What are the dimensions of F = ma?

How are mathematics and science related?

____ [38]

The relationship between math and science is very complicated, yet at the same time very simple. In fact all scientific equations are expressed into some form of mathematical equations. Science is a body of knowledge about the Universe. Mathematics is a language that can describe relationships and change in relationships in a rational way. Science generally uses mathematics as a tool to describe science and vice versa.

6 0

3 years ago

The aurora is caused when electrons and protons, moving in the earth’s magnetic field of ≈5.0×10−5T, collide with molecules of t

ollegr [7]

Answer:

8.79*10^6 rad/s

Explanation:

To find the frequency of the circular orbit for an electron you use the following expression, for the radius of the trajectory of an electron, that travels trough a constant magnetic field:

$r=\frac{mv}{qB}$ (1)

r: radius of the trajectory

m: mass of the electron = 9.1*10^-31 kg

v: speed of the electron = 1.0*10^6 m/s

q: charge of the electron = 1.6*10^-19 C

B: magnitude of the magnetic field = 5.0*10^-5 T

You use the fact that the angular frequency in a circular motion is given by:

$\omega=\frac{v}{r}$

Then, you solve the equation (1) in order to obtain v/r:

$\frac{v}{r}=\omega=\frac{qB}{m}$

Finally, you replace the values of the parameters:

$\omega=\frac{(1.6*10^{-19}C)(5.0*10^{-5}T)}{9.1*10^{-31}kg}\\\\\omega=8.79*10^6\frac{rad}{s}$

hence, the angular frequency is 8.79*10^6 rad/s

The frequency is:

$f=2\pi \omega=5.5*10^7Hz$

5 0

3 years ago

A nitrogen isotope has an atomic number of 7 and an atomic mass of 15. the respective numbers of neutrons, protons, and electron

anygoal [31]

Atomic Number = amount of protons. Atomic mass = protons (7) and neutrons (8)

Electrons will be the protons - any charge the isotope has. For example, a +2 charge would make the electrons 7- (+2) = 5. A -2 charge would be electrons 7 - (-2) = 9

6 0

3 years ago

As a city planner, you receive complaints from local residents about the safety of nearby roads and streets. One complaint conce

WINSTONCH [101]

Answer:

a) x₁ = 290.50 feet , x₂ = 169.74 feet , b) v_max= 41 mph

Explanation:

For this exercise we will work in two parts, the first with Newton's second law to find the acceleration of vehicles

X Axis fr = m a

Y Axis N-W = 0

N = W = mg

The force of friction has the expression

fr = μ N

We replace

μ mg = ma

a = μ g

g = 32 feet / s²

Let's calculate the acceleration for each coefficient and friction

μ a (feet / s2)

0.599 19.168

0.536 17,152

0.480 15.360

0.350 11.200

These are the acceleration values, for the maximum distance we use the minimum acceleration (a₁ = 11,200 feet / s²) and for the minimum braking distance we use the maximum acceleration (x₂ = 19,168 feet / s²)

v² = v₀² - 2 a x

When the speed stops it is zero

x₁ = v₀² / 2 a₁

Let's reduce speed

v₀ = 55mph (5280 foot / 1 mile) (1h / 3600s) = 80,667 feet / s²

Let's calculate the maximum braking distance

x₁ = 80.667² / (2 11.2)

x₁ = 290.50 feet

The minimum braking distance

x₂ = 80.667² / (2 19.168)

x₂ = 169.74 feet

b) maximum speed to stop at distance x = 155 feet

0 = v₀² - 2 a x

v₀ = √2 a x

We calculate the speed for the two accelerations

v₀₁ = √ (2 11.2 155)

v₀₁ = 58.92 feet / s

v₀₂ = √ (2 19.168 155)

v₀₂ = 77.08 feet / s

To stop at the distance limit in the worst case the maximum speed must be 58.92 feet / s = 40.85 mph = 41 mph

5 0

3 years ago

Distinguish between nonsampling error and sampling error. Choose the correct answer below.

kiruha [24]

Answer:

The correct answer is D.

Non-sampling error is the error that results from under-coverage, non-response bias, response bias, or data-entry errors. Sampling error is the error that results because a sample is being used to estimate information about a population.

Explanation:

Sampling error is related to the variation between the true values of the sample and the population. If occurred, it is always random depending upon the sample chosen.

Non-sampling error can be random as well as non-random. Non-sampling error can occur irrespective of the sample chosen. It is related to the inappropriate analysis of the data.

5 0

3 years ago