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Sagot :
The equations for rotary motion is based on motion in a circular path
a) Time taken by clothes to come up to speed during washing is approximately 1.325 s
b) The tub turns approximately 24.016 revolutions in the 20.0 s interval
Reasons:
Known parameter are;
Operating speed of an automatic washing machine = 5.5 rad·s⁻¹
Average angular acceleration of the washing machine, α = 4.15 rad·s⁻²
Angular speed in the spin-dry mode, ω = 6.0 revolution per second
Time it takes to reach angular speed in spin-dry mode = 7.0 s
a) The relationship between angular acceleration and time are;
[tex]\alpha = \dfrac{\Delta \omega}{\Delta t}[/tex], [tex]\Delta t = \dfrac{\Delta \omega}{\alpha}[/tex]
Where;
Δω = ω₂ - ω₁ = 5.5 rad·s⁻¹
Δt = The time it takes to accelerate
Therefore;
[tex]\Delta t = \dfrac{5.5 \ rad\cdot s^{-1}}{4.15 \ rad \cdot s^{-2}} \approx 1.325 \ s[/tex]
The time it takes for the clothes to come up to speed during the washing mode, Δt ≈ 1.325 s
b) The angular acceleration of the spin-dry mode is given as follows;
6 revolutions per second = 2·π ×6 rad per second = 12·π rad/s
[tex]\alpha = \dfrac{\Delta \omega}{\Delta t}[/tex]
The acceleration during spin up
[tex]\therefore \alpha = \dfrac{12 \cdot \pi }{7.0} \ rad \cdot s^{-2} \approx 5.39 \ rad \cdot s^{-2}[/tex]
The acceleration during slowing down;
[tex]\therefore \alpha = \dfrac{12 \cdot \pi }{13.0} \ rad \cdot s^{-2} \approx 2.9 \ rad \cdot s^{-2}[/tex]
The angle turned in the 20.0 second interval is therefore;
[tex]\dfrac{1}{2} \times 5.39 \times 7^2 + 12 \cdot \pi \times 7-\dfrac{1}{2} \times 2.9 \times 13^2 \approx 150.9[/tex]
The angle turned in the 20.0 s is approximately 150.9 radians
[tex]Number \ of \ revolutions \ =\dfrac{\theta}{2 \cdot \pi}[/tex]
Therefore;
[tex]Number \ of \ revolutions \ in \ 20.0 \ s =\dfrac{150.9 }{2 \cdot \pi} \approx 24.016[/tex]
The number of revolutions of the tub in the 20.0 s interval is approximately 24.016 revolutions
Learn more about constant angular acceleration here:
https://brainly.com/question/14057630
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