Weighing a Bacterium Scientists are using tiny, nanoscale cantilevers 4 micrometers long and 500 nanometers wide-essentially miniature diving boards-as a sensitive way to measure mass. The cantilevers oscillate up and down with a frequency that depends on the mass placed near the tip, and a laser beam is used to measure the frequency. A single E. coli bacterium was measured to have a mass of 710 femtograms = 7.10×10−16 kg with this device, as the cantilever oscillated with a frequency of 17.1 MHz .
Treating the cantilever as an ideal, massless spring, find its effective force constant.

The final angular speed of the sphere is 4ω.

Angular momentum will remain conserved.

A spinning system's ability to conserve angular momentum ensures that its spin will not change until it is subjected to an external torque; in other words, the rotation's speed will not change as long as the net torque is zero.

Angular momentum is given by,

L = Iω

where,

L = angular momentum

I = moment of inertia

ω = angular speed

The moment of inertia of a solid sphere is,

I = \(\frac{2}{5} MR^{2}\)

For the question,

L₁ = L₂

I₁ω₁ = I₂ω₂

Given,

R₁ = R

R₂ = R/2

ω₁ = ω

To find,

ω₂ =?

Substituting the values in the equation,

I₁ω₁ = I₂ω₂

\(\frac{2}{5}\)(MR²)ω = \(\frac{2}{5}\) M(R/2)²ω₂

R²ω = (R²/4)ω₂

ω = (1/4)ω₂

ω₂ = 4ω

Hence, the final angular speed of the sphere is 4ω.

Learn more about conservation of angular momentum here:

https://brainly.com/question/12998770

#SPJ4

4ω is the final angular speed of the sphere.

When a solid sphere of radius r rotates about a diameter with an angular speed w, the sphere then collapses under the action of internal forces to a final radius r/2, 4ω is the final angular speed of the sphere.

Angular momentum will remain conserved.

Angular momentum is given by,

L = Iω

where,

L = angular momentum

I = moment of inertia

ω = angular speed

The moment of inertia of a solid sphere is,

I = \(\frac{2}{5}\)\(MR^{2}\)

For the given problem,

L₁ = L₂

I₁ω₁ = I₂ω₂

We are given,

R₁ = R

R₂ = R/2

ω₁ = ω

To find,

ω₂ =?

On substitution of the values in the equation,

I₁ω₁ = I₂ω₂

\(\frac{2}{5}\)(MR²)ω = \(\frac{2}{5}\) M(R/2)²ω₂

R²ω = (R²/4)ω₂

ω = (1/4)ω₂

ω₂ = 4ω

Hence, we can conclude that the final angular speed of the sphere is 4ω.

To learn more about conservation of angular momentum visit:

https://brainly.com/question/1597483

#SPJ4

Answer:

Time taken to reach the tree

they have given the maximum height which is 25m

therefore...

v=u+at (upward)

0 = 45sin(20)-9.81t

t = 1.56s

It must be either speeding up, or slowing down, or turning. There are no other possibilities.

1a) The total energy stored when all three weights are raised by 70 cm is 80.5 J.

1b) The height of the tank is 2 m.

2b) The potential energy is converted into kinetic energy when the water flows out of the taps 6.32 m/s.

3a) The mass of water that goes over the falls every second is 1 x 10⁶ kg.

3b) The gravitational potential energy of 1 kg of water at the top of the falls 1000 J.

3c) The speed of the water as it reaches the bottom if all the GPE stored in 1 kg of water is transferred to kinetic energy is 44.72 m/s.

3d) The water will not be falling as fast as the speed calculated in part c suggests because of the presence of air resistance and the fact that the water falls through a medium (air) which offers resistance to its motion.

3e) The energy transferred when the GPE stored in the water falling in one second is transferred to other energy stores is finally stored in thermal energy stores due to the heat generated by the water as it hits the bottom.

