1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
forsale [732]
3 years ago
6

A mass weighting 48 lbs stretches a spring 6 inches. The mass is in a medium that exerts a viscous resistance of 27 lbs when the

mass has a velocity of 6 ft/sec. Suppose the object is displaced an additional 6 inches and released.
Required:
a. Find an equation for the object's displacement, u(t), in feet after t seconds.
b. What is the mass of the object?
c. What is the damping coefficient?
d. What is the spring constant?
Physics
1 answer:
Mademuasel [1]3 years ago
8 0

Answer:

a)

u(t)=0.499ft.e^{-\frac{144.76lb/s}{2(48lb)}t}cos(\omega t)\\\\u(t)=0.499ft.e^{-1.5t}cos(\omega t)

b)

m = 48lb

c)

b = 144.76lb

Explanation:

The general equation of a damping oscillate motion is given by:

u(t)=u_oe^{-\frac{b}{2m}t}cos(\omega t-\alpha)    (1)

uo: initial position

m: mass of the block

b: damping coefficient

w: angular frequency

α: initial phase

a. With the information given in the statement you replace the values of the parameters in (1). But first, you calculate the constant b by using the information about the viscous resistance force:

|F_{vis}|=bv\\\\b=\frac{|F_{vis}|}{v}\\\\|F_{vis}|=27lbs=27*32.17ft.lb/s^2=868.59ft.lb/s^2\\\\b=\frac{868.59}{6}lb/s=144.76lb/s

Then, you obtain by replacing in (1):

6in = 0.499 ft

u(t)=0.499ft.e^{-\frac{144.76lb/s}{2(48lb)}t}cos(\omega t)\\\\u(t)=0.499ft.e^{-1.5t}cos(\omega t)

b.

mass, m = 48lb

c.

b = 144.76 lb/s

You might be interested in
Trial 1: Get a textbook and put a sheet of paper on top of it. Fold the paper as needed to keep the paper from sticking over the
siniylev [52]

Answer:

1)  the two objects reach the floor at the same time.

2)the book reaches the floor much earlier than the foil

In conclusion, the difference in motion between the two systems subjected to the same acceleration depends on the weight of the body and friction force, when the body has less weight, the friction of the air affects it more

Explanation:

This interesting experiment has the following results

1) first case. Sheet on top of book

In this case the two objects reach the floor at the same time.

This shows that the acceleration in the two objects is the same and we call it the acceleration of gravity.

The speed of the body increases as it goes down linearly.

This occurs because the book that receives air resistance is much heavier, so the resistance has almost no effect on its movement, the sheet does not have the air resistance because it goes down next to the book.

2) second case. Book and sheet next to each other.

In this case the book reaches the floor much earlier than the foil.

This is because the resisting force of the air has almost no effect on the book and its movement is little affected by this force.

In the case of the blade, it has very little weight, therefore as its speed increases, the resistance force of the air rapidly equals the weight of the blade.

           W_sheet - fr = 0

so after this, since the acceleration is zero, it goes down at constant speed, this speed is called the terminal velocity.

In conclusion, the difference in motion between the two systems subjected to the same acceleration depends on the weight of the body and friction force, when the body has less weight, the friction of the air affects it more.

3 0
2 years ago
What would be an example of a chemical change that took a long time to occur
weqwewe [10]
<span>rusting takes a long time, and rusting is a chemical change</span>
3 0
3 years ago
Read 2 more answers
What form of government concentrates power in a central government
spin [16.1K]
The answer is
Unitary system : All government power is held by a central government
8 0
3 years ago
Read 2 more answers
Give two examples of events that show that the speed of sound is very much slower than the speed of light
jeka94

Answer:

1) Lightning, you see the lightning first and then hear the thunder.

2)When a person far away from you hits a ball with a bat, you can see them striking the ball first and then you will hear the sound of ball striking against the bat.

6 0
3 years ago
I. The spring does work on the box from the moment the box first hits the spring to the moment the spring first reaches its maxi
nalin [4]

Answer:

Negative

Explanation:

If the box is heading right in the positive direction, the work will be negative. The spring has an opposite force to that of the box.

Hope this helped. :)

6 0
2 years ago
Other questions:
  • Light of intensity 2.00 W/m2 passes through the pupil of one of your eyes and eventually falls on your retina. The radius of the
    5·1 answer
  • A dog runs with an initial speed if 7.5m/s on a waxed floor. it slides to a stop in 15 seconds. What is the acceleration ​
    6·1 answer
  • Calculated the gravitational potential energy of a 93.0 kg sky diver who is 550 m above the ground
    5·1 answer
  • Can I have help please? Ill need you to explain the answer, so ill put double the points, please dont scam me, i just want to do
    10·1 answer
  • A digital speedometer constantly reads zero mph. Technician A says the problem may be the vehicle speed sensor. Technician B say
    11·1 answer
  • A system of releases 125kJ of heat while 104kJ of work is done in the system. Calcilate the change om imternal energy (in kJ)
    9·1 answer
  • A hollow Spherical conductor of radius 12 cm is
    11·1 answer
  • What would be the path of an object thrown in the air if there was no gravity?
    5·2 answers
  • An aluminum block of mass 12.00 kg is heated from 20 c to 118 c. if the specific heat of aluminum is 913 j-1 kg k-1 then how muc
    8·1 answer
  • A stone of weight 10N falls from the top of a 250m high cliff. a) Calculate how much work is done by the force of gravity in pul
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!