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Keith_Richards [23]
4 years ago
6

Why is mathematics important to science?

Physics
1 answer:
bearhunter [10]4 years ago
3 0
Mathematics<span> is </span>important to science<span> because when </span>scientific findings in nature are expressed mathematically, they are easier to verify or disprove by experiment. <span>Without mathematics we would ultimately have no nice way of understanding or analyzing the relationships between quantities we observe and measure.</span>
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Which of the following statements about energy in systems are true?
oee [108]

Answer:

Laws of Thermodynamics

Energy exists in many forms, such as heat, light, chemical energy, and electrical energy. Energy is the ability to bring about change or to do work. Thermodynamics is the study of energy.

First Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another. Click here for another page (developed by Dr. John Pratte, Clayton State Univ., GA) covering thermodynamics.

The Second Law of Thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." This is also commonly referred to as entropy. A watchspring-driven watch will run until the potential energy in the spring is converted, and not again until energy is reapplied to the spring to rewind it. A car that has run out of gas will not run again until you walk 10 miles to a gas station and refuel the car. Once the potential energy locked in carbohydrates is converted into kinetic energy (energy in use or motion), the organism will get no more until energy is input again. In the process of energy transfer, some energy will dissipate as heat. Entropy is a measure of disorder: cells are NOT disordered and so have low entropy. The flow of energy maintains order and life. Entropy wins when organisms cease to take in energy and die.

Potential vs. Kinetic energy

Potential energy, as the name implies, is energy that has not yet been used, thus the term potential. Kinetic energy is energy in use (or motion). A tank of gasoline has a certain potential energy that is converted into kinetic energy by the engine. When the potential is used up, you're outta gas! Batteries, when new or recharged, have a certain potential. When placed into a tape recorder and played at loud volume (the only settings for such things), the potential in the batteries is transformed into kinetic energy to drive the speakers. When the potential energy is all used up, the batteries are dead. In the case of rechargeable batteries, their potential is reelevated or restored.

In the hydrologic cycle, the sun is the ultimate source of energy, evaporating water (in a fashion raising it's potential above water in the ocean). When the water falls as rain (or snow) it begins to run downhill toward sea-level. As the water get closer to sea-level, it's potential energy is decreased. Without the sun, the water would eventually still reach sea-level, but never be evaporated to recharge the cycle.

Chemicals may also be considered from a potential energy or kinetic energy standpoint. One pound of sugar has a certain potential energy. If that pound of sugar is burned the energy is released all at once. The energy released is kinetic energy (heat). So much is released that organisms would burn up if all the energy was released at once. Organisms must release the energy a little bit at a time.

Energy is defined as the ability to do work. Cells convert potential energy, usually in the from of C-C covalent bonds or ATP molecules, into kinetic energy to accomplish cell division, growth, biosynthesis, and active transport, among other things.

Learning Objectives 

These learning objectives are taken from my Biology for Nonmajors class (BIO 102). I have tried to add a link to each that will direct you to a part of this chapter or another website that will facilitate your completion of the objective.

Define energy; be able to state the first and second laws of thermodynamics.

Entropy is a measure of the degree of randomness or disorder of systems. Explain how life maintains a high degree of organization.

8 0
3 years ago
Two point charges exert a 6.10 N force on each other. What will the force become if the distance between them is increased by a
anzhelika [568]

Answer:

0.0953125 N

Explanation:

Applying,

F = kq'q/r²................. Equation 1

Where F = electrostatic force, k = coulomb's constant, q' and q = first and second charge respectively, r = distance between the charge.

From the equation,

If both charges remain constant,

Therefore,

F = C/r²

C = Constant =  product of the two charge(q' and q) and k

Fr² = F'r'²................ Equation 2

From the question,

Given: F = 6.10 N

Assume: r = x m, r' = 8x

Substitute these value into equation 2

6.1(x²) = F'(8x)²

F' = 6.1/64

F' = 0.0953125 N

Hence the new force will become 0.0953125 N

5 0
3 years ago
Four point charges are individually brought from infinity and placed at the corners of a square. Each charge has the identical v
Brut [27]

To solve this problem we will apply the concept of voltage given by Coulomb's laws. From there we will define the charges and the distance, and we will obtain the total value of the potential difference in the system.

