Hydroelectric power uses: wind water coal the sun

The circumference of a sphere was measured to be

professor190 [17]

To solve this problem we will apply the concepts related to the calculation of the surface, volume and error through the differentiation of the formulas given for the calculation of these values in a circle. Our values given at the beginning are

$\phi = 76cm$

$Error (dr) = 0.5cm$

The radius then would be

$\phi = 2\pi r \\76cm = 2\pi r\\r = \frac{38}{\pi} cm$

And

$\frac{d\phi}{dr} = 2\pi \\d\phi = 2\pi dr \\0.5 = 2\pi dr$

PART A ) For the Surface Area we have that,

$A = 4\pi r^2 \\A = 4\pi (\frac{38}{\pi})^2\\A = \frac{5776}{\pi}$

Deriving we have that the change in the Area is equivalent to the maximum error, therefore

$\frac{dA}{dr} = 4\pi (2r) \\dA = 4r (2\pi dr)$

Maximum error:

$dA = 4(\frac{38}{\pi})(0.5)$

$dA = \frac{76}{\pi}cm^2$

The relative error is that between the value of the Area and the maximum error, therefore:

$\frac{dA}{A} = \frac{\frac{76}{\pi}}{\frac{5776}{\pi}}$

$\frac{dA}{A} = 0.01315 = 1.31\%$

PART B) For the volume we repeat the same process but now with the formula for the calculation of the volume in a sphere, so

$V = \frac{4}{3} \pi r^3$

$V = \frac{4}{3} \pi (\frac{38}{\pi})^3$

$V = \frac{219488}{3\pi^2}$

Therefore the Maximum Error would be,

$\frac{dV}{dr} = \frac{4}{3} 3\pi r^2$

$dV = 2r^2 (2\pi dr)$

$dV = 4r^2 (\pi dr)$

Replacing the value for the radius

$dV = 4(\frac{38}{\pi})^2(0.5)$

$dV = \frac{2888}{\pi^2} cm^3$

And the relative Error

$\frac{dV}{V} = \frac{ \frac{2888}{\pi^2}}{ \frac{219488}{3\pi^2} }$

$\frac{dV}{V} = 0.03947$

$\frac{dV}{V} = 3.947\%$

3 0

3 years ago

a particle of mass 1.3kg is sliding down a frictionless slope inclined at 30 to the horizontal. the acceleration of the particle

OverLord2011 [107]

Answer:

$4.9\ m/sec^2$

Explanation:

The computation of acceleration of the particle down the slope is shown below:-

data provided in the question

Particle of mass = 1.3 kg i,e sliding down

Inclined = 30 to the horizontal

based on the above information

Force is given by

$N = mg\ cos \theta$ ............ 1

and sliding force is given by

$F = mg\ sin\alpha$

$a = g(sin\ 30^{\circ})$

$= 9.8\times \frac{1}{2} m/sec^2$

= $= 4.9\ m/sec^2$

Hence, the acceleration of the particle down the slope is 4.9 m/sec^2

4 0

3 years ago

What happens to the velocity of the car when the upward pull of the cable is greater than the downward pull of gravity as the ca

Sunny_sXe [5.5K]

For a car that is pulled by a cable we can say that there are two forces on it

1. force of gravity downwards

2. tension force due to cable upwards

so here if upward force due to cable is more than the weight of the car then we have net upward force on the car

Due to this force the velocity of car will increase with time because here car is also moving upwards and we know that when net force will act in the direction of velocity of car then the velocity will always increase.

So here we can say that velocity of car will increase in this case

3 0

4 years ago

In a gravitational-free environment, an object of unknown mass is connected to a spring with k = 40 N/m. The spring is compresse

iVinArrow [24]

Newton's Third Law of Motion states that springs exert a restoring force when they are pulled. The relationship between the spring force, spring constant, and spring displacement is governed by Hooke's Law.

Mass of the object= k*x/a= 26kg

what is Hooke's law?

The force (F) required to extend or compress a spring by a certain distance (x) scales linearly with respect to that distance, according to the empirical law known as Hooke's law.

according to Hooke's law

f=-k x (-ve because spring is compressing)

from force equation f=ma m-=mass, a= acceleration , k=spring constant, x= displacemt due to compression

so, ma=-k x, (mass can not be -ve so remove -ve sign)

m=k x/a= 40*2/3=26.67 kg

To learn more about : Hooke's law

Ref : brainly.com/question/7324904

#SPj9

5 0

2 years ago

If a car accelerated from 5 m/s to 25 m/s in 10 seconds what is it's acceleration?

Alex_Xolod [135]

Answer:

a= (25-5) /10=2m/s^2

............

6 0

3 years ago