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
hram777 [196]
3 years ago
10

To start a lawn mower, you must pull on a rope wound around theperimeter of a flywheel. After you pull the rope for 0.95 s, thef

lywheel is rotating at 4.5 revolutions per second, at which pointthe rope disengages. This attempt at starting the mower does notwork, however, and the flywheel slows, coming to rest 0.24 s afterthe disengagement. Assume constant acceleration during both spin-upand spin-down.
(a) Determine the average angularacceleration during the 4.5-s spin-up and again during the 0.24-sspin-down.

(b) What is the maximum angular speed reachedby the flywheel?

(c) Determine the ratio of the number ofrevolutions made during spin-up to the number made duringspin-down.
Physics
1 answer:
Molodets [167]3 years ago
3 0

Answer:

29.76245 rad/s², -117.80972 rad/s²

28.2743 rad/s

3.95833

Explanation:

\omega_f = Final angular velocity

\omega_i = Initial angular velocity

\alpha = Angular acceleration

\theta = Angle of rotation

t = Time taken

Equation of rotational motion

\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\frac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\frac{4.5\times 2\pi-0}{0.95}\\\Rightarrow \alpha=29.76245\ rad/s^2

Angular acceleration during speed up is 29.76245 rad/s²

\omega_f=\omega_i+\alpha t\\\Rightarrow \alpha=\frac{\omega_f-\omega_i}{t}\\\Rightarrow \alpha=\frac{0-4.5\times 2\pi}{0.24}\\\Rightarrow \alpha=-117.80972\ rad/s^2

Angular acceleration during spin down is -117.80972 rad/s²

Angular speed is given by

\omega=2\pi 4.5=28.2743\ rad/s

Maximum angular speed reached by the flywheel is 28.2743 rad/s

\theta=\omega_it+\frac{1}{2}\alpha t^2\\\Rightarrow \theta=0\times t+\frac{1}{2}\times 29.76245\times 0.95^2\\\Rightarrow \theta=13.4303\ rad

\theta=\omega_it+\frac{1}{2}\alpha t^2\\\Rightarrow \theta=2\pi 4.5\times 0.24+\frac{1}{2}\times -117.80972\times 0.24^2\\\Rightarrow \theta=3.39292\ rad

The ratio would be \dfrac{13.4303}{3.39292}=3.95833

You might be interested in
An object is 50 cm from a converging lens with a focal length of 40 cm . A real image is formed on the other side of the lens, 2
Leno4ka [110]

Answer:

d) -4.0

Explanation:

The magnification of a lens is given by

M=-\frac{q}{p}

where

M is the magnification

q is the distance of the image from the lens

p is the distance of the object from the lens

In this problem, we have

p = 50 cm is the distance of the object from the lens

q = 250 cm - 50 cm is the distance of the image from the lens (because the image is 250 cm from the obejct

Also, q is positive since the image is real

So, the magnification is

M=-\frac{200 cm}{50 cm}=-4.0

7 0
3 years ago
A 1.05 kg block slides with a speed of 0.865 m/s on a frictionless horizontal surface until it encounters a spring with a force
djyliett [7]

Answer:

a) U = 0 J    

k = 0.393 J

E = 0.393 J

b) U = 0.0229J

k = 0.370 J

E = 0.393 J

c) U = 0.0914 J

k = 0.302 J

E = 0.393 J

d) U = 0.206 J

k = 0.187 J

E = 0.393 J

e) U = 0.366 J

k = 0.027 J

E = 0.393 J

Explanation:

Hi there!

The equations of kinetic energy and elastic potential energy are as follows:

k = 1/2 · m · v²

U = 1/2 · ks · x²

Where:

m = mass of the block.

v = velocity.

ks = spring constant.

x = displacement of the string.

a) When the spring is not compressed, the spring potential energy will be zero:

U = 1/2 · ks · x²

U = 1/2 · 457 N/m · (0 cm)²

U = 0 J

The kinetic energy of the block will be:

k = 1/2 · m · v²

k = 1/2 · 1.05 kg · (0.865 m/s)²

k = 0.393 J

The mechanical energy will be:

E = k + U = 0.393 J + 0 J = 0.393 J

This energy will be conserved, i.e., it will remain constant because there is no work done by friction nor by any other dissipative force (like air resistance). This means that the kinetic energy will be converted only into spring potential energy (there is no thermal energy due to friction, for example).

b) The spring potential energy will be:

U = 1/2 · 457 N/m · (0.01 m)²

U = 0.0229 J

Since the mechanical energy has to remain constant, we can use the equation of mechanical energy to obtain the kinetic energy:

E = k + U

0.393 J = k + 0.0229 J

0.393 J - 0.0229 J = k

k = 0.370 J

c) The procedure is now the same. Let´s calculate the spring potential energy with x = 0.02 m.

U = 1/2 · 457 N/m · (0.02 m)²

U = 0.0914 J

Using the equation of mechanical energy:

E = k + U

0.393 J = k + 0.0914 J

k = 0.393 J - 0.0914 J = 0.302 J

d) U = 1/2 · 457 N/m · (0.03 m)²

U = 0.206 J

E = 0.393 J

k = E - U = 0.393 J - 0.206 J

k = 0.187 J

e) U = 1/2 · 457 N/m · (0.04 m)²

U = 0.366 J

E = 0.393 J

k = E - U = 0.393 J - 0.366 J = 0.027 J.

4 0
3 years ago
A man pushes on a wall what does Newton third law say must happen
Verdich [7]
If a man pushes on a wall with some force then according to Newton's third law, wall will also apply force on man with same magnitude but opposite in direction.
8 0
3 years ago
Read 2 more answers
All of the following are types of symbiotic relationships except for
nevsk [136]
The answer is D. the way I remember it is they all end with -alism.

3 0
3 years ago
Find the Kinetic Energy of a<br>trailer of mass 30,000 kg moving at a<br>Speed of 60 km/h​
olasank [31]

Explanation: Formulas you need to use:

K=0.5mass(Velocity^2)

km/h / 3.6 ===>M/S

Step 1:

convert km/h to m/s

Put the values in the formula :

3 0
3 years ago
Other questions:
  • Please help on this one? PLEASE.
    14·1 answer
  • Which celestial body would have the strongest gravitational pull on a satellite orbiting 100 km above its surface?
    9·2 answers
  • Where does every piece of matter begin?
    11·1 answer
  • a car travelling at 50km/h from rest covers a distance of 10km in 40minutes. Calculate the acceleration​
    9·1 answer
  • The average standard rectangular building brick has a mass of 3.10 kg and dimensions of 225 m x 112 m x 75 m. The gravitational
    8·1 answer
  • An electric flux of 147 N*m^2/C passes through a flat horizontal surface that has an area of 0.824 m^2. The flux is due to a uni
    11·1 answer
  • Plz help...Thanks.
    6·1 answer
  • Hybrid plants usually have increased Vigar true or false
    5·1 answer
  • Can someone please answer this, ill give you brainliest and your getting 100 points.
    5·2 answers
  • If the conductivity of the solution is NOT affected by increasing the solute concentration, what does that indicate about both t
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!