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
N76 [4]
3 years ago
5

A certain spring is found not to obey Hooke’s law; it exerts a restoring force Fx(x)=−αx−βx2 if it is stretched or compressed, w

here α=60.0N/m and β=18.0N/m2. The mass of the spring is negligible. (a) Calculate the potential-energy function U(x) for this spring. Let U = 0 when x = 0. (b) An object with mass 0.900 kg on a frictionless, horizontal surface is attached to this spring, pulled a distance 1.00 m to the right (the +x-direction) to stretch the spring, and released. What is the speed of the object when it is 0.50 m to the right of the x = 0 equilibrium position?
Physics
1 answer:
Masteriza [31]3 years ago
4 0

Answer:U(x) = 30x^2 +6x^3

V^2=8.28m/s

Explanation:The law of conservation of energy is given by K1+U1= K2+U2 ...eq 1

Kinetic energy K.E= 1/2 mv^2

Restoring force function F(x)= -60x - 18x^2

But F(x)= -dU/dx

dU(x)=-F(x)dx

Integrating U(x)= -integral F(x)dx + U(0)

Substituting, we get

U(x) = - integral(-60x-18x^2)dx+U(0)

U(x)= 30x^2+6x^3+U(0)

U=0 at x=0

Therefore U(x)= 30x^2+6x^3

b) Given : x1=1.00m,x2= 0.50m ,V1=0, V2=?

Substituting into eq (a)

U1= 30(1.00)^2+6(1.00)^3=36J

Using x2=0.5 into eq(a)

U2=30(0.50)^2+6(0.50)^3=8.25J

Object at rest K1=0

0+36=K2+8.25

K2=27.75J

Given; m =0.900kg, V2=?

27.75=1/2×0.900×V2^2

V2= SQRT(2×27.75)/0.81

V2= 8.28m/s

You might be interested in
slader Question: A Model Rocket Is Launched Straight Upward With An Initial Speed Of 50m/s. Iit Accelerates With A Constant Upwa
xenn [34]

Answer:

Maximum height reached by the rocket is

y_{max} = 308 m

total time of the motion of rocket is given as

T = 16.44 s

Explanation:

Initial speed of the rocket is given as

v_i = 50 m/s

acceleration of the rocket is given as

a = 2 m/s^2

engine stops at height h = 150 m

so the final speed of the rocket at this height is given as

v_f^2 - v_i^2 = 2 a d

v_f^2 - 50^2 = 2(2)(150)

v_f = 55.68 m/s

so maximum height reached by the rocket is given as the height where its final speed becomes zero

so we will have

v_f^2 - v_i^2 = 2 a d

0 - 55.68^2 = 2(-9.81)(y - 150)

y_{max} = 308 m

Now the total time of the motion of rocket is given as

1) time to reach the height of 150 m

v_f - v_i = at

55.68 - 50 = 2 t

t_1 = 2.84 s

2) time to reach ground from this height

\Delta y = v_y t + \frac{1}{2}gt^2

-150 = 55.68 t - \frac{1}{2}(9.81) t^2

t_2 = 13.6 s

so total time of the motion of rocket is given as

T = 13.6 + 2.84 = 16.44 s

3 0
3 years ago
A block is resting on a platform that is rotating at an angular speed of 2.4 rad/s. The coefficient of static friction between t
Sloan [31]

Answer:

r = 0m is the Minimum distance from the axis at which the block can remain in place wothout skidding.

Explanation:

From a sum of forces:

Ff = m*a   where Ff = μ * N    and a = \frac{V^2}{r}=\omega^2*r

N - m*g = 0   So, N = m*g.   Replacing everything on the original equation:

\mu*m*g = m*\omega^2*r   (eq2)

Solving for r:

r = \frac{\mu*g}{\omega^2}=1.41m

If we analyze eq2 you can conclude that as r grows, the friction has to grow (assuming that ω is constant), so the smallest distance would be 0 and the greatest 1.41m. Beyond that distance, μ has to be greater than 0.83.

