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
sergiy2304 [10]
2 years ago
7

A wheel has a radius of r = 2.0 m and it rolls down a smooth incline. The height of the incline is h = 8.0 m . What is the angul

ar velocity ω of the wheel at the bottom of the incline?
Express your answer in radians per second.
Physics
2 answers:
Zolol [24]2 years ago
7 0

The angular velocity of the wheel depends on the mass, radius and the

mode of rotation of the wheel (with or without slipping).

  • The angle velocity at the bottom of the incline, ω ≈ <u>4.43 rad/sec</u>

Reasons:

The given parameters are;

Radius of the wheel, r = 2.0 m

Height of the incline, h = 8.0 m

Required:

Angular velocity of the wheel at the bottom of the incline.

Solution:

The potential energy of the wheel at the top of the hill, P.E. = m·g·h

Sum \ of \  the \  kinetic  \ energy  \ of  \ the \  wheel,  \ K.E. = \mathbf{\displaystyle \frac{1}{2} \cdot m \cdot v^2 + \frac{1}{2} \cdot I \cdot \omega ^2}

Where;

v = The translational velocity of the wheel = ω·r

I = The moment of inertia of the wheel = m·r²

Therefore'

Sum \ of \   K.E. = \displaystyle \frac{1}{2} \cdot m \cdot (\omega \cdot r)^2 + \frac{1}{2} \cdot m \cdot r^2 \cdot \omega ^2 =  \mathbf{m \cdot r^2 \cdot  \omega^2}

At the bottom of the hill, the potential energy is converted to kinetic energy

Therefore;

P.E. = Sum of K.E.

m·g·h = m·r²·ω²

g·h = r²·ω²

\displaystyle \omega = \sqrt{ \frac{g \cdot h}{r^2} } = \mathbf{ \frac{\sqrt{g \cdot h} }{r}}

Where;

g = Acceleration due to gravity ≈ 9.81 m/s²

Therefore;

\displaystyle \omega = \frac{\sqrt{9.81 \times 8} }{2} \approx \mathbf{ 4.43}

  • The angular velocity of the of the wheel at the bottom of the incline, ω ≈ 4.43 rad/sec

Learn more about the law of conservation of energy here:

brainly.com/question/4723473

brainly.com/question/2292427

brainly.com/question/816294

zepelin [54]2 years ago
4 0

The angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec

The angular velocity (ω) of an object is the rate at which the object's angle position is changing in relation to time.

For a wheel attached to an incline angle, the angular velocity can be computed by considering the conservation of energy theorem.

As such the total kinetic energy (K.E) and rotational kinetic energy (R.K.E) at a point is equal to the total potential energy (P.E) at the other point.

i.e.

P.E = K.E + R.K.E

\mathbf{mgh = \dfrac{1}{2}m(r \times \omega)^2 + \dfrac{1}{2}\times I \times \omega^2}

\mathbf{gh = \dfrac{1}{2}(r \times \omega)^2 + \dfrac{1}{2}\times r^2 \times \omega^2}

\mathbf{2 \times \dfrac{gh}{r^2} =\omega^2 +  \omega^2}

\mathbf{2 \omega^2=2 \times \dfrac{9.81 \times 8 m }{2.0 ^2}  }

\mathbf{\omega^2=\dfrac{39.24 }{2}}

\mathbf{\omega=\sqrt{19.62 } \ rad/sec}

\mathbf{\omega=4.429 \ rad/sec}

Therefore, we can conclude that the angular velocity of the wheel at the bottom of the incline is 4.429 rad/sec

Learn more about angular velocity here:

brainly.com/question/1452612

You might be interested in
An archer fish launches a droplet of water from the surface of a small lake at an angle of 70° above the horizontal. He is aimin
Norma-Jean [14]

Answer:

a). v=2776 m/s

Explanation:

The speed of the water droplet for the fish be successful is

Taking the distance in axis 'x' and 'y'

x_{tx}=40cm\frac{1m}{100cm}=0.40m\\x_{ty}=23cm\frac{1m}{100cm}=0.23m

The time is the velocity in axis 'x' with the angle 70 so

t=\frac{0.40m}{v_{x}*cos(70)}

Now using the time in terms of velocity the motion in axis 'y' can find the velocity to be the fish successful

x_{yf}=x_{yo}+v_{o}*t+\frac{1}{2}*g*t^{2}\\0.23m=0.40m\frac{vo*sin(70)}{vo*cos(70)} +\frac{1}{2}*9.8*(\frac{0.40}{vo*cos(70)} )^{2}\\0.23m=0.40m*vo*tan(70)+4.9*(\frac{0.16m^{2} }{vo^{2} *cos(70)^{2} }) \\vo^{2}cos(70)^{2}=\frac{0.16m^{2} }{0.177}\\vo=\sqrt{\frac{0.9021}{cos(70)^{2}}} \\vo=2.776 \frac{m}{s}