1a) To calculate the amount of energy stored in the three weights, we use the formula given below:

E = mgh

Where,E = Energy (Joules)

m = Mass (kg)

g = Gravity (10 N/kg)

h = Height (m)

For the 4.5 kg weight:

E = 4.5 x 10 x 0.7 = 31.5 J

For each of the 3.5 kg weight:

E = 3.5 x 10 x 0.7 = 24.5 J

Thus, the total energy stored when all three weights are raised by 70 cm is:

31.5 J + 24.5 J + 24.5 J = 80.5 J

1b) To calculate how far the 4.5 kg weight must be lifted to store 45 J of energy, we use the formula:

E = mghh = E/mg = 45 / (4.5 x 10) = 1 m2a)

To calculate the gravitational potential energy stored in the water in the tank when it is full, we use the formula given below:

E = mgh

Where,E = Energy (Joules)

m = Mass (kg)

g = Gravity (10 N/kg)

h = Height (m)

The mass of 1 litre of water is 1 kg and the tank can hold 200 litres of water. Therefore, the total mass of water in the tank is:

Mass = 200 kg

The height of the tank is 2 m.

Therefore, the gravitational potential energy stored in the water in the tank is:

E = mgh = 200 x 10 x 2 = 4000 J

Assumptions made in the answer:

We have assumed that the tank is full.

2b) To calculate the speed at which the water would come out of the bathroom and kitchen taps, we use the formula given below:

PE = KEPE = mghKE = 1/2mv²

Where,PE = Potential Energy (Joules)

KE = Kinetic Energy (Joules)

m = Mass (kg)

g = Gravity (10 N/kg)

h = Height (m)

v = Velocity (m/s)

Assuming that the potential energy of the water in the tank is converted into kinetic energy when the water flows out of the taps, the potential energy stored in the water in the tank is given by:

PE = mgh = 200 x 10 x 2 = 4000 J

The potential energy is converted into kinetic energy when the water flows out of the taps.

Therefore, KE = 1/2mv²v² = 2KE/mv² = 2(4000)/200 = 40 m²/s²v = √(40) = 6.32 m/s (speed of the water coming out of the taps)

3a) To calculate the mass of water that goes over the falls every second, we use the formula given below:

Mass = Volume x Density

Where,Volume = 1000 m³/s, Density = 1000 kg/m³, Mass = 1000 x 1000 = 1000000 kg = 1 x 10⁶ kg

3b) To calculate the gravitational potential energy of 1 kg of water at the top of the falls, we use the formula:

E = mgh

Where,m = 1 kg, g = 10 N/kg, h = 100 m, E = 1 x 10 x 100 = 1000 J

3c) To calculate the speed of the water as it reaches the bottom if all the GPE stored in 1 kg of water is transferred to kinetic energy, we use the formula given below:

PE = KEP

E = mgh

KE = 1/2mv²

Where,PE = Potential Energy (Joules)

KE = Kinetic Energy (Joules)

m = Mass (kg)

g = Gravity (10 N/kg)

h = Height (m)

v = Velocity (m/s)

Assuming that all the potential energy is converted into kinetic energy when the water reaches the bottom,

PE = KEKE = mghv² = 2mghv² = 2(1)(10)(100)v² = 2000v = √(2000) = 44.72 m/s

3d) The water will not be falling as fast as the speed calculated in part c suggests because of the presence of air resistance and the fact that the water falls through a medium (air) which offers resistance to its motion.

3e) To calculate the total energy transferred per second as the GPE stored in the water falling in one second is transferred to other energy stores, we use the formula given below:

Power = Energy / Time

Where,Power = 1 x 10⁶ x 10 x 100 = 1 x 10⁹ W = 1 GW (assuming that 1 m³ of water falls every second)3f)

The energy transferred when the GPE stored in the water falling in one second is transferred to other energy stores is finally stored in thermal energy stores due to the heat generated by the water as it hits the bottom.

For more such questions on potential energy, click on:

https://brainly.com/question/14427111

#SPJ8

Answer:

mutualistic relationship

Answer:

Explanation:

b

Answer:

protect public from pollution

Explanation: got it right

Based on leah's informal experiment we can say, unbalanced forces from Joey pushing the car causes the car to change direction.

