Physics, 28.05.2020 20:57 hmskevinjacobo5471

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 which 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

Answers: 2

Show answers

Answers

Answer from: haley5306

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

Answer from: Quest

Ifound this on google “your outer ear collects sound waves and reflects them into a tiny tube called the ear canal. at the end of the ear canal is a thin, skin-like membrane stretched tightly over the opening, called the eardrum.” i hope this you for what your looking for

Answer from: Quest

the moon affects the earth gravitation ally, causing certain motions of that body and also producing tides in its ocean and atmosphere. the tidal wave in our atmosphere is, however, far too minute to be an effective cause in any known meteorological phenomenon.

explanation:

Another question on Physics

Physics, 22.06.2019 15:00

Mechanical energy is when the amount of kinetic and potential energies added together remains the same. conserved created lost

Answers: 1

Answer

Physics, 22.06.2019 19:30

Visualize the problem and identify special cases first examine the problem by drawing a picture and visualizing the motion. apply newton's 2nd law, ∑f⃗ =ma⃗ , to each body in your mind. don't worry about which quantities are given. think about the forces on each body: how are these consistent with the direction of the acceleration for that body? can you think of any special cases that you can solve quickly now and use to test your understanding later? one special case in this problem is if m2=0, in which case block 1 would simply fall freely under the acceleration of gravity: a⃗ 1=−gj^.

Answers: 1

Answer

Physics, 23.06.2019 02:30

If jason ii needs 15 kw of power at 300 volts to operate, what amperage of current must flow through the cable?

Answers: 1

Answer

Physics, 23.06.2019 15:30

Boiling water in a pan is a good example of convection a.the warm water rises and the cooler water sinks. b.the water is touching the bottom of the pan, but not the heat source. c.boiling water can cook hard boiled eggs. d.boiling water is an example of radiation and not convection.

Answers: 2

Answer

You know the right answer?

The 10-kg double wheel with radius of gyration of 125mm about o is connected to the spring of stiffn...

Questions