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3 years ago

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6.1.115 To approximate the speed of the current of a river, a circular paddle wheel with radius 4 ft. is lowered into the water

. If the current causes the wheel to rotate at a speed of 18 revolutions per minute, what is the speed of the current?

1 answer:

shtirl [24]3 years ago

5 0

Answer:

1.2 ft/s or 72 ft/min

Explanation:

To solve this problem, we can use the relationship between the angular and linear speed for this particular movement (rotation). As the speed of the current is tangent to the trajectory of the wheel we can define as follows:

$v= \omega r=18 \frac{rev}{min} \times \frac{1min}{60s}\times 4 ft\\v= 1.2 \frac{ft}{s}= 72 \frac{ft}{min}$

The speed of the current is 72 ft/min

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From the question we are told that

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Read 2 more answers

An unstrained horizontal spring has a length of 0.26 m and a spring constant of 180 N/m. Two small charged objects are attached

MakcuM [25]

Answer:

a)

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b)

both q1 and q1 are 8.35 × 10⁻⁶ C or -8.35 × 10⁻⁶ C

Explanation:

Given that;

L = 0.26 m

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x = 0.039 m

a)

we know that two like charges always repel each other while two unlike charges attract each other. Since the spring stretches by 0.039 m, the charges have the same sign.

b)

Spring force F = kx

F = 180 × 0.039

F = 7.02 N

Now, Electrostatic force F = Keq²/r²

where r = L + x = ( 0.26 + 0.039 )

we know that proportionality constant in electrostatics equations Ke = 9×10⁹ kg⋅m3⋅s−2⋅C−2

so from the equation; F = Keq²/r²

Fr² = Keq²

q = √ ( Fr² / Ke )

we substitute

q = √ ( 7.02 N × ( 0.26 + 0.039 )² / 9×10⁹ )

q = √ ( 7.02 N × ( 0.26 + 0.039 )² / 9×10⁹ )

q = √ (0.627595 / 9×10⁹)

q = √(6.97 × 10⁻¹¹)

q = 8.35 × 10⁻⁶ C

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