4 0
3 years ago
Why is hip-hop &amp; Zumba dance exercises so popular? does dancing make you a better person?
Studentka2010 [4]

Answer:

not realy

Explanation:

dancing is a way of exercise and liking a song or you're just happy etc.

7 0
3 years ago
The radius of a small ball is around 3.79747 cm. The radius of a basketball is about 3.16 times larger. What is the ratio of the
Svetradugi [14.3K]

Explanation:

The ratio of the areas is the square of the ratio of the radii.

A/A = 3.16² = 9.99

The ratio of the volumes is the cube of the ratio of the radii.

V/V = 3.16³ = 31.6

3 0
3 years ago
The first and second coils have the same length, and the third and fourth coils have the same length. They differ only in the cr
stealth61 [152]

Answer:

\frac{R_2}{R_1}=\frac{A_1}{A_2}\\\frac{R_4}{R_3}=\frac{A_3}{A_4}

Explanation:

The resistance of a conductor is directly proportional to its length and is inversely proportional to its cross-sectional area, this dependence is given by:

R=\frac{\rho L}{A}

\rho is the material's resistance, L is the legth and A is the cross-sectional area.

For the first and second coils, we have:

R_1=\frac{\rho L}{A_1}\\R_2=\frac{\rho L}{A_2}\\\rho L=R_1A_1\\\rho L=R_2A_2\\R_1A_1=R_2A_2\\\frac{R_2}{R_1}=\frac{A_1}{A_2}

For the third and fourth coils, we have:

R_3=\frac{\rho L'}{A_3}\\R_4=\frac{\rho L'}{A_4}\\\rho L'=R_3A_3\\\rho L'=R_4A_4\\R_3A_3=R_4A_4\\\frac{R_4}{R_3}=\frac{A_3}{A_4}

6 0
3 years ago
A 350-g mass is attached to a spring whose spring constant is 64 N/m. Its maximum acceleration is 5.3 m/s2. What is the frequenc
max2010maxim [7]

The frequency of oscillation is 2.153 Hz

What is the frequency of spring?

Spring Frequency is the natural frequency of spring with a weight at the lower end. Spring is fixed from the upper end and the lower end is free.

For the mass-spring system in this problem,

The Frequency of spring is calculated with the equation:

f = \frac{1}{2\pi } \sqrt{\frac{k}{m} }

Where,

f = frequency of spring

k = spring constant = 64 N/m

m = mass attached to spring = 350g = 0.350 kg

a = maximum acceleration = 5.3 m/s^2

Substituting the values in the equation,

f = \frac{1}{2\pi } \sqrt{\frac{64}{0.350} }

f = \frac{1}{2\pi } ( 13.522)

f = 2.1535 Hz

Hence,

The frequency of oscillation is 2.153 Hz

Learn more about frequency here:

<u>brainly.com/question/13978015</u>

#SPJ4

6 0
1 year ago
Other questions:
  • Why is it hard to breath on top of a mountain?
    5·1 answer
  • A rubber toy duck is at rest on an inclined plane. When the angle of inclination of the plane is increased to 36.0°, the toy duc
    14·1 answer
  • 4. You make the following measurements of an object: 42 kg and 22 m3. What would the object’s density be?
    13·1 answer
  • A photon of wavelength 3.7 nm Compton scatters from an electron at an angle of 90°. What is the modified wavelength? (Enter your
    7·2 answers
  • A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains
    9·1 answer
  • What type of waves carry energy at a right angle to the direction of the energy flow?
    12·2 answers
  • Does mass affect the final velocity of an object if the object begins with a high initial velocity? Why or why not?
    9·1 answer
  • What are Radio Waves?
    11·2 answers
  • If three balls of different materials were dropped at the same time from the same height, which would hit the ground first? (Ass
    7·1 answer
  • Is the force of gravity that attracts my body to the Earth related to the force of gravity between the planets and the Sun
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!