Textbook Question
A certain simple pendulum has a period on the earth of 1.60 s. What is its period on the surface of Mars, where g = 3.71 m/s2?
3
views
Ch 14: Periodic Motion
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 14, Problem 43a
You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take the pendulum bob to reach its highest speed?
Verified step by step guidance1
Understand that the pendulum's motion can be approximated as simple harmonic motion for small angles. The angle given, 3.50°, is small enough to use this approximation.
The period of a simple pendulum is given by the formula: , where is the length of the pendulum and is the acceleration due to gravity (approximately 9.81 m/s²).
Calculate the period using the given length of the pendulum, .
The pendulum reaches its highest speed at the lowest point of its swing, which is halfway through its period. Therefore, the time to reach the highest speed is half of the period: .
Substitute the calculated period into the expression for half the period to find the time it takes for the pendulum bob to reach its highest speed.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Simple Harmonic Motion
Simple harmonic motion (SHM) describes the oscillatory motion of systems like pendulums, where the restoring force is proportional to the displacement. In a simple pendulum, the motion is approximately SHM for small angles, allowing us to use formulas for period and frequency to analyze its motion.
Recommended video:
Guided course
07:52
Simple Harmonic Motion of Pendulums
Pendulum Period
The period of a simple pendulum, which is the time for one complete oscillation, depends on its length and the acceleration due to gravity. It is given by the formula T = 2π√(L/g), where L is the pendulum length and g is the gravitational acceleration. This formula helps determine the timing of various points in the pendulum's swing.
Recommended video:
Guided course
06:28Satellite Period
Kinetic and Potential Energy in Pendulums
In a pendulum, energy oscillates between kinetic and potential forms. At the highest point, energy is all potential, while at the lowest point, it is all kinetic. The pendulum reaches its highest speed at the lowest point, where potential energy is minimal and kinetic energy is maximal.
Recommended video:
Guided course
06:53Energy in Pendulums
Related Practice
Textbook Question
You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. How much time does it take if the pendulum is released at an angle of 1.75° instead of 3.50°?
2
views
Textbook Question
A building in San Francisco has light fixtures consisting of small 2.35-kg bulbs with shades hanging from the ceiling at the end of light, thin cords 1.50 m long. If a minor earthquake occurs, how many swings per second will these fixtures make?
2
views
Textbook Question
A 0.500-kg glider, attached to the end of an ideal spring with force constant k = 450 N/m, undergoes SHM with an amplitude of 0.040 m. Compute the total mechanical energy of the glider at any point in its motion
2
views
Textbook Question
A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is at its highest point.
1
views
Textbook Question
A mass is oscillating with amplitude A at the end of a spring. How far (in terms of A) is this mass from the equilibrium position of the spring when the elastic potential energy equals the kinetic energy?
1
views