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
Stolb23 [73]
3 years ago
6

You attach a 3.10 kg weight to a horizontal spring that is fixed at one end. You pull the weight until the spring is stretched b

y 0.100 m and release it from rest. Assume the weight slides on a horizontal surface with negligible friction. The weight reaches a speed of zero again 0.400 s after release (for the first time after release). What is the maximum speed of the weight (in m/s)? m/s
Physics
1 answer:
dolphi86 [110]3 years ago
6 0

Answer:

0.785 m/s

Explanation:

Hi!

To solve this problem we will use the equation of motion of the harmonic oscillator, <em>i.e.</em>

x(t) = A cos(\omega t )+B sin(\omega t) - (1)

\frac{dx}{dt}(t) = \omega (B cos(\omega t )- A sin(\omega t) - (1)

The problem say us that the spring is released from rest when the spring is stretched by 0.100 m, this condition is given as:

x(0) = 0.100

\frac{dx}{dt}(0) = 0

Since cos(0)=1 and sin(0) = 0:

x(0)=A

\frac{dx}{dt}(0) = -B\omega

We get

A =0.100\\B = 0

Now it say that after 0.4s the weigth reaches zero speed. This will happen when the sping shrinks by 0.100. This condition is written as:

x(0.4) = - 0.100

Since

x(t) = 0.100 cos(\omega t)\\ -0.100=x(0.4)=0.100cos(\omega 0.4)

This is the same as:

-1 = cos(0.4\omega)

We know that cosine equals to -1 when its argument is equal to:

(2n+1)π

With n an integer

The first time should happen when n=0

Therefore:

π = 0.4ω

or

ω = π/0.4  -- (2)

Now, the maximum speed will be reached when the potential energy is zero, <em>i.e. </em>when the sping is not stretched, that is when x = 0

With this info we will know at what time it happens:

0 = x(t) = 0.100cos(\omega t)

The first time that the cosine is equal to zero is when its argument is equal to π/2

<em>i.e.</em>

t_{maxV}=\pi /(2\omega)

And the velocity at that time is:

\frac{dx}{dt}(t_{maxV} ) =- 0.100\omega sin(\omega t_{maxV})\\\frac{dx}{dt}(t_{maxV} ) =- 0.100\omega sin(\pi/2)\\

But sin(π/2) = 1.

Therefore, using eq(2):

\frac{dx}{dt}(t_{maxV} ) = 0.100*\omega = 0.100\frac{\pi}{0.400} = \pi/4

And so:

V_{max} = \pi / 4 =0.785

You might be interested in
you slide abox of books at constant speed up a30 degree ramp, applying a force of 200 newtons directed up the slope. The coeffic
Tomtit [17]

The work done is 400 J

Explanation:

The work done by you in pushing the box along the slope is given by

W=Fd

where

F is the magnitude of the force applied

d is the distance covered by the box along the slope

Here we have the following:

F = 200 N is the magnitude of the force applied

d=\frac{h}{sin \theta} is the distance covered, where

h = 1 m is the vertical rise

\theta=30^{\circ} is the slope of the plane

Substituting and solving, we find

W=F\frac{h}{sin \theta}=\frac{(200)(1)}{sin 30^{\circ}}=400 J

Learn more about work:

brainly.com/question/6763771

brainly.com/question/6443626

#LearnwithBrainly

5 0
3 years ago
In a solution, the solvent is present in the larger amount. <br> A True <br> B False
lana [24]
Th statement represented above : In a solution, the solvent is present in the larger amount is definitely FALSE. I choose this answer as a correct one as it also could be a solutions of alcohol ot for example <span>walter which means it's not so solid and liquid respectively. Hope it's clear! Regards!</span>
8 0
3 years ago
The SI unit of average spped and velocity.​
Verdich [7]

<em>meter per</em><em> </em><em>second</em><em> </em><em>is </em><em>the </em><em>main </em><em>answer </em><em>of</em><em> </em><em>both</em>

3 0
2 years ago
In a motor, the combined effect of electric currents and magnetic forces turn electrical energy into which of the following?
lord [1]
A motor is built to use all those things and produce mechanical energy.
6 0
3 years ago
Read 2 more answers
Describe the difference between potencial and kinetic energy
avanturin [10]
Potential energy is energy stored in an object. kinetic energy is energy of motion
8 0
3 years ago
Other questions:
  • Which two statements explain how water weathers and erodes rock?
    12·2 answers
  • The temperature of a lead fishing weight rises from 26∘c to 38∘c as it absorbs 11.3 j of heat. what is the mass of the fishing w
    15·1 answer
  • What is the dead load of a bridge
    15·1 answer
  • The speed of an object determines the amount of inertia?
    15·2 answers
  • A wire is placed within a magnetic field, and a current starts to flow through
    6·1 answer
  • Which type of radioactive decay results in no change in mass number and atomic number for the starting nucleus?
    8·1 answer
  • A heat engine cycle is executed with steam in the saturation dome. The pressure of steam is 1.1 MPa during heat addition and 0.3
    14·1 answer
  • How can you show that an electric current has a magnet affect​
    6·1 answer
  • Which of the following, by scientific definition is NOT work? lifting boxes of books, pedaling on your bike, holding a book over
    8·1 answer
  • What is the acceleration at 3 seconds?<br><br> Please explain your answer. Thank you :]
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!