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Nataliya [291]
3 years ago
12

A disk rotates about its central axis starting from rest and accelerates with constant angular acceleration. At one time it is r

otating at 9.80 rev/s; 80.0 revolutions later, its angular speed is 18.0 rev/s. Calculate (a) the angular acceleration (rev/s2), (b) the time required to complete the 80.0 revolutions, (c) the time required to reach the 9.80 rev/s angular speed, and (d) the number of revolutions from rest until the time the disk reaches the 9.80 rev/s angular speed.

Physics
1 answer:
Masja [62]3 years ago
6 0

Answer:

Part (a) - 1.42 rev/s

Part (b) - 5.78s

Part (c) - 6.90s

Part (d) - 33.81 rev

Explanation:

The solution to this problem requires the knowledge of constant angular acceleration motion. The equations used here are similar to those used in constant linear acceleration motion. The detailed solutio is presented in the attachment below.

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(a) What is the cost of heating a hot tub containing 1440 kg of water from 10.0°C to 40.0°C, assuming 75.0% efficiency to take h
BaLLatris [955]

Answer:

a) E = 6.024\,USD, For m kilograms, it is 4184m J., 3600000 joules, b) i = 88.200\,A

Explanation:

a) The amount of heat needed to warm water is given by the following expression:

Q_{needed} = m_{w}\cdot c_{w}\cdot (T_{f}-T_{i})

Where:

m_{w} - Mass of water, measured in kilograms.

c_{w} - Specific heat of water, measured in \frac{J}{kg\cdot ^{\circ}C}.

T_{f}, T_{i} - Initial and final temperatures, measured in ^{\circ}C.

Then,

Q_{needed} = (1440\,kg)\cdot \left(4184\,\frac{J}{kg\cdot ^{\circ}C} \right)\cdot (40^{\circ}C - 10^{\circ}C)

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The energy needed in kilowatt-hours is:

Q_{needed} = 180748800\,J\times \left(\frac{1}{3600000}\,\frac{kWh}{J} \right)

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The electric energy required to heat up the water is:

E = \frac{50.208\,kWh}{0.75}

E = 66.944\,kWh

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E = (66.944\,kWh)\cdot \left(0.09\,\frac{USD}{kWh} \right)

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The heat needed to raise the temperature a degree of a kilogram of water is 4184 J. For m kilograms, it is 4184m J. Besides, a kilowatt-hour is equal to 3600000 joules.

b) The current required for the electric heater is:

i = \frac{Q_{needed}}{\eta \cdot \Delta V \cdot \Delta t}

i = \frac{180748800\,J}{0.75\cdot (220\,V)\cdot (3.45\,h)\cdot \left(3600\,\frac{s}{h} \right)}

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Explanation:

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From the equation, it can be noted that if we let Vx equal to zero,
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Answer:

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