Forces that are opposite in direction and equal in size are termed as balanced forces. Since the car move across the table with constant speed, we can say acceleration is zero and net forece is also zero, until and unless Joey or Leah push the car. To change the direction and speed of the car, a net external force is required to be acted upon the car. A net external force by Joey is an unbalanced force which will change the direction and gives the speed to the car in opposite direction. Hence, it is an unbalanced force applied by the Joey that pushes the car in the other direction. Due to this force car starts to move back to Leah. Without, unbalanced force there will be no change in the direction of the car's motion or speed.

To learn more about force visit the link- https://brainly.com/question/12785175

#SPJ4

Answer:

Explanation:

A

A road map is an example of a graphical model. Correct option is A.

A road map is an example of a graphical model because it represents real-world information using graphical elements, such as lines, symbols, colors, and labels, to convey spatial relationships and information about roads, landmarks, and geographical features. Graphical models are visual representations that help convey complex information in a simplified and easily understandable way.

In the case of a road map, it uses graphical elements to represent various features of a geographic area, such as highways, streets, intersections, bodies of water, cities, and points of interest. These graphical representations allow users to quickly understand the layout of roads, distances between locations, and how to navigate from one place to another.

Graphical models are particularly effective for representing spatial and visual information, making them an essential tool for tasks like navigation, planning trips, and understanding geographical relationships.

To know more about road map:

https://brainly.com/question/30952193

#SPJ3

because the ocean releases heat more slowly than land, coastal areas tend to be more temperate. Upwelling in many coastal regions provides a cool contrast in air temperature over the ocean and land that is conducive to frequent summer fog.

A sequence of equally spaced timing pulses may be easily generated by a 'Ring counter circuit.'

A ring counter is a shift register (a cascade connection of flip-flops) with the output of the last flip-flop connected to the input of the first flip-flop. A ring counter is known as a circular shift register, that is, the output of the last flip-flop is connected to the input of the first flip-flop, with the structure of a shift register.

The most important benefit of a ring counter circuit is that it produces a series of equally spaced timing pulses, as well as reducing the complexity of the circuit. A Ring Counter is used to generate a repetitive pulse sequence, also known as a 'circular shift register,' which is used in digital circuits to store and transfer binary data.

It is a register with a clock input signal that can be either asynchronous or synchronous, depending on the application.

Therefore, the sequence of equally spaced timing pulses can be generated by a ring counter circuit.

To know more about ring counter circuit click here:

https://brainly.com/question/30009204

#SPJ4

Whether your linear regression model fits the data better than a model with no independent variables is determined by the F-test of overall significance.

When we examine how alternative regression statistics, like R-squared, fit with the F-test of overall significance. How well your model fits the data is indicated by R-squared, and the F-test is related to it.

An extremely adaptable statistical test is the F-test. They have a wide range of applications. F-tests can assess the fits of various linear models since they can examine numerous model terms at once. T-tests, on the other hand, can only evaluate one term at a time.

The F-test of overall significance is the hypothesis test for this relationship. If the overall F-test is significant, you can conclude that R-squared does not equal zero, and the correlation between the model and dependent variable is statistically significant.

Therefore, Whether your linear regression model fits the data better than a model with no independent variables is determined by the F-test of overall significance.

To learn more about F test, refer to the link:

https://brainly.com/question/14099492

#SPJ1

Answer:

It would stretch about 6 inches, but it depends on the metal.

Explanation:

pls mark brainliest with the crown

Answer:

3N

Explanation:

Answer:

  ρ = 1.6 0 10⁻⁵ Ω/ m

Explanation:

In this exercise we are asked to find the resistivity of the wire, it indicates the length L = 1.0 m, the diameter of 0.33 mm.

