PHYS 2420 Problem Set 13 PDF

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PHYS 2420 Introductory Mechanics for physics majors (CRN 28672) Prof. Jorge Munoz Problem Set 13 Assigned: 4/23/19

Due: 4/29/19 (during the workshop)

1. Warm up problems: (Exercises 15.1, 15.3) a. An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the period, frequency, angular frequency, amplitude, and maximum speed of the glider? (3.3 s, 0.30 Hz, 1.90 rad/s, 0.25 m, 0.48 m/s) b. When a guitar string plays the note “A,” the string vibrates at 440 Hz. What is the period of the vibration? (2.27 ms) Note: this is one of my favorite wikimedia files: https://upload.wikimedia.org/wikipedia/commons/a/ad/Piano_key_frequencies.png 2. A 250 g ball collides with a wall. The figure below shows the ball’s velocity and the force exerted on the ball by the wall. What is v fx , the ball’s rebound velocity? (Exercise 11.13) (6.0 m/s)

3. Fred (mass of 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus Maximus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip and they fall to the ground. Which way do they slide and how far? The coefficient of kinetic friction between football uniforms and Astroturf is 0.30. (Exercise 11.21) (0.076 m) 4. A package of mass m is released from rest at a warehouse loading dock and slides down the 3.0m-high, frictionless chute shown in the figure below to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass 2 m , from the bottom of the chute. Suppose the packages stick together. What is their common speed after the collision? Suppose the collision between the packages is perfectly elastic. To what height does the package of mass m rebound? (Exercise 11.25) (2.56 m/s and 0.33 m)

5. Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backwards off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dan’s mass is 50 kg and the skateboard’s mass is 5.0 kg. (Exercise 11.28) (3.6 m/s) 6. A 100 g granite cube slides down a 40 ° frictionless ramp. At the bottom, just as it exits onto a horizontal table, it collides with a 200 g steel cube at rest. How high above the table should the granite cube be released to give the steel cube a speed of 150 cm/s? (Problem 11.55) (0.258 m) 7. You have been asked to design a “ballistic spring system” to measure the speed of bullets. A spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block and stops in the block. The spring’s maximum compression d is measured. Find an expression for the bullet’s speed v B in terms of m , M , k , and d . What was the speed of a 10 g bullet if the block’s mass is 2.0 kg and if the spring, with k =50 N/m, was compressed by 45 cm? (Problem 2 2 2 m+ M m+ M M g m+ M 2 gd− 2 +k (d−Mg /k ) 2 2 m k m m , 453 m/s) 11.56) ( 1 /2 [ ] v B= ¿

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8. A block attached to a spring with unknown spring constant oscillates with a period of 2.0 s. What is the period if (a) the mass is doubled? (b) the mass is halved? (c) the amplitude is doubled? (d) the spring constant is doubled? (Exercise 15.14) (2.0 s, 2.8 s, 1.41 s, 1.41 s) 9. A grandfather clock ticks each time the pendulum passes through the lowest point. If the pendulum is modeled as a simple pendulum, how long must it be or the ticks to occur once a second? (Exercise 15.24) (0.99 m) 10. A molecular bond can be modeled as a spring between two atoms that vibrate with simple harmonic motion. The figure below shows a SHM approximation for the potential energy of an HCl molecule. Because the chlorine atom is so much more massive than the hydrogen atom, it is reasonable to assume that the hydrogen atom ( m=1.67 ×10−27 kg) vibrates back and forth while the chlorine atom remains at rest. Use the graph to estimate the vibrational frequency of the HCl molecule. (Problem 15.63) ( 7.9 × 1013 Hz) (This problem is not hard, you just need the mass and spring constant to get the frequency, and the spring constant measures how narrow the parabola is.)...