 rpm. (a) A motor spins up the flywheel with a constant torque of 50 N m. How long does it take the flywheel to reach top speed? (b) How much energy is stored in the flywheel? (c) The flywheel is disconnected from the motor and connected to a machine to which it will deliver energy. Half the energy store in the flywheel is delivered in 2.0 s. What is the average power delivered to the machine? (d) How much torque does the flywheel exert on the machine? (Problem 12.64) (177 s; 5.55 × 105 J; 1.39 × 105 W; 1.30 kN m) 10. Blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in the figure below. The pulley turns on frictionless bearings. Mass m1 slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest. (a) Assume the pulley is massless. Find the acceleration of m1 and the tension in the string. (b) Suppose the pulley has mass mp and radius R. Find the acceleration of m1 and the tensions in the upper and lower portions of the string. Verify m2 g ; T =m 1 a ; that your answers agree with part (a) if you set mp = 0. (Problem 12.65) ( a= m1 +m 2 m2 g a= ; T upper =m 1 a ; T lower =a (m 1+ I / R2 ) ) 1 m1 +m 2+ m p 2...