An spring has a period of 4 seconds. What is its frequency?

A spring is hung from the ceiling. When a block is attached to its end, it stretches 2.6 cm before reaching its new equilibrium

Kaylis [27]

Answer:

f = 3.09 Hz

Explanation:

This is a simple harmonic motion exercise where the angular velocity is

w² = $\frac{k}{m}$

to find the constant (k) of the spring, we use Hooke's law with the initial data

F = - kx

where the force is the weight of the body that is hanging

F = W = m g

we substitute

m g = - k x

k = $- \frac{m g}{x}$

we calculate

k = $- \frac{9.8 m}{- 2.6 \ 10^{-2}}$

k = 3.769 10² m

we substitute in the first equation

w² = $\frac{ 3.769 \ 10^2 \ m }{m}$

w = 19.415 rad / s

angular velocity and frequency are related

w = 2πf

f = $\frac{w}{2\pi }$

f = 19.415 / 2pi

f = 3.09 Hz

7 0

3 years ago

Which has greater kinetic energy, a car traveling at 40 mph or a half-as-massive car traveling at 80 mph?

ziro4ka [17]

Answer:

The 80 mph car

Because the formula says 1/2 mass but for the velocity it is squared

8 0

3 years ago

L'aigua es una mescla de d'oxigen i hidrogen

pshichka [43]

Answer:

Una Mezcla Homogénea es aquella mezcla en la que las sustancias que la forman poseen una combinación uniforme.Son ejemplos de Mezclas Homogéneas: Compuesta

Explanation:

Aire (es una mezcla de gases homogénea formada principalmente por de nitrógeno, oxígeno, vapor de agua, dióxido de carbono...)

Leche (mezcla de agua, carbohidratos, proteínas...)

Bebida alcohólica (mezcla de agua y alcohol etílico)

Acero (mezcla de elementos aleados como el hierro, el carbono y otras sustancias)

Petróleo (mezcla de hidrocarburos)

Agua de mar (mezcla de agua, cloruro sódico y otras sustancias)

Mezcla de agua y sal disuelta

Agua azucarada (mezcla de agua y azúcar)

Aleación metálica (las aleaciones metálicas son mezclas en las que se combinan diferentes metales de una manera homogénea y definida)

Perfume (mezcla de agua y otras sustancias olorosas cuya composición es uniforme)

3 0

3 years ago

The caste system in India is illegal. True or False

anzhelika [568]

<span>Discrimination is illegal, but caste system is legal.
So answer: False</span>

4 0

3 years ago

The 1.53-kg uniform slender bar rotates freely about a horizontal axis through O. The system is released from rest when it is in

OlgaM077 [116]

Answer:

The spring constant = 104.82 N/m

The angular velocity of the bar when θ = 32° is 1.70 rad/s

Explanation:

From the diagram attached below; we use the conservation of energy to determine the spring constant by using to formula:

$T_1+V_1=T_2+V_2$

$0+0 = \frac{1}{2} k \delta^2 - \frac{mg (a+b) sin \ \theta }{2} \\ \\ k \delta^2 = mg (a+b) sin \ \theta \\ \\ k = \frac{mg(a+b) sin \ \theta }{\delta^2}$

Also;

$\delta = \sqrt{h^2 +a^2 +2ah sin \ \theta} - \sqrt{h^2 +a^2}$

Thus;

$k = \frac{mg(a+b) sin \ \theta }{( \sqrt{h^2 +a^2 +2ah sin \ \theta} - \sqrt{h^2 +a^2})^2}$

where;

$\delta$ = deflection in the spring

k = spring constant

b = remaining length in the rod

m = mass of the slender bar

g = acceleration due to gravity

$k = \frac{(1.53*9.8)(0.6+0.2) sin \ 64 }{( \sqrt{0.6^2 +0.6^2 +2*0.6*0.6 sin \ 64} - \sqrt{0.6^2 +0.6^2})^2}$

$k = 104.82\ \ N/m$

Thus; the spring constant = 104.82 N/m

b

The angular velocity can be calculated by also using the conservation of energy;

$T_1+V_1 = T_3 +V_3 \\ \\ 0+0 = \frac{1}{2}I_o \omega_3^2+\frac{1}{2}k \delta^2 - \frac{mg(a+b)sin \theta }{2} \\ \\ \frac{1}{2} \frac{m(a+b)^2}{3} \omega_3^2 + \frac{1}{2} k \delta^2 - \frac{mg(a+b)sin \ \theta }{2} =0$