An object moving with constant acceleration changes speed from 20 mi./s to 60 mi./s in 2.0 seconds what is the acceleration

Find the moments of inertia Ix, Iy, I0 for a lamina that occupies the part of the disk x2 y2 ≤ 36 in the first quadrant if the d

Tasya [4]

Answer:

I(x) = 1444×k × ${\pi}$

I(y) = 1444×k × ${\pi}$

I(o) = 3888×k × ${\pi}$

Explanation:

Given data

function = x^2 + y^2 ≤ 36

function = x^2 + y^2 ≤ 6^2

to find out

the moments of inertia Ix, Iy, Io

solution

first we consider the polar coordinate (a,θ)

and polar is directly proportional to a²

so p = k × a²

so that

x = a cosθ

y = a sinθ

dA = adθda

so

I(x) = ∫y²pdA

take limit 0 to 6 for a and o to $\pi /2$ for θ

I(x) = $\int_{0}^{6}\int_{0}^{\pi/2}$ y²p dA

I(x) = $\int_{0}^{6}\int_{0}^{\pi/2}$ (a sinθ)²(k × a²) adθda

I(x) = k $\int_{0}^{6}a^(5)$ da × $\int_{0}^{\pi/2}$ (sin²θ)dθ

I(x) = k $\int_{0}^{6}a^(5)$ da × $\int_{0}^{\pi/2}$ (1-cos2θ)/2 dθ

I(x) = k $({r}^{6}/6)^(5)_0$ × ${θ/2 - sin2θ/4}^{\pi /2}_0$

I(x) = k × $({6}^{6}/6)$ × ( ${\pi /4} - sin\pi /4)$

I(x) = k × $({6}^{5})$ × ${\pi /4}$

I(x) = 1444×k × ${\pi}$ .....................1

and we can say I(x) = I(y) by the symmetry rule

and here I(o) will be I(x) + I(y) i.e

I(o) = 2 × 1444×k × ${\pi}$

I(o) = 3888×k × ${\pi}$ ......................2

3 0

2 years ago

There is a seasaw that's holding two men. The seesaw has a length of 18m that can pivot from a point at its center. Man 1 has a

Alex

Answer:

Distance= 2.3864m

Explanation:

So that the balance is in equilibrium parallel to the floor, we must match the moment each man makes with respect to the pivot point.

In many cases the point of application of force does not coincide with the point of application in the body. In this case the force acts on the object and its structure at a certain distance, by means of an element that transfers that action of this force to the object.

This combination of force applied by the distance to the point of the structure where it is applied is called the moment of force F with respect to the point. The moment will attempt a rotation shift or rotation of the object. The distance from the force to the point of application is called the arm.

Mathematically it is calculated by expression:

M= F×d

The moment caused by the first man is:

M1= 75kg × (9.81m/s²) × 1.75m= 1287.5625 N×m

The moment caused by the second man must be equal to that caused by the first by which:

M2= 1287.5625 N×m= 55kg × (9.81m/s²) × distance ⇒

⇒distance= (1287.5625 N×m)/( (55kg × (9.81m/s²) )= 2.3864m

At this distance from the pivot point, the second should sit down so that the balance is balanced parallel to the ground.

3 0

2 years ago

Some one help my science homework is due tomorrow and I'm so stuck with question 8-9, and 11-12

yuradex [85]

Off the top of my head, I only know 9 and 11, so I'll answer those two.

9) A heterotroph is an organism that relies on other organisms for food/energy
An autotroph can produce its own food from inorganic compounds (light)

11) Vascular plants have specialized tubes for transporting nutrients
Nonvascular plants do not have such tubes and are simpler

5 0

3 years ago

Which option is a force?<br> O A. Mass<br> O B. Velocity<br> O C. Acceleration<br> O D. Weight

olga_2 [115]

Answer:

Weight is a force.

Explanation:

Force acting on an object is defined in terms of mass and its acceleration. Its mathematical force is given by

F = ma

Weight of an object is force that the Earth exerts on an object. It can be given by the formula as follows :

W = mg

g is acceleration due to gravity on the surface of earth

Hence, the correct option is (d).

6 0

3 years ago

The distance between a Point on one wave and the same point on the next cycle of the wave

Gala2k [10]

Answer:

wavelength

Explanation:

the definition of wavelength is the distance between two consecutive waves. with that being said, the point from the crest of one wave to the crest of another would be wave length

8 0

1 year ago