PHYS 2211 Module 13 Self Assessment Practice Problems

Module 13 Self Assessment Practice Problems

13.1
A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?
Answer: 2.37 N/m
13.2
The length of nylon rope from which a mountain climber is suspended has an effective force constant of 1.4 x 104 N/m.
(a) What is the frequency at which he bounces, given his mass plus and the mass of his equipment are 90.0 kg?
(b) How much would this rope stretch to break the climber’s fall if he free-falls 2.00 m before the rope runs out of slack? Hint: Use conservation of energy.
(c) Repeat both parts of this problem in the situation where twice this length of nylon rope is used.
Answer: (a) 1.99 Hz (b) 44.3 cm (c) 65.0 cm
13.3
A pendulum with a period of 2.00000 s in one location (g = 9.8 m/s2) is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location?
Answer: 9.82002 m/s2
13.4
A diver on a diving board is undergoing SHM. Her mass is 55.0 kg and the period of her motion is 0.800 s. The next diver is a male whose period of simple harmonic oscillation is 1.05 s. What is his mass if the mass of the board is negligible?
Answer: 94.7 kg
13.5
A 2.00-kg block lies at rest on a frictionless table. A spring, with a spring constant of 100 N/m is attached to the wall and to the block. A second block of 0.50 kg is placed on top of the first block. The 2.00-kg block is gently pulled to a position x = +A and released from rest. There is a coefficient of friction of 0.45 between the two blocks.
(a) What is the period of the oscillations?
(b) What is the largest amplitude of motion that will allow the blocks to oscillate without the 0.50-kg block sliding off?
Answer: (a) 0.99 s (b) 0.11 m
13.6
A novelty clock has a 0.0100-kg-mass object bouncing on a spring that has a force constant of 1.25 N/m.
(a) What is the maximum velocity of the object if the object bounces 3.00 cm above and below its equilibrium position?
(b) How many joules of kinetic energy does the object have at its maximum velocity?
Answer: (a) 0.335 m/s (b) 5.61 x 10-4 J
13.7
A 0.500-kg mass suspended from a spring oscillates with a period of 1.50 s. How much mass must be added to the object to change the period to 2.00 s?
Answer: 0.389 kg
13.8
Four passengers with combined mass 250 kg compress the springs of a car with worn-out shock absorbers by 4.00 cm when they enter it. Model the car and passengers as a single body on a single ideal spring. If the loaded car has a period of vibration of 1.92 s, what is the period of vibration of the empty car?
Answer: 1.88 s
13.9

A 1.80-kg connecting rod from a car engine is pivoted about a horizontal knife edge as shown in the figure. The center of gravity of the rod was located by balancing and is 0.200 m from the pivot. When it is set into small amplitude oscillation, the rod makes 100 complete swings in 120 s. Calculate the moment of inertia of the rod about the rotation axis through the pivot.
Answer: 0.129 kg•m2
13.10
We want to support a thin hoop (Icm = MR2) by a horizontal nail and have the hoop make one complete small-angle oscillation each 2.0 s. What must the hoop’s radius be?
Answer: 0.50 m