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
almond37 [142]
3 years ago
6

A mass weighing 32 pounds stretches a spring 2 feet. Determine the amplitude and period of motion if the mass is initially relea

sed from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.
Physics
1 answer:
grandymaker [24]3 years ago
5 0

A mass weighing 32 pounds stretches a spring 2 feet.

(a) Determine the amplitude and period of motion if the mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of 6 ft/s.

(b) How many complete cycles will the mass have completed at the end of 4 seconds?

Answer:

A = 1.803 ft

Period = \frac{\pi}{2} seconds

8 cycles

Explanation:

A mass weighing 32 pounds stretches a spring 2 feet;

it implies that the mass (m) = \frac{w}{g}

m= \frac{32}{32}

= 1 slug

Also from Hooke's Law

2 k = 32

k = \frac{32}{2}

k = 16 lb/ft

Using the function:

\frac{d^2x}{dt} = - 16x\\\frac{d^2x}{dt} + 16x =0

x(0) = -1        (because of the initial position being above the equilibrium position)

x(0) = -6          ( as a result of upward velocity)

NOW, we have:

x(t)=c_1cos4t+c_2sin4t\\x^{'}(t) = 4(-c_1sin4t+c_2cos4t)

However;

x(0) = -1 means

-1 =c_1\\c_1 = -1

x(0) =-6 also implies that:

-6 =4(c_2)\\c_2 = - \frac{6}{4}

c_2 = -\frac{3}{2}

Hence, x(t) =-cos4t-\frac{3}{2} sin 4t

A = \sqrt{C_1^2+C_2^2}

A = \sqrt{(-1)^2+(\frac{3}{2})^2 }

A=\sqrt{\frac{13}{4} }

A= \frac{1}{2}\sqrt{13}

A = 1.803 ft

Period can be calculated as follows:

= \frac{2 \pi}{4}

= \frac{\pi}{2} seconds

How many complete cycles will the mass have completed at the end of 4 seconds?

At the end of 4 seconds, we have:

x* \frac{\pi}{2} = 4 \pi

x \pi = 8 \pi

x=8 cycles

You might be interested in
21. Calculate the acceleration of the bus from point D to E. Show your work.
Marat540 [252]

21) Acceleration from D to E: 1 m/s^2

22) The acceleration of the bus from D to E is 1 m/s^2

Explanation:

21)

The acceleration of an object is equal to the rate of change of velocity of the object. Mathematically:

a=\frac{v-u}{t}

where

u is the initial velocity

v is the final velocity

t is the time elapsed

In this problem, we want to measure the acceleration of the bus from point D to point E. We have:

- Initial velocity at point D: u = 0

- Final velocity at point E: v = 5 m/s

- Time elapsed from D to E: t = 21 - 16 = 5 s

Therefore, the acceleration between D and E is

a=\frac{5-0}{5}=1 m/s^2

22) This question is the same as 21), so the result is the same.

Learn more about acceleration:

brainly.com/question/9527152

brainly.com/question/11181826

brainly.com/question/2506873

brainly.com/question/2562700

#LearnwithBrainly

4 0
3 years ago
Which is produced in a synthesis reaction?
yulyashka [42]

Answer:

Single Compound

Explanation:

A synthesis reaction takes two or more reactants and reacts chemically to turn them all into one substance.  

An example of a synthesis reaction is the reaction that takes place between sodium (Na) and chlorine (Cl) to create table salt.

3 0
3 years ago
The turn on voltage for forward basing a PN junction diode is within the range of​
Tems11 [23]

Answer: A PN-junction diode is formed when a p-type semiconductor is fused to an n-type semiconductor creating a potential barrier voltage across the diode junction

Explanation: hope this helped

5 0
3 years ago
If the mass of a materials is 44grams and the volume of the material is 11cm^3 what would the density of the material be
jok3333 [9.3K]
Density =mass/volume
density= (0.044kg/(11 x10^-6)
4000kg/m^3
8 0
3 years ago
A soap box derby car at the top of a ramp has more _________ energy and at the finish line at the bottom of the ramp it has more
astra-53 [7]
Kinetic, potential because, at the top of the ramp it’s going faster. Potential at the bottom of the ramp is potential because, it’s not doing any motion.
5 0
3 years ago
Other questions:
  • A 0.28-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 500 N/m. T
    10·2 answers
  • Which is an example of a physical change? wood rots. gasoline ignites. water evaporates. a nail rusts. description?
    9·2 answers
  • En el mar, la luz visible alcanza una profundidad de aproximadamente 200 metros (zona fotica). ¿De dónde obtienen energías las p
    13·1 answer
  • How to solve 56 equals 1/2 velocity squared
    15·1 answer
  • If the coefficient of friction is 0.3900 and the cylinder has a radius of 2.700 m, what is the minimum angular speed of the cyli
    9·1 answer
  • The least common fossils are those that have been<br> petrified<br> frozen<br> buried<br> distilled
    15·1 answer
  • Identify global climate zones and characteristics of each
    5·1 answer
  • Pretty cool, the atoms that exist in your body are some of the same atoms that have existed since the beginning of the universe.
    9·2 answers
  • Một vật dao động điều hòa có phương trình là x = 4sin(πt + π/3) (cm; s). Lúc t = 0,5s vật có li độ và vận tốc là
    13·1 answer
  • A 2. 7-cm-diameter parallel-plate capacitor has a 1. 8 mm spacing. The electric field strength inside the capacitor is 1. 2×105
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!