What are the four elements that Aristotle included in his model of matter

A rotating merry go-round makes one complete revolution in 4.2 s. (a) what is the linear speed of a child seated 1.3 m from the

gregori [183]

The radius, r, of the child from the center of the wheel is
r = 1.3 m

The wheel makes one revolution in 4.2 s. Its angular velocity is
ω = (2π rad)/(4.2 s) = 1.496 rad/s

The linear speed of the child is the tangential velocity, given by
v = rω
= (1.3 m)*(1.496 rad/s)
= 1.945 m/s

Answer: 1.95 m/s (nearest hundredth)

6 0

3 years ago

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Consider the motion of a 4.00-kg particle that moves with potential energy given by U(x) = + a) Suppose the particle is moving w

gtnhenbr [62]

Correct question:

Consider the motion of a 4.00-kg particle that moves with potential energy given by

$U(x) = \frac{(2.0 Jm)}{x}+ \frac{(4.0 Jm^2)}{x^2}$

a) Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

b) What is the magnitude of the force on the 4.00-kg particle when it is located at x = 5.00 m?

Answer:

a) 3.33 m/s

b) 0.016 N

Explanation:

a) given:

V = 3.00 m/s

x1 = 1.00 m

x = 5.00

$u(x) = \frac{-2}{x} + \frac{4}{x^2}$

At x = 1.00 m

$u(1) = \frac{-2}{1} + \frac{4}{1^2}$

= 4J

Kinetic energy = (1/2)mv²

$= \frac{1}{2} * 4(3)^2$

= 18J

Total energy will be =

4J + 18J = 22J

At x = 5

$u(5) = \frac{-2}{5} + \frac{4}{5^2}$

$= \frac{4-10}{25} = \frac{-6}{25} J$

= -0.24J

Kinetic energy =

$\frac{1}{2} * 4Vf^2$

= 2Vf²

Total energy =

2Vf² - 0.024

Using conservation of energy,

Initial total energy = final total energy

22 = 2Vf² - 0.24

Vf² = (22+0.24) / 2

$Vf = \sqrt{frac{22.4}{2}$

= 3.33 m/s

b) magnitude of force when x = 5.0m

$u(x) = \frac{-2}{x} + \frac{4}{x^2}$

$\frac{-du(x)}{dx} = \frac{-d}{dx} [\frac{-2}{x}+ \frac{4}{x^2}$

$= \frac{2}{x^2} - \frac{8}{x^3}$

At x = 5.0 m

$\frac{2}{5^2} - \frac{8}{5^3}$

$F = \frac{2}{25} - \frac{8}{125}$

= 0.016N

8 0

3 years ago

Sarah is looking for a way to move her boat across the water without touching it directly. She included paperclips in the boat d

Zigmanuir [339]

Answer:

When there is no detergent in the water, you'll achieve a floating paper clip!

Explanation:

3 0

3 years ago

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The area of an equilaterla triangle is increasing at a rate of 5 m^2/hr. find the rate at witch the height is chganging when the

Lena [83]

The rate at which the height is changing is ( 5 / x ) m / hr

We know that,

Area of an equilateral triangle A = $\sqrt{3}$ $x^{2}$ / 4

h = $\sqrt{3}$ x / 2

Where,

x = Side

h = Height

Given that,

dA / dt = 5 $m^{2}$ / hr

h = $\sqrt{3}$ x / 2

Differentiate both sides with respect to t

dh / dt = ( $\sqrt{3}$ / 2 ) ( dx / dt )

dx / dt = ( 2 / $\sqrt{3}$ ) ( dh / dt )

A = $\sqrt{3}$ $x^{2}$ / 4

Differentiate both sides with respect to t

dA / dt = ( $\sqrt{3}$ / 4 ) ( 2x ) ( dx / dt )

5 = ( $\sqrt{3}$ / 4 ) ( 2x ) ( 2 / $\sqrt{3}$ ) ( dh / dt )

dh / dt = ( 5 / x ) m / hr

Rate of change of height is defined as the rate at which height of an object changes with respect to time. It is represented as dh / dt

Therefore, the rate at which the height is changing is ( 5 / x ) m / hr

To know more about Rate of change of height

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6 0

1 year ago

Charge is flowing through a conductor at the rate of 420 C/min. If 742 J. of electrical energy are converted to heat in 30 s., w

Y_Kistochka [10]

Answer:

3.53 V

Explanation:

Electric charge: The is the rate of flow of electric charge along a conductor.

The S.I unit of electric charge is C.

Mathematically it is expressed as,

Q = It ............................ Equation 1

Where Q = electric charge, I = current, t = time.

I = Q/t.......................... Equation 2

From the question, charge flows through the conductor at the rate of 420 C/mim

Which means in 1 min, 420 C of charge flows through the conductor.

Hence,

Q = 420 C, t = 1 min = 60 seconds

Substitute into equation 2

I = 420/60

I =7 A

Also

P = VI......................... Equation 3

Where P = power, V = potential drop, I = current.

V = P/I................... Equation 4

Note: Power = Energy/time

From the question, P = 742/30 = 24.733 W. and I = 7 A.

Substitute these values into equation 4

V = 24.733/7

V = 3.53 V

Hence the potential drop across the conductor = 3.53 V

4 0

3 years ago