We have that the Number of stitches per sec and he mass of oscillation motion is mathematically given as
a) Nt=25stitches per sec
b) m=2.033e-5kg
<h3>
Number of
stitches per sec and he mass of oscillation motion</h3>
Question Parameters:
This <u>sewing </u>machine is capable of stitching 1,500 stiches in one minute.
If the <em>sewing </em>machine has a spring constant of 0.5 N/m,
Generally the equation for the Number of stitches per sec is mathematically given as
Nt=N/t
Therefore
Nt=1500/60
Nt=25stitches per sec
b)
Generally the equation for the Time t is mathematically given as
![T=2\pi\sqrt{\frac{m}{k}}](https://tex.z-dn.net/?f=T%3D2%5Cpi%5Csqrt%7B%5Cfrac%7Bm%7D%7Bk%7D%7D)
Therefore
![0.04=2\pi\sqrt{\frac{m}{0.5}}\\\\m=\frac{0.5*0.04^2}{4\pi^2}](https://tex.z-dn.net/?f=0.04%3D2%5Cpi%5Csqrt%7B%5Cfrac%7Bm%7D%7B0.5%7D%7D%5C%5C%5C%5Cm%3D%5Cfrac%7B0.5%2A0.04%5E2%7D%7B4%5Cpi%5E2%7D)
m=2.033e-5kg
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W = force * displacement
W = 32 pounds * 10 feet
Now you need to convert it to newton and meters
W = 142 N * 3.048 m = 434 J
(I approximated the conversions- I hope it helps)
Pluto would be placed 39.74 feet far from the Sun.
Astronomers use the gap between Earth and the sun, which is ninety-three million miles, as a new unit of measure called the Astronomical Unit.
Map scale refers to the connection (or ratio) between the space on a map and the corresponding distance on the ground. For example, on a 1:one hundred thousand scale map, 1cm at the map equals 1km on the ground.
The distance between the earth and solar, a = around 150 million km, is defined as one Astronomical Unit (AU). The radius of the solar, the solar is around 700,000 km.
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The angle of the ladder inclined with respect to the horizontal after being moved a distance of 0.82 m closer to the building is 53.84°
cos θ = Adjacent side / Hypotenuse
θ
= 47°
Hypotenuse = Length of ladder = 8.5 m
cos 47° = Adjacent side / 8.5
Adjacent side = Initial distance of base of ladder from the building = 5.8 m
Adjacent side 2 = Final distance of base of ladder from the building
Adjacent side 2 = 5.8 - 0.82 = 4.98 m
cos θ
= Adjacent side 2 / Hypotenuse
cos θ
= 4.98 / 8.5 = 0.59
θ
=
( 0.59 )
θ
= 53.84°
The formula used above is one of trigonometric ratios. Trigonometric ratios can used only in a right angled triangle where one of the angles in at 90 degrees and the other two angles are less than 90 degrees.
Therefore, the angle of the ladder inclined with respect to the horizontal after being moved is 53.84°
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