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goldfiish [28.3K]
3 years ago
8

Each ball has a negligible size and a mass of 11.5 kg and is attached to the end of a rod whose mass may be neglected. The rod i

s subjected to a torque M = (t2+2) N⋅m, where t is in seconds. Each ball has a speed v = 2 m/s when t = 0.
Determine the speed of each ball when t = 3 s.

Express your answer to three significant figures and include the appropriate units.
Physics
1 answer:
Digiron [165]3 years ago
7 0

Answer:

3.31m/s

Explanation:

Angular momentum for 3s is

L = L_i_n_i + L_3_s

L = 2(11.5kg) + \int\limits^ {3s}_ {0s} {(t^2 + 2)} \, dt

L = 23kg+(\frac{t^3}{3} +2t)^ {3s}_ {0s}\\\\L=38kgm/s

Moment if inertia is

I = 2ml^2

I = 2(11.5)(0.5)^2\\\\I=5.75kgm^2

Angular speed

ω = L/I

= 38 / 5.75\\\\=6.61

The speed of each ball is

V = ωL

= 6.61\times0.5\\\\= 3.31m/s

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A rectangular tank is filled to a depth of 10m with freshwater and open to air at atmospheric pressure.
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Answer:

<em>1.</em> <em>39068.07 N</em>

<em>2. 19534.036 N</em>

Explanation:

depth of water h = 10 m

atmospheric pressure Patm = 101325 Pa

density of water p = 1000 kg/m^3

acceleration due to gravity g = 9.81 m/s^2

pressure due to depth of water = pgh

P = 1000 x 9.81 x 10 = 98100 Pa

total pressure on the bottom of the tank is Patm + p = 101325 + 98100 = 199425 Pa

Left plug has diameter = 50 cm = 0.5 m

radius = 0.5/2 = 0.25 m

height = 1 cm = 0.01 m

<em>height below tank surface = 10 - 0.01 = 9.99</em>

pressure at this depth =  1000 x 9.81 x 9.99 = 98001.9 Pa

<em>total pressure = Patm + P = 101325 + 98001.9 = 199326.9 Pa</em>

surface area of plug = πr^{2} = 3.142 x 0.25^{2} = 0.196 m^{2}

<em>force required to lift left plug = pressure x area</em>

F =  199326.9 x 0.196 = <em>39068.07 N</em>

<em>The right side is a hemisphere with the same diameter, therefore surface area is half of the left plug</em>

A = 0.196/2 = 0.098 m^{2}

force F required to lift right plug =  199326.9  x 0.098 =<em> 19534.036 N</em>

6 0
3 years ago
Which is an example of a trace fossil?
hodyreva [135]

Answer: The correct answer is A). Animal burrow because burrow fossils represent the preserved byproducts of behavior rather than physical remains, they are considered a kind of trace fossil. One common kind of burrow fossil is known as Skolithos, and the similar Trypanites, Ophiomorpha and Diplocraterion.

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3 years ago
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In young’s double slit experiment, the measured fringe width is 0.5 mm for a Sodium light of 589 nm at a distance of 1.5 m. A br
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Answer:

(A).  The order of the bright fringe is 6.

(B). The width of the bright fringe is 3.33 μm.

Explanation:

Given that,

Fringe width d = 0.5 mm

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Distance of screen and slit D = 1.5 m

Distance of bright fringe y = 1 cm

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Using formula of wavelength

\lambda=\dfrac{dy}{mD}

m=\dfrac{d y}{\lambda D}

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m=\dfrac{1\times10^{-2}\times0.5\times10^{-3}}{589\times10^{-9}\times1.5}

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Using formula of width of fringe

\beta=\dfrac{yd}{D}

Put the value in to the formula

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3 0
3 years ago
A tennis ball is dropped from a roof. If it takes 38.9 seconds to reach the ground, how fast is the ball moving just before it h
Ilya [14]

Answer:

The velocity of the ball before it hits the ground is 381.2 m/s

Explanation:

Given;

time taken to reach the ground, t = 38.9 s

The height of fall is given by;

h = ¹/₂gt²

h = ¹/₂(9.8)(38.9)²

h = 7414.73 m

The velocity of the ball before it hits the ground is given as;

v² = u² + 2gh

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u is the initial velocity of the on the root = 0

v is the final velocity of the ball before it hits the ground

v² = 2gh

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v = √(2 x 9.8 x 7414.73 )

v = 381.2 m/s

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