Ask question

Ask question

All categories

3 years ago

12

A typical laboratory centrifuge rotates at 4000 rpm. Testtubes have to be placed into a centrifuge very carefully because ofthe

very large accelerations.
Part A) What is the acceleration at the end of a test tubethat is 10 cm from the axis of rotation?
Part B) For comparison, what is the magnitude of theacceleration a test tube would experience if dropped from a heightof 1.0 m and stopped in a 1.0-ms-long encounter with a hardfloor?

1 answer:

Bogdan [553]3 years ago

4 0

Answer:

A) a_c = 1.75 10⁴ m / s², B) a = 4.43 10³ m / s²

Explanation:

Part A) The relation of the test tube is centripetal

a_c = v² / r

the angular and linear variables are related

v = w r

we substitute

a_c = w² r

let's reduce the magnitudes to the SI system

w = 4000 rpm (2pi rad / 1 rev) (1 min / 60s) = 418.88 rad / s

r = 1 cm (1 m / 100 cm) = 0.10 m

let's calculate

a_c = 418.88² 0.1

a_c = 1.75 10⁴ m / s²

part B) for this part let's use kinematics relations, let's start looking for the velocity just when we hit the floor

as part of rest the initial velocity is zero and on the floor the height is zero

v² = v₀² - 2g (y- y₀)

v² = 0 - 2 9.8 (0 + 1)

v =√19.6

v = -4.427 m / s

now let's look for the applied steel to stop the test tube

v_f = v + a t

0 = v + at

a = -v / t

a = 4.427 / 0.001

a = 4.43 10³ m / s²

You might be interested in

The position of a particle moving along the x-axis depends on the time according to the equation x = ct2 - bt3, where x is in me

Sav [38]

Answer:

(a): $\rm meter/ second^2.$

(b): $\rm meter/ second^3.$

(c): $\rm 2ct-3bt^2.$

(d): $\rm 2c-6bt.$

(e): $\rm t=\dfrac{2c}{3b}.$

Explanation:

Given, the position of the particle along the x axis is

$\rm x=ct^2-bt^3.$

The units of terms $\rm ct^2$ and $\rm bt^3$ should also be same as that of x, i.e., meters.

The unit of t is seconds.

(a):

Unit of $\rm ct^2=meter$

Therefore, unit of $\rm c= meter/ second^2.$

(b):

Unit of $\rm bt^3=meter$

Therefore, unit of $\rm b= meter/ second^3.$

(c):

The velocity v and the position x of a particle are related as

$\rm v=\dfrac{dx}{dt}\\=\dfrac{d}{dx}(ct^2-bt^3)\\=2ct-3bt^2.$

(d):

The acceleration a and the velocity v of the particle is related as

$\rm a = \dfrac{dv}{dt}\\=\dfrac{d}{dt}(2ct-3bt^2)\\=2c-6bt.$

(e):

The particle attains maximum x at, let's say, $\rm t_o$ , when the following two conditions are fulfilled:

$\rm \left (\dfrac{dx}{dt}\right )_{t=t_o}=0.$
$\rm \left ( \dfrac{d^2x}{dt^2}\right )_{t=t_o}$

Applying both these conditions,

$\rm \left ( \dfrac{dx}{dt}\right )_{t=t_o}=0\\2ct_o-3bt_o^2=0\\t_o(2c-3bt_o)=0\\t_o=0\ \ \ \ \ or\ \ \ \ \ 2c=3bt_o\Rightarrow t_o = \dfrac{2c}{3b}.$

For $\rm t_o = 0$ ,

$\rm \left ( \dfrac{d^2x}{dt^2}\right )_{t=t_o}=2c-6bt_o = 2c-6\cdot 0=2c$

Since, c is a positive constant therefore, for $\rm t_o = 0$ ,

$\rm \left ( \dfrac{d^2x}{dt^2}\right )_{t=t_o}>0$

Thus, particle does not reach its maximum value at $\rm t = 0\ s.$

For $\rm t_o = \dfrac{2c}{3b}$ ,

$\rm \left ( \dfrac{d^2x}{dt^2}\right )_{t=t_o}=2c-6bt_o = 2c-6b\cdot \dfrac{2c}{3b}=2c-4c=-2c.$

Here,

$\rm \left ( \dfrac{d^2x}{dt^2}\right )_{t=t_o}$

Thus, the particle reach its maximum x value at time $\rm t_o = \dfrac{2c}{3b}.$

7 0

3 years ago

A ray of light travelled from water into the air an angle of incidence of 30°. Calculate;

Dima020 [189]

Answer:

speed = distance/time

just find the speed if it

3 0

2 years ago

A dog runs to chase a ball. He travels 6m in 3.2 seconds. How fast is the dog running?

Artyom0805 [142]

So v=d/s so the answer is 6/3.2 so the answer is 1.87m/s

4 0

3 years ago

Can someone with an IQ score of 120 be gifted? Based on psychological thought, explain why or why not and give an example. ILL M

Pani-rosa [81]

Hello!

Yes, someone with an IQ score of 120 can be gifted.

An IQ score of 120 means that the individual is moderately gifted. Although this IQ doesn't qualify for gifted education programs, research shows that people with IQs of about 145-180 don't perform significantly better than people with 120s IQ in terms of success.

As an example, professor Dean Simonton from the University of California found that an optimum leader should have an IQ in the 120-125 range, so having an IQ of 120 would mean that the individual is gifted for leadership.

Have a nice day!

7 0

2 years ago

Read 2 more answers

(a) find the magnitude of the gravitational force between a planet with mass 7.50 3 1024 kg and its moon, with mass 2.70 3 1022

anzhelika [568]

<span>The magnitude of the gravitational force between two bodies is the product of their masses divided by the square of the distance between them. So we have F = M1*M2 / r^2. M1 = 7.503 * 10e24 and M2 = 2.703 * 10e22 and r= 2.803 * 10e8; r^2 = 5.606 *10e16. So we have 7.503 *2.703 *10^(24+22) = 20.280 * 10^(46). Then we divide our answer by 5.606 * 10e16 which is the distance ; then we have 3.6175 * 10 e (46- 16) = 3.6175 * 10e30. To find the acceleration we use Newton's second law F = ma. F is 3.6175 * 10e30 and M is 7.503 * 10e24 so a = F/M and then we have 3.6175/7.503 * 10e (30-24) = 0.48 * 10e6. Similarly for moon, we have a = 3.6715/2.703 * 10e(30-22). = 1.358 * 10e8</span>

4 0

3 years ago