Which of the following is one reason why an experiment should have the larger sample size possible

A block with mass m =6.9 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.29 m.

crimeas [40]

1) The spring constant is 233.2 N/m

2) The oscillation frequency is 0.93 Hz

3) The speed of the block is 3.2 m/s

4) The maximum acceleration is $23.9 m/s^2$

5) The net force on the block is 104.9 N

Explanation:

1)

At equilibrium, the weight of the mass is equal to the restoring force of the spring. Therefore, we can write:

$mg=kx$

where

m = 6.9 kg is the mass hanging on the spring

$g=9.8 m/s^2$ is the acceleration of gravity

k is the spring constant

x = 0.29 m is the stretching of the spring

Solving for k, we find

$k=\frac{mg}{x}=\frac{(6.9)(9.8)}{0.29}=233.2 N/m$

2)

The oscillation frequency of a spring-mass system is given by

$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$

where

k is the spring constant

m is the mass

In this problem,

k = 233.2 N/m is the spring constant

m = 6.9 kg is the mass

Substituting, we find the frequency:

$f=\frac{1}{2\pi}\sqrt{\frac{233.2}{6.9}}=0.93 Hz$

3)

The velocity of the block at time t is given by the equation:

$v(t) = -v_0 cos(\omega t)$

where

$v_0 = 4.1 m/s$ is the initial speed

$\omega$ is the angular frequency

t is the time

The angular frequency can be found from the frequency:

$\omega=2\pi f=2\pi(0.93)=5.84 rad/s$

And substituting t = 0.42 s, we find the velocity of the block at this time:

$v(t)=-4.1 cos ((5.84)(0.42))=3.2 m/s$

4)

The maximum acceleration of the block is given by

$a_{max} = \omega^2 A$ (1)

where

$\omega=5.84 rad/s$ is the angular frequency

A is the amplitude

The amplitude is related to the initial velocity by the equation:

$v_0=\omega A$ (2)

Combining (1) and (2), we find

$a_{max}=v_0 \omega$

And substituting $v_0 = 4.1 m/s$ , we find

$a_{max}=(4.1)(5.84)=23.9 m/s^2$

5)

The acceleration at time t can be found by calculating the derivative of v(t), and it is given by the equation

$a(t) = a_{max} sin(\omega t)$

where

$a_{max}=23.9 m/s^2$ is the maximum acceleration

$\omega=5.84 rad/s$ is the angular frequency

t is the time

Substituting t = 0.42 s,

$a(t)=(23.9)sin((5.84)(0.42))=15.2 m/s^2$

Finally, the net force on the block can be found by using Newton's second law:

$F=ma=(6.9)(15.2)=104.9 N$

#LearnwithBrainly

4 0

3 years ago

Most stars in the Milky Way's halo are _________. blue or white in color very young very old found inside molecular clouds

Alina [70]

Answer:

Most stars in the Milky Way's halo are very old

very oldThere is no recycling of gas in the halo, so halo stars are quite old.

6 0

2 years ago

Simple pendulum, is show in several states In case A the mass is travelling back down to the bottom and is in between the bottom

uysha [10]

The angular acceleration is maximum in case C

Explanation:

The motion of the bob in the simple pendulum is a portion of a circular motion. In a circular motion, the angular acceleration is related to the tangential acceleration by

$a=\alpha r$

where

a is the tangential acceleration

$\alpha$ is the angular acceleration

r is the radius (the length of the pendulum)

Moreover for a pendulum, the tangential acceleration is given by the component of the acceleration of gravity in the tangential direction, so

$a=g sin \theta$

where

g is the acceleration of gravity

$\theta$ is the angle of the pendulum with the vertical

So we have

$\alpha = \frac{g sin \theta}{r}$

Since g and r are constant, we see that the angular acceleration is proportional to the angle: the larger the angle, the larger the angular acceleration, and the smaller the angle, the smaller the angular acceleration.

Therefore, the angular acceleration is maximum when the pendulum is at its maximum height, and zero when it is at the lowest position. So, the correct statements are

It is maximum in case C

Learn more about periodic motion:

brainly.com/question/5438962

#LearnwithBrainly

3 0

3 years ago

In a heat engine, Qh and Qc represents high temperature substance and low temperature substance respectively. Which of the follo

ElenaW [278]

The efficiency of a heat engine is given by the expression $eff =\frac{Q_h-Q_c}{Q_h}$