A car is brought to rest in a distance of 484 m using a

Some bacteria are propelled by biological motors that spin hair-like flagella. A typical bacterial motor turning at a constant a

Anestetic [448]

Answer:

(a) $\omega=1.41*10^3\frac{rad}{s}$

(b) $t=4.46*10^{-3}s$

Explanation:

The angular speed is a measure of the rotation speed. Thus, It is defined as the angle rotated by a unit of time:

$\omega=\frac{\theta}{t}(1)$

The arc length in a circle is given by:

$s=r\theta\\\theta=\frac{s}{r}(2)$

s is the length of an arc of the circle, so $v=\frac{s}{t}$ .

Replacing (2) in (1):

$\omega=\frac{s}{t}\frac{1}{r}\\\omega=\frac{v}{r}$

a) Now, we calculate the angular speed:

$\omega=\frac{2.21*10^{-5}\frac{m}{s}}{1.57*10^{-8}m}\\\omega=1.41*10^3\frac{rad}{s}$

b) We use (1) to calculate the time it takes to make one revolution, which means that $\theta$ is $2\pi$ .

$\omega=\frac{\theta}{t}\\t=\frac{\theta}{\omega}\\t=\frac{2\pi}{1.41*10^3\frac{rad}{s}}\\t=4.46*10^{-3}s$

8 0

3 years ago

For what value of the ratio r/a of plate radius to separation between the plates does the electric field at the point x=a/2 on t

SIZIF [17.4K]

solution:

E\delta =\frac{R}{\epsilon0}(1-\frac{A}{\sqrt{4R^{2}}-ac}

=\frac{R}{\epsilon0}(1-\frac{1}{\sqrt{4r^{2}/^{_a{2}}+1}})

=\frac{R}{\epsilon0}(1-\frac{1}{\sqrt{4x^2+1}})

x=\frac{r}{a}

infinite case,

Ei=\frac{r}{\epsilon0}

\therefore e\delta =ei(1-\frac{1}{\sqrt{4x^{2}+1}})

we have to find x when,

ei-e\delta =1% ,y=ei=1/100 ei

or,ei-ei+\frac{ei}{\sqrt{4x^2+1}} = 1/100ei

\frac{1}{\sqrt{4x^2+1}}=\frac{1}{100}

4x^2+1 =10^4

x=\frac{\sqrt{\frac{10^4-1}{4}}}=49.99\approx 50

\therefore \frac{r}{a}\approx 50

6 0

3 years ago

Scientists think that convection currents flow in earth’s

torisob [31]

Answer: convection currents does flow because God created the earth and God it makes life flow

Explanation:

God

7 0

3 years ago

0.001225 kg/L x 720 000 000L =?

I am Lyosha [343]

Answer:

0.001225 kg/L × 720 000 000 L = 882000 kg

Explanation:

Given:

The equation to solve is given as:

0.001225 kg/L × 720 000 000 L = ?

Let us write each term of the product in terms of power of 10.

As 0.001225 has 6 digits after the decimal place, therefore, we use the exponent 6 for 10 and the sign is negative. This gives,

$0.001225\ kg/L = 1225\times 10^{-6}\ kg/L$

Now, for 720000000 L there are 6 zeros after 720. So, we use exponent 6 but with a positive sign. This gives,

$720000000\ L=720\times 10^{6}\ L$

Now, finding the product, we get:

$0.001225\ kg/L\times 720000000\ L\\\\=1225\times 10^{-6}\ kg/L\times 720\times 10^6\ L\\\\=(1225\times 720)\times (10^6\times 10^{-6})\ (\frac{kg}{L}\times L)\\\\=882000\times 10^{6-6}\ kg\\\\=882000\times 10^0\ kg\\\\=882000\times 1\ kg\\\\=882000\ kg$

Therefore, the product is equal to:

0.001225 kg/L × 720 000 000 L = 882000 kg

6 0

4 years ago

(5) A 4 kg. object rests on a flat, horizontal surface with a static

baherus [9]

Answer:

F = 9.81 [N]

Explanation:

To solve this problem we must use Newton's third le which tells us that the sum of forces on a body that remains static must be equal to one resulting from these forces in the opposite direction.

Let's perform a summation of forces on the vertical axis-y to determine the normal force N.

∑F = 0 (axis-y)

$N - m*g = 0$

where:

m = mass = 4 [kg]

g = gravity acceleration = 9.81 [m/s²]

$N - (4*9.81)=0\\N = 39.24 [N]$

Now we know that the frictional force can be calculated using the following equation.

f = μ*N

where:

f = friction force [N]

μ = friction coefficient = 0.25

N = normal force = 39.24 [N]

Now replacing:

$f = 0.25*39.24\\f = 9.81[N]$

Then we perform a sum of forces on the X-axis equal to zero. This sum of forces allows us to determine the minimum force to be able to move the object in a horizontal direction.

∑F = 0 (axis-x)

$F-f=0\\F-9.81=0\\F= 9.81[N]$

If the coefficient was smaller, a smaller force (F) would be needed to start the movement, this can be easily seen by replacing the value of 0.25, by smaller values, such as 0.1 or 0.05.

If the coefficient were larger, a larger force would be needed.

3 0

3 years ago