4 0
2 years ago
Two spectators at a soccer game in Montjuic Stadium see, and a moment later hear, the ball being kicked on the playing field. Th
Akimi4 [234]

Answer:

a) The distance of spectator A to the player is 79.2 m

b) The distance of spectator B to the player is 43.9 m

c) The distance between the two spectators is 90.6 m

Explanation:

a) Knowing the time it takes the sound to reach both spectators, we can calculate their position relative to the player, using this equation:

x = v * t

where:

x = position of the spectators

v = speed of sound

t = time

Then, the position for spectator A relative to the player is:

x = 343 m/s * 0.231 s = 79.2 m

b)For spectator B:

x = 343 m/s * 0.128 s

x = 43.9 m

The distance of spectator A and B to the player is 79.2 m and 43.9 m respectively.

c) To calculate the distance between the spectators, please see the attached figure. Notice that the distance between the spectators is the hypotenuse of the triangle formed by the sightline of both. We already know the longitude of the two sides. Then, using Pythagoras theorem:

(Distance AB)² = A² + B²

(Distance AB)² = (79.2 m)² + (43.9 m)²

Distance AB = 90. 6 m

6 0
3 years ago
Use the drop-down menus to identify the type of energy each phrase describes.
Tresset [83]

The shortest wavelength of visible light = violet light

Energy that can be felt as heat but not seen = infrared

Short, invisible rays that can cause eye damage = ultraviolet

Visible light with the longest wavelength = red light

Explanation:

Electromagnetic waves are waves consisting of oscillations of the electric and the magnetic field, occurring in a plane perpendicular to the direction of motion the wave.

They are the only type of waves able to travel without a medium, and they are transverse in nature.

All electromagnetic waves travel in a vacuum at the speed of light, which value is:

c=3.0\cdot 10^8 m/s

Electromagnetic waves are classified into 7 different classes, depending on their wavelength/frequency, and they have different properties. From shortest to longest wavelength (and from highest to lowest frequency), they are:

Gamma rays

X rays

Ultraviolet

Visible light

Infrared radiation

Microwaves

Radio waves

Moreover, the visible light of the spectrum is further divided into different colors, according to how our eye perceive them; from shortest to longest wavelength:

violet

blue

green

yellow

orange

red

Therefore, we have:

  • The shortest wavelength of visible light is violet light, which has wavelength between 380 and 450 nm
  • The longest wavelength of visible light is red light, which has wavelenght between 620 and 750 nm
  • Infrared radiation is a type of radiation that is felt as heat by our body, however it cannot be seen because it falls outside the spectrum of visible light
  • Ultraviolet radiation is also invisible to human eye; it has shorter wavelength than visible light and therefore it has more frequency (and more energy), therefore it can cause damage, especially to the eye

Learn more about electromagnetic waves:

brainly.com/question/9184100

brainly.com/question/12450147

#LearnwithBrainly

5 0
3 years ago
Read 2 more answers
Compare and contrast Ursa Major and the Milky Way
Natali [406]
One thing thats the same is there both universes.

One thing diffrent is that in the milky way there is proven life on earth but ursa major is proven without life.
7 0
2 years ago
Other questions:
  • Describe a change caused by kinetic energy as well as a change that involves potential energy
    12·2 answers
  • A 75-m-long train begins uniform acceleration from rest. the the train has a speed of 23 m/s when it passes a railway worker tan
    5·1 answer
  • What weather condition creates a tornado?
    15·1 answer
  • If the change in velocity increases, what happens to the acceleration during the same time period?
    14·2 answers
  • Can someone help me please it is number 7
    7·1 answer
  • Air at 1.3 bar, 500 K and a velocity of 40 m/s enters a nozzle operating at steady state and expands adiabatically to the exit,
    6·1 answer
  • Im just so confused on this how can dogs eat raw meat without getting sick but they cant eat chocolate but hoomanz cant eat raw
    6·2 answers
  • A projectile lands at the same height from which it was launched. which initial velocity will result
    6·1 answer
  • A bicyclist travels the first 1600 m of a trip at an average speed of 8 m/s, travels the next 1200 m in 90 s and spends the last
    12·1 answer
  • DeWayne meets a potential employer at a restaurant, who gives him a phone number. Because he doesn't have anything to write with
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!