For this exercise we start by using ohm's law

           V = i R

           R = \(\frac{V}{i}\)

           R = 1.5 / 8.0

           R = 0.1875 Ω

now we use the relation of resistance

           R = ρ L / A

            ρ = R A / L

the area of ​​the wire is

           A =π r²

           r = d/2

           A = π d²/ 4

           A = π (0.33 10⁻³)²/4

           A = 8.55 10⁻⁵ m²

we substitute

           ρ = 0.1875  8.55 10⁻⁵ / 1.0

           ρ = 1.6 0 10⁻⁵ Ω/ m

Thermal insulators stop the loss of accumulated heat, metal flat plates absorb solar radiation, and tubes absorb solar energy with the least amount of heat loss.

To know more about vacuum :

https://brainly.com/question/11615301

#SPJ9

Answer:

4000 km

Explanation:

Answer: 1,6 KM

Explanation:

To determine the distance from the epicenter of an earthquake if P waves take 12 minutes to arrive, we need to use the formula:

distance = (time * 8) / 60

where "time" is the time it takes for the P waves to arrive in minutes, and "distance" is the distance from the epicenter in kilometers.

Substituting the given value of time, we get:

distance = (12 * 8) / 60

distance = 1.6 kilometers

Therefore, the distance from the epicenter of the earthquake is approximately 1.6 kilometers.

Answer:

These measurement units are part of the metric system. Unlike the U.S. customary system of measurement, the metric system is based on 10s. For example, a liter is 10 times larger than a deciliter, and a centigram is 10 times larger than a milligram.

Answer: Unlike the U.S. customary system of measurement, the metric system is based on s. For example, a liter is times larger than a deciliter, and a centigram is times larger than a milligram

So,  If the silica cyliner of the radiant wall heater is rated at 1.5 kw its temperature when operating is 1025.3 K

To estimate the operating temperature of the radiant wall heater, we need to use the equation for power radiated by the radiant wall heater.

The power radiated by the radiant wall heater is given by P = εσAT⁴ where

Since P = εσAT⁴

P = εσ(2πrh)T⁴

Making T subject of the formula, we have

T = ⁴√[P/εσ(2πrh)]

Since P = 1.5 kW = 1.5 × 10³ W

Substituting the values of the variables into the equation, we have

T = ⁴√[P/εσ(2πrh)]

T = ⁴√[1.5 × 10³ W/(1 × 6 × 10⁻⁸ W/m²-K⁴ × 2π × 6 × 10⁻³ m × 0.6 m)]

T = ⁴√[1.5 × 10³ W/(43.2π  × 10⁻¹¹ W/K⁴)]

T = ⁴√[1.5 × 10³ W/135.72  × 10⁻¹¹ W/K⁴)]

T = ⁴√[0.01105 × 10¹⁴ K⁴)]

T = ⁴√[1.105 × 10¹² K⁴)]

T = 1.0253 × 10³ K

T = 1025.3 K

So, If the silica cylinder of the radiant wall heater is rated at 1.5 kw its temperature when operating is 1025.3 K

Learn more about temperature of radiant wall heater here:

https://brainly.com/question/14548124

Answer:

it's because the eclipse hides the moon and Venus and the sun

Explanation:

I found it

Diamond at 20°C is expected to have the greatest index of refraction.

The index of refraction is a property that describes how light propagates through a medium. It is a measure of how much the speed of light is reduced when passing through a particular material. The higher the index of refraction, the slower light travels through that material.

Among the given options, diamond is known for having a very high index of refraction. This is due to its dense molecular structure and high refractive index value, which is approximately 2.42. Diamond's unique crystal lattice and high optical density result in a substantial bending of light as it passes through the material.

Carbon dioxide at 0°C, liquid water at 20°C, and other materials generally have lower indices of refraction compared to diamond. While carbon dioxide and liquid water can refract light to some extent, their refractive indices are significantly lower than that of diamond.

Among the given options, diamond at 20°C is expected to have the greatest index of refraction. Its dense molecular structure and high refractive index value allow for a significant bending of light as it passes through the material.

