PHYSICS COLLEGE

A hollow sphere of radius 0.25 m is rotating at 13 rad/s about an axis that passes through its center. the mass of the sphere is 3.8 kg. assuming a constant net torque is applied to the sphere, how much work is required to bring the sphere to a stop?

Answers

Answer 1

Answer:

The work required to bring the sphere to stop is equal to the kinetic energy possessed by the sphere.

Kinetic energy of a rotating body is given by,

K.E = $(1)/(2)Iw^(2)$

Here, I= Moment of inertia of hollow sphere,

Since, the hollow sphere is rotating about the axis passing through its center, I = $(2)/(3)MR^(2)$

M= Mass of the sphere= 3.8 kg,

R= Radius of gyration= Radius of the sphere= 0.25 m

w= Angular speed of the sphere = 13 rad/s

Substituting the values,

Kinetic energy = $(1)/(2) *(2)/(3) (3.8)(0.25)^(2)(13.0)^(2)$

= 13.4 J

∴ Work required to bring the sphere to stop is 13.4 J.

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Halogen lightbulbs allow their filaments to operate at a higher temperature than the filaments in standard incandescent bulbs. For comparison, the filament in a standard lightbulb operates at about 2900K, whereas the filament in a halogen bulb may operate at 3400K. Which bulb has the higher peak frequency? Calculate the ratio of the peak frequencies. The human eye is most sensitive to a frequency around 5.5x10^14 Hz. Which bulb produces a peak frequency close to this value?

Answers

Answer:

Halogen

0.85294

Explanation:

c = Speed of light = $3* 10^8\ m/s$

b = Wien's displacement constant = $2.897* 10^(-3)\ mK$

T = Temperature

From Wien's law we have

$\lambda_m=(b)/(T)\n\Rightarrow \lambda_m=(2.897* 10^(-3))/(2900)\n\Rightarrow \lambda_m=9.98966* 10^(-7)\ m$

Frequency is given by

$\nu=(c)/(\lambda_m)\n\Rightarrow \nu=(3* 10^8)/(9.98966* 10^(-7))\n\Rightarrow \nu=3.00311* 10^(14)\ Hz$

For Halogen

$\lambda_m=(b)/(T)\n\Rightarrow \lambda_m=(2.897* 10^(-3))/(3400)\n\Rightarrow \lambda_m=8.52059* 10^(-7)\ m$

Frequency is given by

$\nu=(c)/(\lambda_m)\n\Rightarrow \nu=(3* 10^8)/(8.52059* 10^(-7))\n\Rightarrow \nu=3.52088* 10^(14)\ Hz$

The maximum frequency is produced by Halogen bulbs which is closest to the value of $5.5* 10^(14)\ Hz$

Ratio

$(3.00311* 10^(14))/(3.52088* 10^(14))=0.85294$

The ratio of Incandescent to halogen peak frequency is 0.85294

Which is a characteristic of thermal energy transfer through convection

Answers

Answer: The thermal energy transfer is When a fluid, such as air or a liquid, is heated and then travels away from the source, it carries the thermal energy along.

Explanation: heat transfer is called convection. hopefully this was helpful.

A 120-V rms voltage at 60.0 Hz is applied across an inductor, a capacitor, and a resistor in series. If the peak current in this circuit is 0.8484 A, what is the impedance of this circuit

Answers

Answer:

200 $\Omega$

Explanation:

The computation of the impedance of the circuit is shown below:

Provided that

RMS voltage = 120 v

Frequency = 60.0 Hz

RMS current = 0.600 A

Based on the above information, the formula to compute the impedance is

$Z=(V_(max))/(I_(peak))$

where,

$V_(max) = √(2) * V_(rms)$

$= √(2) * 120$

$= 169.7 V$

And, $I_Peak = 0.8484$

Now placing these above values to the formula

So, the impedance of the circuit is

$= (169.7)/(0.8484)$

= 200 $\Omega$

While testing at 30 feet below the surface in Lake Minnetonka, with the sub stopped and in equilibrium, one of the students aboard the sub drops a hammer that goes through the hull of the submarine, and sticks out of the submarine handle first. When this happens, a seal forms immediately around the handle, so that no water enters the sub. What is the new equilibrium position for the sub?

Answers

Answer:

Explanation:

The equilibrium position of the sub is at the surface of the lake

A point charge q1 = 1.0 µC is at the origin and a point charge q2 = 6.0 µC is on the x axis at x = 1 m.(a) Find the electric force on charge q2.
F12 = ? mN
(b) Find the electric force on q1.
F21 = ? mN
(c) What would your answers for Parts (a) and (b) differ if q2 were -6.0 µC?

Answers

To solve this problem we will apply the concepts related to the Electrostatic Force given by Coulomb's law. This force can be mathematically described as

$F = (kq_1q_2)/(d^2)$

Here

k = Coulomb's Constant

$q_(1,2) =$ Charge of each object

d = Distance

Our values are given as,

$q_1 = 1 \mu C$

$q_2 = 6 \mu C$

d = 1 m

$k = 9*10^9 Nm^2/C^2$

a) The electric force on charge $q_2$ is

$F_(12) = ( (9*10^9 Nm^2/C^2)(1*10^(-6) C)(6*10^(-6) C))/((1 m)^2)$

$F_(12) = 54 mN$

Force is positive i.e. repulsive

b) As the force exerted on $q_2$ will be equal to that act on $q_1$ ,

$F_(21) = F_(12)$

$F_(21) = 54 mN$

Force is positive i.e. repulsive

c) If $q_2 = -6 \mu C$ , a negative sign will be introduced into the expression above i.e.

$F_(12) = ((9*10^9 Nm^2/C^2)(1*10^(-6) C)(-6*10^(-6) C))/((1 m)^(2))$

$F_(12) = F_(21) = -54 mN$

Force is negative i.e. attractive

You wish to buy a motor that will be used to lift a 10-kg bundle of shingles from the ground to the roof of a house. The shingles are to have a 1.5-m/s2 upward acceleration at the start of the lift. The very light pulley on the motor has a radius of 0.17 m . Part A Determine the minimum torque that the motor must be able to provide. Express your answer with

Answers

To lift a 10-kg bundle of shingles with an upward acceleration of 1.5 m/s², a motor with a pulley of radius 0.17 m must provide a torque of at least 19 N.m.

We wish to use a motor to lift a 10-kg (m) bund of shingles with an upward acceleration of 1.5 m/s² (a).

The resulting force (F = m.a) is the difference between the tension (T) of the pulley and the weight (w = m.g) of the shingles.

$T-m.g=m.a\nT = m.g+m.a = m(g+a) = 10 kg (9.8m/s^(2)+1.5m/s^(2) )=113 N$

where,

g: gravity

Then, we can calculate the minimum torque (τ) that the motor must apply using the following expression.

$\tau = r * T = 0.17m * 113N = 19N.m$

where,

r: radius of the pulley

To lift a 10-kg bundle of shingles with an upward acceleration of 1.5 m/s², a motor with a pulley of radius 0.17 m must provide a torque of at least 19 N.m.

Learn more: brainly.com/question/19247046

Answer:

$\tau=19.21\ N-m$