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3 years ago

What does the magnitude of centripetal acceleration depend on ?

Physics

1 answer:

MariettaO [177]3 years ago

3 0

Explanation:

Centripetal acceleration ac is the acceleration experienced while in uniform circular motion. It always points toward the center of rotation. It is perpendicular to the linear velocity v and has the magnitude ac=v2r;ac=rω2 a c = v 2 r ; a c = r ω 2 .

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A plate of uniform areal density is bounded by the four curves: where and are in meters. Point has coordinates and . What is the

Natali5045456 [20]

The question is incomplete. The complete question is :

A plate of uniform areal density $\rho = 2 \ kg/m^2$ is bounded by the four curves:

$y = -x^2+4x-5m$

$y = x^2+4x+6m$

$x=1 \ m$

$x=2 \ m$

where x and y are in meters. Point $P$ has coordinates $P_x=1 \ m$ and $P_y=-2 \ m$ . What is the moment of inertia $I_P$ of the plate about the point $P$ ?

Solution :

Given :

$y = -x^2+4x-5$

$y = x^2+4x+6$

$x=1$

$x=2$

and $\rho = 2 \ kg/m^2$ , $P_x=1 \$ , $P_y=-2 \$ .

So,

$dI = dmr^2$

$dI = \rho \ dA \ r^2$ , $r=\sqrt{(x-1)^2+(y+2)^2}$

$dI = (\rho)((x-1)^2+(y+2)^2)dx \ dy$

$I= 2 \int_1^2 \int_{-x^2+4x-5}^{x^2+4x+6}((x-1)^2+(y+2)^2) dy \ dx$

$I= 2 \int_1^2 \int_{-x^2+4x-5}^{x^2+4x+6}(x-1)^2+(y+2)^2 \ dy \ dx$

$I=2 \int_1^2 \left( \left[ (x-1)^2y+\frac{(y+2)^3}{3}\right]_{-x^2+4x-5}^{x^2+4x+6}\right) \ dx$

$I=2 \int_1^2 (x-1)^2 (2x^2+11)+\frac{1}{3}\left((x^2+4x+6+2)^3-(-x^2+4x-5+2)^3 \ dx$

$I=\frac{32027}{21} \times 2$

$= 3050.19 \ kg \ m^2$

So the moment of inertia is $3050.19 \ kg \ m^2$ .

4 0

2 years ago

1. A runner has an initial speed of 2 [m/s] and slowly speeds up with a constant acceleration of

zvonat [6]

Answer:

Final Velocity = 4.9 m/s

Explanation:

We are given;. Initial velocity; u = 2 m/s

Constant Acceleration; a = 0.1 m/s²

Distance; s = 100 m

To find the final velocity(v), we will use one of Newton's equations of motion;

v² = u² + 2as

Plugging in the relevant values to give;

v² = 2² + 2(0.1 × 100)

v² = 4 + 20

v² = 24

v = √24

v = 4.9 m/s

5 0

3 years ago

Un cuerpo suspendido en el aire es capaz de:

Rama09 [41]

Answer:

Explanation:

5 0

3 years ago

A reservoir located in the mountain 250 m above sea level flows through a pipe to a hydroelectric plant in a town at sea level.

Pavlova-9 [17]

Answer:

v₂ = 70 m / s

Explanation:

For this exercise let's use Bernoulli's equation

where subscript 1 is for the top of the mountain and subscript 2 is for Tuesday's level

P₁ + ½ ρ v₁² + ρ g y₁ = P₂ +1/2 ρ v₂² + ρ g y₂

indicate that the pressure in the two points is the same, y₁ = 250 m, y₂ = 0 m, the water in the upper part, because it is a reservoir, is very large for which the velocity is very small, we will approximate it to 0 (v₁ = 0), we substitute

ρ g y₁ = ½ ρ v₂²

v₂ = $\sqrt {2g \ y_1}$

let's calculate

v₂ = √( 2 9.8 250)

v₂ = 70 m / s

6 0

3 years ago

Generation of electricity in coal-burning power plants and nuclear power plants both involve _______.

kolbaska11 [484]

Answer:

Heating water to produce steam which drives a turbine

Explanation:

Generation of electricity in coal-burning power plants and nuclear power plants both involve heating water to produce steam which drives a turbine.

5 0

3 years ago