To know more about  refraction, visit

https://brainly.com/question/27932095

#SPJ11

The dimensions of the quantities "a" are \(L/T\), and the dimensions of "b" are \(L/T^2\). The correct answer is C. \(L/T, L/T^2.\)

To determine the dimensions of the quantities "a" and "b" in the equation \(y = at - bt^2\), we can analyze each term separately.

The first term, at, represents a displacement along the y-axis with respect to time. The dimensions of displacement are typically denoted as length (L). Therefore, the term at has the dimensions of L.

The second term, \(-bt^2\), represents a quantity that is subtracted from the displacement. We have a time-squared term \((t^2)\) multiplied by a coefficient (-b). Since the time squared term implies acceleration (change in velocity per unit time), its dimensions are usually denoted as \(L/T^2\) (length divided by time squared). The coefficient "-b" is dimensionless since it's just a constant.

Combining the terms, we have:

\(y = at - bt^2\)

\(L = L - L/T^2\)

The dimensions on both sides of the equation must be equal, so the dimensions of "a" and "b" are:

a: \(L/T\)

b: \(L/T^2\)

Therefore, the correct answer is option C. \(L/T, L/T^2.\)

To learn more about dimensions follow the link:

https://brainly.com/question/4788668

#SPJ4

The correct question is:

The position y of a particle moving along the y-axis depends on the time t according to the equation \(y = at - bt^2\). The dimensions of the quantities a and b are respectively:

A. \(L^2 /T, L^3 /T^2\)

B. \(L/T^2 , L^2 /T\)

C. \(L/T, L/T^2\)

D. \(L^3 /T, T^2 /L\)

E. none of these

Followers of the humanistic perspective are said to have a(n) optimistic view of human nature. The best answer is c.

The humanistic perspective emphasizes the positive aspects of human nature, such as personal growth, self-awareness, and self-actualization. According to this perspective, people have the potential to lead fulfilling lives and to realize their full potential. Humanistic psychologists believe that individuals have free will and the capacity to make conscious decisions about their lives.

This perspective emphasizes the importance of individual experience and personal choice in shaping behavior and personality. In contrast to the pessimistic views of other schools of psychology, humanistic psychology emphasizes the potential for positive growth and change in individuals. Hence, c is the correct choice.

To know more about human perspective, here

brainly.com/question/19447140

#SPJ4

Answer:

A.6s

Explanation:

Average time=

\(average time \: t = \frac{t1 + t2}{2 } \\ \frac{0 + 12}{2} \\ \frac{ 12}{2} \\ t = 6s\)

The percentage of body weight that is made up of fat when compared to your other tissue, bone and muscles is called body composition.

Body composition refers to the proportion of fat, muscle, bone, and other types of tissue in the body. It is often expressed as a percentage of body weight that is made up of fat. Body composition can be measured using various methods such as skinfold thickness measurements, bioelectrical impedance, and dual-energy x-ray absorptiometry (DXA).

A healthy body composition is generally considered to be one with a low percentage of body fat and a high percentage of muscle mass. It is important to note that body composition is not the same as body weight, as two individuals can weigh the same but have very different body compositions. An imbalance in body composition can lead to health issues such as obesity and increased risk of chronic diseases. Regular exercise and a healthy diet can help to maintain a healthy body composition.

To learn more about body composition visit: https://brainly.com/question/9048015

#SPJ4

Answer:

Explanation:

1.it ocours when an object is thrown into the sky. 2.iy ocurs when an object is falling or being pulled from the sky

The speed of the bullet is determined as 800 m/s.

The speed of the bullet is calculated by applying Newton's second law of motion as shown below.

F = ma

where;

The acceleration of the bullet is calculated as follows;

a = F / m

a = ( 4000 N ) /  ( 0.05 kg )

a = 80,000 m/s²

The speed of the bullet is calculated as follows;

v = at

where;

v = 80,000 m/s²   x   0.01 s

v = 800 m/s

Thus, the speed of the bullet at the given acceleration and time of motion is determined by applying first kinematic equation as shown above. The speed of the bullet measures the rate of change of distance of the bullet with time.

Learn more about speed of bullet here: https://brainly.com/question/13073762

#SPJ1