4: Which of the following is true of an object in a circular motion at a constant speed?

(a) According to Hooke's Law, the force required to hold any spring stretched x meters beyond its natural length is f(x)=kx. Sup

KengaRu [80]

Answer:

a) The work required to stretch the spring from 20 centimeters to 25 centimeters is 0.313 joules, b) The area of the region enclosed by one loop of the curve $r(\theta) = 2\cdot \sin 5\theta$ is $4\pi$ .

Explanation:

a) The work, measured in joules, is a physical variable represented by the following integral:

$W = \int\limits^{x_{f}}_{x_{o}} {F(x)} \, dx$

Where

$x_{o}$ , $x_{f}$ - Initial and final position, respectively, measured in meters.

$F(x)$ - Force as a function of position, measured in newtons.

Given that $F = k\cdot x$ and the fact that $F = 25\,N$ when $x = 0.3\,m - 0.2\,m$ , the spring constant ( $k$ ), measured in newtons per meter, is:

$k = \frac{F}{x}$

$k = \frac{25\,N}{0.3\,m-0.2\,m}$

$k = 250\,\frac{N}{m}$

Now, the work function is obtained:

$W = \left(250\,\frac{N}{m} \right)\int\limits^{0.05\,m}_{0\,m} {x} \, dx$

$W = \frac{1}{2}\cdot \left(250\,\frac{N}{m} \right)\cdot [(0.05\,m)^{2}-(0.00\,m)^{2}]$

$W = 0.313\,J$

The work required to stretch the spring from 20 centimeters to 25 centimeters is 0.313 joules.

b) Let be $r(\theta) = 2\cdot \sin 5\theta$ . The area of the region enclosed by one loop of the curve is given by the following integral:

$A = \int\limits^{2\pi}_0 {[r(\theta)]^{2}} \, d\theta$

$A = 4\int\limits^{2\pi}_{0} {\sin^{2}5\theta} \, d\theta$

By using trigonometrical identities, the integral is further simplified:

$A = 4\int\limits^{2\pi}_{0} {\frac{1-\cos 10\theta}{2} } \, d\theta$

$A = 2 \int\limits^{2\pi}_{0} {(1-\cos 10\theta)} \, d\theta$

$A = 2\int\limits^{2\pi}_{0}\, d\theta - 2\int\limits^{2\pi}_{0} {\cos10\theta} \, d\theta$

$A = 2\cdot (2\pi - 0) - \frac{1}{5}\cdot (\sin 20\pi-\sin 0)$

$A = 4\pi$

The area of the region enclosed by one loop of the curve $r(\theta) = 2\cdot \sin 5\theta$ is $4\pi$ .

5 0

3 years ago

A spearfisher stands in shallow water and sees a fish a few feet in front of her. She throws her spear directly toward the posit

DENIUS [597]

Answer:

the spear will end up above the fish relative to the actual position of the fish.

Explanation:

due to refraction of light coming from the fish the fish will appear slightly above from its real position

So due to this refraction the spearfisher will throw the spear directly at the image of the fish due to which it will not reach the position of fish but it will reach the position above the fish.

So here we can say that the spear will end up above the fish relative to the actual position of the fish

5 0

3 years ago

What do we call the bright, sphere-shaped region of stars that occupies the central few thousand light-years of the milky way ga

Law Incorporation [45]

Answer: The galaxy's bulge

Explanation:

4 0

2 years ago

which process was found after wegeners time, helped scientists find out how the continents actually move.

Genrish500 [490]

I don't quite know what you're asking so I'll just go on a rant :) Wegener created and supported the continental drift theory, which stated that all of the continents once formed a super continent called Pangea. No one at the time believed in the theory though so he spent the rest of his life trying to find evidence to prove it. However, after he died scientists began to find information that supported his theory. When scientists began to study Earth's surface and the layers below, the theory of the tectonic plates was formed. This theory stated that Earth's crust, the lithosphere, was divided into twelve moving plates. This theory did in fact prove that Wegener's theory was correct. Another theory that proved Wegener's theory to be true was the process of Sea Floor Spreading. This theory stated that at divergent plate boundaries, new ocean floor was being created and the old was being pushed away from the boundary, the old sea floor would then be pushed to deep sea trenches created by convergent plate boundaries and essentially recycled back into the Earth. I hope this helped, sorry it is so long :)

6 0

3 years ago

A location on land has the conditions stated below.

ycow [4]

I believe the answer is D. Thunderstorm
Unstable air indicates that <span>the lowest layers of an </span>air<span> mass is low in temperature. Thunderstorms is more likely to happen if there is unstable air mass because it provide a situation where there is more energy for the Thunderstorms to feed off of.</span>

5 0

3 years ago

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