Physics, 14.04.2020 18:12 Bringuplana

A potter spins his wheel at 0.98 rev/s. The wheel has a mass of 4.2 kg and a radius of 0.35 m. He drops a chunk of clay of 2.9 kg directly onto the middle of the wheel. The clay is in the shape of a pancake and has a radius of 0.19 m. Assume both the wheel and the chunk of clay can be modeled as solid cylinders (I = ½ MR2 ). What is the new tangential velocity of the wheel and the clay?

Answers: 2

Show answers

Answers

Answer from: historyfanboy101

The tangential velocity of the wheel is 1.79 m/s and the tangential velocity of the clay is 0.97 m/s

From the law of conservation of angular momentum, initial angular momentum = final angular momentum

L = L' + L'' where L = initial angular momentum of wheel, L' = final angular momentum of wheel, and L'' = angular momentum of clay.

Iω = Iω' + I'ω' where

I = rotational inertia of wheel = 1/2MR² where M = mass of wheel = 4.2 kg and R = radius of wheel = 0.35 m, ω = initial angular speed of wheel = 0.98 rev/s = 0.98 × 2π rad/s = 6.16 rad/s, I' = rotational inertia of clay = 1/2mr² where m = mass of clay = 2.9 kg and r = radius of clay = 0.19 m, ω = final angular speed of wheel + clayAngular speed of wheel + clay

So, making ω' subject of the formula, we have

ω' = Iω/(I + I')

ω' = 1/2MR²ω/(1/2MR² + 1/2mr²)

ω' = MR²ω/(MR² + mr²)

Substituting the values of the variables into the equation, we have

ω' = 4.2 kg × (0.35 m)² × 6.16 rad/s/(4.2 kg × (0.35 m)² + 2.9 kg × (0.19 m)² )

ω' = 4.2 kg × 0.1225 m² × 6.16 rad/s/(4.2 kg × 0.1225 m² + 2.9 kg × 0.0361 m² )

ω' = 0.5145 kgm² × 6.16 rad/s/(0.5145 kg m² + 0.1047 kgm)²

ω' = 3.169kgm²rad/s ÷0.6192kgm²

ω' = 5.12 rad/s

The tangential velocity of the wheel

Since tangential speed v = Rω' where

R = radius of wheel = 0.35 m and ω' = angular speed = 5.12 rad/s

So, substituting these into the equation, we have

v = Rω'

v = 0.35 m × 5.12 rad/s

v = 1.792 m/s

v ≅ 1.79 m/s

The tangential velocity of the wheel is 1.79 m/s

The tangential velocity of the clay

Since tangential velocity v' = rω' where

r = radius of clay = 0.19 m and ω' = angular speed = 5.12 rad/s

So, substituting these into the equation, we have

v = rω'

v = 0.19 m × 5.12 rad/s

v = 0.973 m/s

v' ≅ 0.97 m/s

The tangential velocity of the clay is 0.97 m/s

The tangential velocity of the wheel is 1.79 m/s and the tangential velocity of the clay is 0.97 m/s

Learn more about tangential velocity here:

link

Answer from: ArmyAllen00

$v_{f,w} = 1.791\,\frac{m}{s}$ , $v_{f,c} = 0.972\,\frac{m}{s}$

Explanation:

The situation can be modelled by applying the Principle of Angular Momentum Conservation:

$I_{w} \cdot \omega_{o} = (I_{w} + I_{c})\cdot \omega_{f}$

The final angular speed is:

$\omega_{f} = \frac{I_{w}}{I_{w}+I_{c}}\cdot \omega_{o}$

$\omega_{f} = \left(\frac{\frac{1}{2}\cdot (4.2\,kg)\cdot (0.35\,m)^{2} }{\frac{1}{2}\cdot (4.2\,kg)\cdot (0.35\,m)^{2} + \frac{1}{2}\cdot (2.9\,kg)\cdot (0.19\,m)^{2}}\right)\cdot (0.98\,\frac{rev}{s} )\cdot \left(\frac{2\pi\,rad}{1\,rev} \right)$

$\omega_{f} \approx 5.116\,\frac{rad}{s}$

The tangential velocities of the wheel and the clay are, respectively:

$v_{f, w} = (0.35\,m)\cdot (5.116\,\frac{rad}{s} )$

$v_{f,w} = 1.791\,\frac{m}{s}$

$v_{f, c} = (0.19\,m) \cdot (5.116\,\frac{rad}{s} )$

$v_{f,c} = 0.972\,\frac{m}{s}$

Answer from: Quest

The answer is frictional force

Answer from: Quest

You can find results and justify them? you can test your hypothesis

Another question on Physics

Physics, 21.06.2019 21:00

A150 w lamp emits light of wavelength 590 nm uniformly in all directions. what is the photon flux (photons per unit area per unit time) on a small screen at a distance 2.3 m from the lamp? assume the photons are uniformly distributed over the surface of a sphere of radius 2.3 m.

Answers: 2

Answer

Physics, 22.06.2019 05:30

Explain how the energy of rubber ball is tranforned as it roll down a ramp. give evidence that the energy of the og the ball remains the same at all points on the ramp

Answers: 2

Answer

Physics, 22.06.2019 06:00

When you push downward on a book at rest on a table, you feel an upward force. does this force depend on friction? defend your answer.

Answers: 2

Answer

Physics, 22.06.2019 10:00

Which fact supports the conclusion that there will be fewer farm managers in the future? a) a farmer manager’s duties vary by the type of farm. b) farm technology is replacing some administrative jobs c) farm managers often need experience but not education. d) administrative duties include budgeting and training staff.

Answers: 2

Answer

You know the right answer?

A potter spins his wheel at 0.98 rev/s. The wheel has a mass of 4.2 kg and a radius of 0.35 m. He dr...

Questions