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Elenna [48]
4 years ago
9

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.945 rad/s. You, with a mass of 69.7 kg,

walk clockwise around the platform along its edge at the speed of 1.01 m/s with respect to the platform. Your 20.7 kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 17.7 kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 93.1 kg and radius 1.93 m. Calculate the total angular momentum of the system.
Physics
1 answer:
pickupchik [31]4 years ago
4 0

Answer:

317.22

Explanation:

Given

Circular platform rotates ccw 93.1kg, radius 1.93 m, 0.945 rad/s

You 69.7kg, cw 1.01m/s, at r

Poodle 20.2 kg, cw 1.01/2 m/s, at r/2

Mutt 17.7 kg, 3r/4

You

Relative

ω = v/r

= 1.01/1.93

= 0.522

Actual

ω = 0.945 - 0.522

= 0.42

I = mr^2

= 69.7*1.93^2

= 259.6

L = Iω

= 259.6*0.42

= 109.4

Poodle

Relative

ω = (1.01/2)/(1.93/2)

= 0.5233

Actual

ω = 0.945- 0.5233

= 0.4217

I = m(r/2)^2

= 20.2*(1.93/2)^2

= 18.81

L = Iω

= 18.81*0.4217

= 7.93

Mutt

Actual

ω = 0.945

I = m(3r/4)^2

= 17.7(3*1.93/4)^2

= 37.08

L = Iω

= 37.08*0.945

= 35.04

Disk

I = mr^2/2

= 93.1(1.93)^2/2

= 173.39

L = Iω

= 173.39*0.945

= 163.85

Total

L = 109.4+ 7.93+ 36.04+ 163.85

= 317.22 kg m^2/s

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Answer:

Gravity can never be zero.

Explanation:

The graph shows that the force of gravity is always present despite the amount of distance, indicating that gravity will never be 0. Note, however, that gravity can be extremely small as the distance increases. The limit of the force of gravity as the distance approaches infinity is 0, but never actually touches this value.

7 0
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. An expedition in the arctic sea to study the e ect of climate change on deep-ocean ecosystemrequires precise measurement of te
Sergio039 [100]

Answer:

The complete question contains 2 parts such that

part a: Where the probe is submerged in water. In this case the wattage of heater is 90.47 W

part b: Where the probe is on a vessel. In this case the wattage of heater is So 121.34 W

Explanation:

Part a

For the first part when it is assumed that the probe is submerged in the water. In this case the heat loss is only due to the convective heat transfer which is given as

                                     Q=h \times A \times (T_{body}-T_{surr})

Here

  • Q is the heat loss which is to be calculated
  • A is the area of the body which is given as 4 \pi r^2 \\. It is calculated as

                                           A=4 \pi r^2 \\A=4 \times 3.14 \times  (0.2)^2 \\A=0.5026 m^2

  • Tbody is 10 C
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  • h is the convection coefficient of water which is 18 W/m^2K

                                        Q=h \times A \times (T_{body}-T_{surr})\\Q=18 \times 0.5026 \times (10-0)\\Q=90.47 W\\

So the wattage of heater is 90.47 W

Part b

Now when the probe is above sea water now, the losses are both because of convection and radiation now the loss is given as

                                        Q_{con}=h_{air} \times A \times (T_{body}-T_{air})

Here

  • Q_con is the heat loss due to convection which is to be calculated
  • A is the area of the body which is given as 0.5026 m^2  
  • Tbody is 10 C
  • Tair is -10C
  • h is the convection coefficient of water which is 10 W/m^2K

                                     Q_{con}=h_{air} \times A \times (T_{body}-T_{air})\\Q_{con}=10 \times 0.5026 \times (10+10)\\Q_{con}=100.52 Watts

Radiation loss is given as

                              Q_{rad}=E_{emission}-E_{radiation}\\Q_{rad}=\epsilon A \tau (T_{body}^4-T_{sky}^4)\\          

Here

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  • A is the area of the body which is given as 0.5026 m^2  
  • Tbody is 10+273=283K
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  • ε is the emissivity of the shell which is 0.85
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So the total value of heat loss is

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So the wattage of heater is 121.34 W

                 

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Answer:

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Explanation:

d = diameter of merry-go-round = 2.4 m

r = radius of merry-go-round = (0.5) d = (0.5) (2.4) = 1.2 m

m = mass of merry-go-round = 270 kg

I = moment of inertia of merry-go-round

Moment of inertia of merry-go-round is given as  

I = (0.5) m r² = (0.5) (270) (1.2)² = 194.4 kgm²

M = mass of john = 34 kg

Moment of inertia of merry-go-round and john together after jump is given as

  I' = (0.5) m r² + M r² = 194.4 + (34) (1.2)² = 243.36 kgm²

w = final angular speed

w₀ = initial angular speed of merry-go-round = 20 rpm = 2.093 rad/s

v = speed of john before jump

using conservation of angular momentum

Mvr + I w₀ = I' w

(34) (5) (1.2) + (194.4) (2.093) = (243.36) w

w = 2.51 rad/s

w = 23.98 rpm

5 0
3 years ago
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Answer:

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Explanation:

We have for relative motion the following expression:

\vec{v}_{c/g}=\vec{v}_{c/p}+\vec{v}_{p/g}

Where \vec{v}_{c/g} is the velocity of the cart with respect to the ground, \vec{v}_{c/p} is the velocity of the cart with respect to the plane and \vec{v}_{p/g} is the velocity of the plane with respect to the ground.

We find that:

\vec{v}_{c/p}=-20\hat{y}

\vec{v}_{p/g}=-40\hat{x}+100\hat{y}

Thus:

\vec{v}_{c/g}=-20\hat{y}-40\hat{x}+100\hat{y}=-40\hat{x}+80\hat{y} \, km/h

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Answer:

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Inserting the values

W = (0.5) (0.525) (471² - 69.1²)

W = 5.7 x 10⁴ J

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