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2 years ago

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A 31.4-kg wheel with radius 1.21 m is rotating at 283 rev/min. It must be brought to a stop in 14.8 s. Find the required average

power. Assume the wheel to be a thin hoop.

1 answer:

dsp732 years ago

3 0

The average power required to stop the wheel is 2795 Joule.

To find the answer, we need to know about the linear velocity, acceleration and force on the wheel.

<h3>What is the angular frequency of the rotating wheel?</h3>

Mathematically, angular frequency= 2×π×frequency
So, angular frequency= 2×π× 283 rev/min

= 2×π×(283/60) rev/s

= 30 rad/s

<h3>What's the expression of velocity from angular frequency?</h3>

Mathematically, angular frequency= velocity/radius
So, velocity= angular frequency × radius
Here, radius of the wheel= 1.21m

So, velocity= 30×1.21 m = 36.3 m/s

<h3>What will be the acceleration of the wheel, if the final velocity is zero, initial velocity 36.3m/s and time is 14.8 s?</h3>

Mathematically, acceleration= changeing velocity/time
Here, changing velocity= 36.3m/s and time = 14.8 s
So, acceleration= 36.3/14.8 = 2.45 m/s²

<h3>What's the force experienced by the wheel?</h3>

The force on the wheel= mass× acceleration

= 31.4 × 2.45 = 77 N

<h3>What's the average power of the wheel?</h3>

Mathematically, power= work done / time = force×velocity
Power= 77 × 36.3 = 2795 J.

Thus, we can conclude that the average power of the wheel is 2795 J.

Learn more about the average power here:

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A well-insulated bucket of negligible heat capacity contains 129 g of ice at 0°C.

Luba_88 [7]

Answer:

The final equilibrium temperature of the system is $T = 12.48^oC$

For the ice it would melt completely the mass that would remain is Zero

Explanation:

In the following question we are provided with

Mass of the ice $M_{i}$ = 129 g = 0.129 kg

Mass of the steam $M_s$ = 19 g = 0.019 kg

Initial temperature is $T_i$ = 0°C

Temperature of steam $T_s$ = 100°C

Following the change of state of water in the question

The energy required by ice to change to water is mathematically given as

$Q_A = M_iL_f$

Where $L_f$ is a constant known as heat of fusion and the value is $334*10^3 J/kg$

$Q_A = 0.129 *334 *10^3 = 43086 J$

The energy been released when the steam changes to water is mathematically given as

$Q_B = M_s * L_v$

Where $L_v$ is a constant known as heat of vaporization and the value is $2256*10^3J/kg$

$Q_B = 0.019 * 2256*10^3 = 42864J$

The energy released when the temperature of water decrease from 100°C to 0°C is

$Q_C = M_s *C_water ($ 100°C)

Where $C_{water}$ is the specific heat of water which has a value $4186J/kg \cdot K$

$Q_C = 0.019 *4186*100 = 7953.4$

Looking at the values we obtained we noticed that ]

$Q_B + Q_C > Q_A$

What this means is that the ice will melt

bearing in mind the conservation of energy

looking the way at which water at different temperature were mixed according to the question

Heat lossed by the vapor = heat gained by ice

$Q_B + M_s *C_{water}(100-T) = Q_A + M_i C_{water} T$

$T = \frac{Q_B+M_s *C_{water}(100^oC)-Q_A}{(M_s *C_{water})+(M_i*C_{water})}$

$T = \frac{42864+7953.4-43086}{(0.019+0.129)(4186)}$

$T = 12.48^oC$

3 0

4 years ago

you read a primary source and a secondary source that discuss the same experiment. There is a difference in the conclusion made

Nuetrik [128]

You should trust the primary source more.

This is because the primary source is make its conclusion from direct observation, while the secondary source is possibly making reference to another secondary source or to another primary.

The primary source should be trusted more because it is from direct observation.

4 0

3 years ago

The age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this is powers of ten i

DerKrebs [107]

1.4 times 10 in power of 10

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3 years ago

A solenoid of radius 2.0 mm contains 100 turns of wire uniformly distributed over a length of 5.0 cm. It is located in air and c

tankabanditka [31]

Answer:

The magnetic field strength inside the solenoid is $5.026\times10^{-3}\ T$ .

Explanation:

Given that,

Radius = 2.0 mm

Length = 5.0 cm

Current = 2.0 A

Number of turns = 100

(a). We need to calculate the magnetic field strength inside the solenoid

Using formula of the magnetic field strength

Using Ampere's Law

$B=\dfrac{\mu_{0}NI}{l}$

Where, N = Number of turns

I = current

l = length

Put the value into the formula

$B=\dfrac{4\pi\times10^{-7}\times100\times2.0}{5.0\times10^{-2}}$

$B=0.005026=5.026\times10^{-3}\ T$

(b). We draw the diagram

Hence, The magnetic field strength inside the solenoid is $5.026\times10^{-3}\ T$ .

4 0

3 years ago

A student measures the mass 8cm block of brown sugar to be 12.9g. what is the density of the brown sugar.

antoniya [11.8K]

Correction

A student measures the mass <em><u>8cm3</u></em> block of brown sugar to be 12.9g. what is the density of the brown sugar

Answer:

$1.6\ g/cm^{3}$

Explanation:

Density is defined as mass per unit volume of an object expressed as $\rho=\frac {m}{v}$ where $\rho$ is the density, m is the mass of sugar and v is the volume of the sugar. Considering that the volume is given as 8cm3 for sugar then we substitute this for v and mass of 12.9 g we substitute for g then the density will be

$\rho=\frac {12.9 g}{8 cm3}=1.6125\ g/cm^{3}\approx 1.6\ g/cm^{3}$

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3 years ago