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A circular cylinder has a diameter of 3.0 cm and a mass of 25 g. It floats in water with its long axis perpendicular to the wate

Vilka [71]

Answer:

f = 5.3 Hz

Explanation:

To solve this problem, let's find the equation that describes the process, using Newton's second law

∑ F = ma

where the acceleration is

a = $\frac{d^2 y}{dt^2 }$

B- W = m \frac{d^2 y}{dt^2 }

To solve this problem we create a change in the reference system, we place the zero at the equilibrium point

B = W

In this frame of reference, the variable y' when it is oscillating is positive and negative, therefore Newton's equation remains

B’= m $\frac{d^2 y'}{dt^2 }$

the thrust is given by the Archimedes relation

B = ρ_liquid g V_liquid

the volume is

V = π r² y'

we substitute

- ρ_liquid g π r² y’ = m \frac{d^2 y'}{dt^2 }

$\frac{d^2 y'}{dt^2} + \rho_liquid \ g \ \pi r^2/m ) y' \ =0$

this differential equation has a solution of type

y = A cos (wt + Ф)

where

w² = ρ_liquid g π r² /m

angular velocity and frequency are related

w = 2π f

we substitute

4π² f² = ρ_liquid g π r² / m

f = $\frac{1}{2\pi } \ \sqrt{ \frac{ \rho_{liquid} \ \pi r^2 \ g}{m } }$

calculate

f = $\frac{1}{2 \pi } \sqrt{ \frac{ 1000 \ \pi \ 0.03^2 \ 9.8 }{0.025} }$

f = 5.3 Hz

6 0

2 years ago

the earth has a radius of 6.38×10^16 meter and turns around once on its axis in 24 hour.what is the radial acceleration of perso

Scrat [10]

337493603.8m/s²

Explanation:

Radius of the earth = 6.38 x 10¹⁶m

time = 24hr (86400s)

Unknown:

Centripetal acceleration = ?

Solution:

The centripetal acceleration is directed inward to keep the body from falling off the surface of the earth.

centripetal acceleration = $\frac{v^{2} }{r}$

where v is the velocity and r is the radius

also;

v = wr

where w is the angular velocity

substituting in the equation for centripetal acceleration gives;

a = w²r

also w = $\frac{2 x pi}{T}$

therefore;

a = $\frac{4 \pi ^{2} r }{T^{2} }$

a = $\frac{ 4 x 3.142^{2} x 6.38 x 10^{16} }{86400^{2} }$

a = 337493603.8m/s²

learn more:

Acceleration brainly.com/question/3820012

#learnwithBrainly

5 0

3 years ago

A rope of total mass m hnd length L is suspended vertically with an object of mass M suspended from the lower end. Find an expre

pantera1 [17]

Answer:

Part a)

$v = \sqrt{xg + \frac{MLg}{m}}$

Part b)

t = 12 s

Explanation:

Part a)

Tension in the rope at a distance x from the lower end is given as

$T = \frac{m}{L}xg + Mg$

so the speed of the wave at that position is given as

$v = \sqrt{\frac{T}{\mu}}$

here we know that

$\mu = \frac{m}{L}$

now we have

$v = \sqrt{\frac{ \frac{m}{L}xg + Mg}{m/L}$

$v = \sqrt{xg + \frac{MLg}{m}}$

Part b)

time taken by the wave to reach the top is given as

$t = \int \frac{dx}{\sqrt{xg + \frac{MLg}{m}}}$

$t = \frac{1}{g}(2\sqrt{xg + \frac{MLg}{m}})$

$t = \frac{2}{9.8}(\sqrt{(39.2\times 9.8) + \frac{8(39.2)(9.8)}{1}})$

$t = 12 s$

4 0

2 years ago

Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 168 cm , but its circumference is decreasi

DedPeter [7]

Answer:

103.1 V

Explanation:

We are given that

Initial circumference=C=168 cm

$\frac{dC}{dt}=-15cm/s$

Magnetic field,B=0.9 T

We have to find the magnitude of the emf induced in the loop after exactly time 8 s has passed since the circumference of the loop started to decrease.

Magnetic flux= $\phi=BA=B(\pi r^2)$

Circumference,C= $2\pi r$

$r=\frac{C}{2\pi}$

$r=\frac{168}{2\pi}$ cm

$\frac{dr}{dt}=\frac{1}{2\pi}\frac{dC}{dt}=\frac{1}{2\pi}(-15)=-\frac{15}{2\pi} cm/s$

$\int dr=-\int \frac{15}{2\pi}dt$

$r=-\frac{15}{2\pi}t+C$

When t=0

$r=\frac{168}{2\pi}$

$\frac{168}{2\pi}=C$

$r=-\frac{15}{2\pi}t+\frac{168}{2\pi}$

E= $-\frac{d\phi}{dt}=-\frac{d(B\pi r^2)}{dt}=-2\pi rB\frac{dr}{dt}$

$E=-2\pi(-\frac{5}{2\pi}t+\frac{168}{2\pi})B\times -\frac{15}{2\pi}$

t=8 s

B=0.9

$E=2\pi\times \frac{15}{2\pi}\times 0.9(-\frac{15}{2\pi}(8)+\frac{168}{2\pi})$

$E=103.1 V$

6 0

2 years ago

Consider the circuit shown below V=18.00V. The terminal voltage of the battery is.

Pavel [41]

Resistance is current x potential difference. So therefor run wafff

6 0

1 year ago

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