PHYS 101 Lecture Notes - Lecture 19: Circular Motion, Equilibrium Point, Angular Velocity

49 views6 pages

cerisegiraffe538

7 Dec 2017

School

Department

Course

Professor

For unlimited access to Class Notes, a Class+ subscription is required.

coffeemanatee724 and 28 others unlocked

PHYS 101 Full Course Notes

Verified Note

26 documents

Document Summary

Why ? recall (where k is the spring constant). x=0 is the equilibrium position,and +ve x is towards extension (to right, here). Restoring force . force pushes object back to original position. Period t is time for one complete cycle of the motion; related to frequency f (in cycles/sec, or rev/sec) by: = ka2 ie. the total energy in a harmonic oscillator is proportional to the the oscillation. = k xmax2 = mv2 + kx2 v2 = (2e kx2)/m = (ka2 kx2)/m = (k/m) (a 2 -x 2 ) = (ka2/m) (1- (x2/a2) ) A is the amplitude, in meters, is the max distance from equilibrium. Giancoli example 11-4: spring stretches 0. 150 m when a 0. 300 kg mass is lowered gently on it. spring is then setup horizontally with the same mass on a frictionless table, and pulled 0. 100 m from the equilibrium point. = vmax [ (a2 x2) / a] v = vmax (1 (x2/a2) )

Related Questions

Good Vibes: Introduction to Oscillations

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗ is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.

(d) move to the left until it reaches x=−A and then begin to move to the right.

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged

(b) doubled

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M

(d) L and N

(e) M and P

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

emeraldyak680

PHYS 101 Lecture Notes - Lecture 19: Circular Motion, Equilibrium Point, Angular Velocity

PHYS 101 Full Course Notes

Document Summary

Get access

Related textbook solutions

Physics: Principles with Applications

Related Documents

PHYS 101 Lecture Notes - Fundamental Frequency, Standing Wave, Particle Velocity

PHYS 101 Lecture Notes - Equilibrium Point, Circular Motion

PHYS 101 Chapter Notes - Chapter 11: Simple Harmonic Motion, Transverse Wave, Longitudinal Wave

Related Questions