Physics 1021 Lecture Notes - Lecture 9: Sound, Circular Motion, Bungee Jumping

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5 Dec 2016

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Chapter 3: mechanical objects [spring force, circular motion] Consider a spring with no weight is attached. The end point of the spacing is located at x=0. Its end point is extended to distance x. Hooke"s law: the spring force actin on the ball is equal to a spring constant times the distance the spring is distorted (x) Direction: the force is directed opposite the displacement (x). Hanging grocery scale has a spring in it: spring extension, the weight is acting downwards and the the string is acting upwards. Bathroom scale has a hidden spring: spring compressed. It stretched the spring x=0. 01m and spring constant is k=2000n/m. 0 = kx-mg kx = mg mg = kx = 2000 x 0. 01 = 20n. A student is attached to a bungee jumping rope of length 100m. If the spring constant is k=1000n/m/ find the weight of the student. Weight = kx = 1000 x 2 = 2000.

Related Questions

14.29 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 (a) the maximum speed of the glider; (b) the speed of the glider when it is at x = -0.015 m; (c) the magnitude of the maximum acceleration of the glider; (d) the acceleration of the glider at x = -0.015 m; (e) the total mechanical energy of the glider at any point in its motion.

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

6.) A mass of 0.2 kg attached to a spring oscillates onafrictionless horizontal surface. Its motion is described by x=0.05 m cos(50 rad/s t + 1.57 rad). Find a) the frequencyandperiod; b) the maximum velocity and acceleration; c) theforceconstant and the mechanical energy.

7. A traveling wave in a string of linear density 0.01 kg permeteris described by thewavefunction y =0.02 msin(50 rad/m x - 1750 rad/s t). Find a) the directionofpropagation; b) the wave length and the period; c) the wavespeedand the tension in the string.

8. A copper wire of cross section area 0.04 cm²andlength 1.2 m is heated from the room temperature 20⁰Cto 40 ⁰C. Find a) the change of its lengthin theprocess; b) the force needed at each end if it were stretchedat T= 20 ⁰C with the same extension. ( The coefficientoflinear expansion for copper is 1.7 x 10^-5 /K .TheYoung's modulus for copper is 1.1 x 10¹¹N/m².)

Physics 1021 Lecture Notes - Lecture 9: Sound, Circular Motion, Bungee Jumping

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