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
AveGali [126]
3 years ago
15

The 10-kg double wheel with radius of gyration of 125mm about o is connected to the spring of stiffness k = 600 n/m by a cord wh

ich is wrapped securely around the inner hub. if the wheel is released from rest on the incline with the spring stretched 225 mm, calculate the maximum velocity v of its center o during the ensuing motion. the wheel rolls without slipping
Physics
1 answer:
morpeh [17]3 years ago
7 0

Answer:

Explanation:

Here, spring constant is (k) and the inclination angle of the surface is θ

The initial and final positions of the double wheel are considered. Then change in gravitational potential energy, change in kinetic energy, and the change in elastic potential energy of spring are calculated.

Calculate the change in total kinetic energy

\Delta T=\frac{1}{2} mv^2+\frac{1}{2} Iw^2\\\\=\frac{1}{2} mv^2+\frac{1}{2} (mk^2)(\frac{v}{r} )^2

Here, mass of the double wheel is m

velocity of the wheel is v

mass moment of inertia of the wheel is I

angular velocity of the wheel is ω

the radius of gyration of the wheel is k

Substitute 10kg for m, 0.125 for k and 0.2 for r

\Delta T =\frac{1}{2} (10kg)v^2+\frac{1}{2} *10kg*(0.125)^2*(\frac{v}{0.2} )^2\\\\=6.953v^2

Determine the inclination of the surface with horizontal.

\theta = \tan ^-^1(\frac{1}{5} )\\\\=11.31^\circ

Calculate the change in gravitational potential energy

\Delta V= mg(x \sin \theta)

Here, acceleration due to gravity is g

and the displacement of wheel in horizontal direction is x

Substitute 10kg for m, 9.81m/s² for g, 11.31° for θ

\Delta V= 10*9.81*(x \sin 11.31^\circ)\\\\=19.23x

The angle rotated by the wheel α to move x distance is obtained as

x=200\alpha

\alpha =\frac{x}{200}

Calculate the stretch in the spring

s = (200+75)\alpha

substitute x/200 for α

s=(200+75)\frac{x}{200} \\\\=1.375x

Calculate the final stretch in the spring.

x_2=0.225-s

substitute 1.375x for s

x_2=0.2225-1.375x

Calculate the change in the elastic potential energy of the spring

\Delta V_e = \frac{1}{2} k(x_2^2-x^2_1)

Substitute 600N/m for k, 0.225 for x₁ and (0.225 - 1.375x) for x₂

\Delta V_e = \frac{1}{2} *600((0.225-1.375x)^2-(0.225)^2)\\\\=567.18x^2-185.62x

Write the conservation of energy equation for the initial and final positions of the wheel.

\Delta T+\Delta V+\Delta V_e = 0

Substitute 6.953v² for ΔT, 19.23x for ΔV and (567.18x² - 185.62x) for ΔV_e

6.953v^2+19.23x+(567.18x^2-185.62x)=0\\\\\v^2=-81.573x62+23.931x---(1)..........(1)

Calculate the value of  x for which maximum velocity is obtained by differentiating

\frac{d}{dx} (v) = 0

Differentiate Equation (1) with respect to x.

2v\frac{dv}{dx} =-(2 \times 81.573)x+23.931

Substitute 0 for dv/dx

2v(0)=-(2*81.573)x+23.931\\\x=0.1467m

Substitute 0.1467 m in Equation (1)

v^2=-81.573(0.1467m)^2+23.931(0.1467m)\\\\v=1.325m/s

The maximum velocity of the wheel’s center O is 1.325 m/s

You might be interested in
Joan wants to take a 30.0N object up to the 3rd floor of her office building,which is 10m above the ground floor.It is too big t
34kurt
P=W/t
P=F×s/t
P=30×10/5= 60 W
5 0
3 years ago
What is Aristotle famous for?
Mila [183]

Answer:

History

Explanation:

Im. Sorry. Im. Not. Much. Help

8 0
3 years ago
11 Design Imagine that a scientistdiscovered a way to make africtionless surface. What wouldbe some useful applications forthis
m_a_m_a [10]

Answer:

You could move something across the Earth with a little push. It would make fuel really efficient on those pathways. You could make a floor that is impossible to walk on. Everybody would just fall without traction.

Explanation:

3 0
3 years ago
An accepted value for the acceleration due to gravity is 9.801 m/s2. In an experiment with pendulums, you calculate that the val
Fed [463]

g Generally the accepted value of acceleration due to gravity is 9.801 m/s^2

as per the question the acceleration due to gravity is found to be 9.42m/s^2 in an experiment performed.

the difference between the ideal and observed value is 0.381.

hence the error is -\frac{0.381}{9.801} *100

                                                            =3.88735 percent

the error is not so high,so it can be  accepted.

now we have to know why this occurs-the equation of time period of the simple pendulum is give as-T=2\pi\sqrt[2]{l/g}

                                                      g=4\pi^2\frac{l}{T^2}

As the experiment is done under air resistance,so it will affect to the time period.hence the time period will be more which in turn decreases the value of g.

if this experiment is done in a environment of zero air resistance,we will get the value of g which must be approximately equal to 9.801  m/s^2

5 0
3 years ago
Dan is 50 years old, is beginning to look back at the successes and failures in his life, and hopes to use this reflection to de
Mice21 [21]

Answer:

C. Midlife Crisis.

Explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Another machine uses aninput force of 200 newtons to produce an output force of 80 newtons
    9·1 answer
  • Identify whether the features and functions belong to the Hubble Space Telescope or the ALMA radio telescope. 1.installed on lan
    11·2 answers
  • Arun places a beaker of water on a hotplate and turns the hotplate on. The temperature in the room is 25 ºC. After the water hea
    8·1 answer
  • What is the electrostatic force between and electron and a proton separated by 0.1 mm? 2.3 × 10^-20N, attractive.
    5·1 answer
  • if a current of 0.01 A is flowing through a circuit with two resistors in a series what is the voltage?
    8·1 answer
  • A 1.0 kg cart moving at 2.0 m/s collides with a stationary 2.0 kg cart.how fast do the two move together if they become stuck to
    15·1 answer
  • Which options lists a form of kinetic energy followed by a form of potential
    14·1 answer
  • Which of the following statements is true? Thunderstorms are not dangerous The eye of a hurricane is the most danger Tornadoes f
    6·1 answer
  • A skydiver, with a mass of 60 kg is falling at a velocity of 30 m/s. Calculate his kinetic energy.
    12·1 answer
  • A car travels 30 kilometers north for 2 hours, then travels 45 kilometers east for 3 hours. The car then drives south for 30 kil
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!