The length of diagonal is given as

l = 2a

The distance of the center of the square from each of the corners is

r = \frac{2a}{2}= a

The potential electric at the center due to each cornet charge is

V_1 = \frac{kQ_1}{r_1}

V_2 = \frac{kQ_2}{r_2}

V_3 = \frac{kQ_3}{r_3}

V_4 = \frac{kQ_4}{r_4}

The total electric potential at the center of the given square is

V = V_1+V_2+V_3+V_4

V = \frac{kQ_1}{r_1}+ \frac{kQ_2}{r_2}+\frac{kQ_3}{r_3}+\frac{kQ_4}{r_4}

Al the charges are equal, and the distance are equal to a, then

V = \frac{kQ}{a}+ \frac{kQ}{a}+\frac{kQ}{a}+\frac{kQ}{a}

V = \frac{4kQ}{a}

Therefore the correct option is E.

3 0
4 years ago
A student on a skateboard is moving at a speed of 1.40 m/s at the start of a 2.15 m high and 12.4 m long incline. The total mass
saw5 [17]

Answer:

W = 609.97J

Explanation:

In order to calculate the work done by the student, you take into account that the total work is equal to the change of the kinetic energy of the student, as follow:

W_T=\Delta K\\\\W+W_g-W_f=\frac{1}{2}m(v^2-v_o^2)\\\\W+Mgsin\alpha d-F_fd=\frac{1}{2}m(v^2-v_o^2)         (1)

The work done by the friction force is negative because it is against the motion of the student.

W: work done by the student = ?

Wf: work done by the friction force

Wg: work done by the gravitational force

Ff: total friction force = 41.0N

m: mass of the skateboard = 53.0kg

d: distance traveled by the student

v: final speed of the student = 6.90m/s

vo: initial speed of the student = 1.40m/s

α: angle of the incline

You first calculate the distance d, with the Pythagoras' theorem

d=\sqrt{(2.15m)^2+(12.4m)^2}=12.58m

Furthermore, the angle α is:

\alpha=tan^{-1}(\frac{2.15m}{12.4m})=9.83\°

Then, you solve the equation (1) for W and replace the values of all parameters:

W=\frac{1}{2}m(v^2-v_o^2)+F_fd-Mgsin\alpha d\\\\W=\frac{1}{2}(53.0kg)((6.90m/s)^2-(1.40m/s)^2)+(41.0N)(12.58m)\\-(53.0kg)(9.8m/s^2)sin(9.83\°)(12.58m)\\\\W=609.97J

The work done by the student is 609.97J

6 0
4 years ago
A block of mass 12.2 kg is sliding at an initial velocity of 6.65 m/s in the positive x-direction. The surface has a coefficient
valentina_108 [34]

Explanation:

Given that,

Mass of the block, m = 12.2 kg

Initial velocity of the block, u = 6.65 m/s

The coefficient of kinetic friction, \mu_k=0.253

(a)The force of kinetic friction is given by :

f=\mu_k mg

mg is the normal force

So,

f=0.253\times 12.2\times 9.8\\\\f=30.24\ N

(b) Net force acting on the block in the horizontal direction,

f = ma

a is the acceleration of the block

a=\dfrac{f}{m}\\\\a=\dfrac{30.24}{12.2}\\\\a=2.47\ m/s^2

(c) Let d is the distance covered by the block before coming to the rest. Using third equation of motion as follows :

v^2-u^2=2ad\\\\d=\dfrac{v^2-u^2}{2a}\\\\d=\dfrac{-(6.65)^2}{2\times 2.47}\\\\d=-8.95\ m

Hence, this is the required solution.

3 0
3 years ago
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