Please help me I need this for a test

A bug is 12 cm from the center of a turntable that is rotating with a frequency of 45 rev/min . What minimum coefficient frictio

Agata [3.3K]

Answer:

The minimum coefficient of friction is 0.27.

Explanation:

To solve this problem, start with identifying the forces at play here. First, the bug staying on the rotating turntable will be subject to the centripetal force constantly acting toward the center of the turntable (in absence of which the bug would leave the turntable in a straight line). Second, there is the force of friction due to which the bug can stick to the table. The friction force acts as an intermediary to enable the centripetal acceleration to happen.

Centripetal force is written as

$F_c = m\frac{v^2}{r}$

with v the linear velocity and r the radius of the turntable. We are not given v, but we can write it as

$v = r\omega$

with ω denoting the angular velocity, which we are given. With that, the above becomes:

$F_c = m\frac{v^2}{r}=m\omega^2 r$

Now, the friction force must be at least as much (in magnitude) as Fc. The coefficient (static) of friction μ must be large enough. How large?

$F_r=\mu mg \geq m\omega^2 r = F_c\implies\\\mu \geq \frac{\omega^2 r}{g}$

Let's plug in the numbers. The angular velocity should be in radians per second. We are given rev/min, which can be easily transformed by a factor 2pi/60:

$\frac{1 rev}{1 min}\cdot\frac{\frac{2\pi rad}{rev}}{\frac{60s}{1 min}}=\frac{2\pi}{60}\frac{rad}{s}$

and so 45 rev/min = 4.71 rad/s.

$\mu \geq \frac{\omega^2 r}{g}=\frac{4.71^2\frac{1}{s^2}\cdot 0.12m}{9.8\frac{m}{s^2}}=0.27$

A static coefficient of friction of at least be 0.27 must be present for the bug to continue enjoying the ride on the turntable.

3 0

3 years ago

Now, find the concentration of H+ ions to OH– ions listed in Table B of your Student Guide for a solution at a pH = 11. Then div

Hunter-Best [27]

Answer

1.0/5

4

IlaMends

Ambitious

2.1K answers

12.9M people helped

Explanation:

When pH of the solution is 11.

..(1)

At pH = 11, the concentration of ions is .

When the pH of the solution is 6.

..(2)

At pH = 6, the concentration of ions is .

On dividing (1) by (2).

The ratio of hydrogen ions in solution of pH equal to 11 to the solution of pH equal to 6 is .

Difference between the ions at both pH:

This means that Hydrogen ions in a solution at pH = 7 has ions fewer than in a solution at a pH = 6

8 0

3 years ago

Read 2 more answers

A sled with no initial velocity accelerates at a rate of 3.2 m/s2 down a hill. How long does it take the sled to go 15 m to the

grin007 [14]

S = ut + 1/2 at^2
a = 3.2 m/s^2
s = 15m
Find t
15 = 1/2(3.2)t^2
15 = 3.2t^2/2
30 = 3.2t^2
30/ 3.2 = 9.38
Square root of 9.38 = 3.06
It takes 3.06 seconds

3 0

3 years ago

_____ occurs when a subject opens there eyes and devotes their attention to an object and the eeg rhythm changes to fast, irregu

slega [8]

Answer: B. Alpha block

Explanation:

3 0

3 years ago

an airplane flies at a speed of 100 m/s and starts to accelerate constantly at a rate of 50 m/s2. how fast is the plane flying a

mart [117]

Answer:

331.7m/s

Explanation:

Given parameters:

Initial velocity = 100m/s

Acceleration = 50m/s²

Distance = 1km = 1000m

Unknown:

Final velocity = ?

Solution:

To solve this problem, we have to apply the right motion equation shown below;

v² = u² + 2aS

v is the final velocity

u is the initial velocity

a is the acceleration

S is the distance

Now insert the parameters and solve;

v² = 100² + (2 x 50 x 1000)

v² = 110000

v = √110000 = 331.7m/s

4 0

3 years ago