Concept explainers
A ball of mass m oscillates on a spring with spring constant k = 200 N/m. The ball’s position is x = (0.350 m)cos(15.0t), with t measured in seconds.
a. What is the amplitude of the ball’s motion?
A. 0.175 m
B. 0.350 m
C. 0.700 m
D. 7.50 m
E.15.0 m
b. What is the frequency of the ball’s motion?
A. 0.35 Hz
B. 2.39 Hz
C. 5.44 Hz
D. 6.28 Hz
E. 15.0 Hz
c. What is the value of the mass m?
A. 0.45 kg
B. 0.89 kg
C. 1.54 kg
D. 3.76 kg
E. 6.33 kg
d. What is the total mechanical energy of the oscillator?
A. 1.65 J
B. 3.28 J
C. 6.73 J
D. 10.1 J
E. 12.2 J
e. What is the ball’s maximum speed?
A. 0.35 m/s
B. 1.76 m/s
C. 2.60 m/s
D. 3.88 m/s
E. 5.25 m/s
Want to see the full answer?
Check out a sample textbook solutionChapter 14 Solutions
COLLEGE PHYS:STRATEGIC APPR. VOL2 >IC<
Additional Science Textbook Solutions
Lecture- Tutorials for Introductory Astronomy
Essential University Physics: Volume 2 (3rd Edition)
College Physics (10th Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
University Physics (14th Edition)
Introduction to Electrodynamics
- A clock is constructed so that it keeps perfect time when its simple pendulum has a period of 1.000 s at locations where g = 9.800 m/s2. The pendulum bob has length L = 0.248 2 m, and instead of keeping perfect time, the clock runs slow by 1.500 minutes per day. (a) What is the free-fall acceleration at the clocks location? (b) What length of pendulum bob is required for the clock to keep perfect time?arrow_forwardA spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency , the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (c) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. (g) Determine the velocity and acceleration of the particle when t = 0.500 s.arrow_forward(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?arrow_forward
- A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 7.50 N is applied. A 0.500-kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is displaced from the origin to x = 5.00 cm and released from rest at t = 0. (a) What is the force constant of the spring? (b) What are the angular frequency , the frequency, and the period of the motion? (c) What is the total energy of the system? (d) What is the amplitude of the motion? (c) What are the maximum velocity and the maximum acceleration of the particle? (f) Determine the displacement x of the particle from the equilibrium position at t = 0.500 s. (g) Determine the velocity and acceleration of the particle when t = 0.500 s.arrow_forward(a) If frequency is not constant for some oscillation, can the oscillation be simple harmonic motion? (b) Can you mink of any examples of harmonic motion where the frequency may depend on the amplitude?arrow_forwardA simple pendulum is 5.00 in long. (a) What is the period of simple harmonic motion for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s2? (b) What is its period if the elevator is accelerating downward at 5.00 m/s2? (c) What is the period of simple harmonic motion for the pendulum if it is placed in a truck that is accelerating horizontally at 5.00 m/s2?arrow_forward
- A baby bounces up and down in her crib. Her mass is 12.5 kg, and the crib mattress can be modeled as a light spring with force constant 700 N/m. (a) The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency? (b) If she were to use the mattress as a trampoline losing contact with it for part of each cyclewhat minimum amplitude of oscillation does she require?arrow_forwardAn object-spring system moving with simple harmonic motion has an amplitude A. (a) What is the total energy of the system in terms of k and A only? (b) Suppose at a certain instant the kinetic energy is twice the elastic potential energy. Write an equation describing this situation, using only the variables for the mass m, velocity v, spring constant k, and position x. (c) Using the results of parts (a) and (b) and the conservation of energy equation, find the positions x of the object when its kinetic energy equals twice the potential energy stored in the spring. (The answer should in terms of A only.)arrow_forwardSuppose you have a 0.750kg object on a horizontal surface connected to a spring that has a force constant of 150N/m. There is simple friction between me object and surface with a static coefficient of friction =0.100. (a) How far can the spring be stretched without moving the mass? (b) If the object is set into oscillation with an amplitude twice the distance found in part (a), and me kinetic coefficient of friction is k=0.0850, what total distance does it travel before stopping? Assume it starts at me maximum amplitude.arrow_forward
- A spring has a length of 0.200 m when a 0.300kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is The unloaded length of the spring?arrow_forward(a) A hanging spring stretches by 35.0 cm when an object of mass 450 g is hung on it at rest. In this situation, we define its position as x = 0. The object is pulled down an additional 18.0 cm and released from rest to oscillate without friction. What is its position x at a moment 84.4 s later? (b) Find the distance traveled by the vibrating object in part (a), (c) What If? Another hanging spring stretches by 35.5 cm when an object of mass 440 g is hung on it at rest. We define this new position as x = 0. This object is also pulled down an additional 18.0 cm and released from rest to oscillate without friction. Find its position 84.4 s later, (d) Find the distance traveled by the object in part (c). (e) Why are the answers to parts (a) and (c) so different when the initial data in parts (a) and (c) are so similar and the answers to parts (b) and (d) are relatively close? Does this circumstance reveal a fundamental difficulty in calculating the future?arrow_forwardA 2.00-kg block hangs without vibrating at the end of a spring (k = 500. N/m) that is attached to the ceiling of an elevator car. The car is rising with an upward acceleration of g/3 when the acceleration suddenly ceases (at t = 0). (a) What is the angular frequency of oscillation of the block after the acceleration ceases? (b) By what amount is the spring stretched during the time that the elevator car is accelerating?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College