A grocery cart with a mass of 15 kg is being pushed at constant speed up a 12∘ ramp by a force FP which acts at an angle of 17∘ below the horizontal.
a. Find the work done by the force F⃗ P on the cart if the ramp is 6.5 m long.
b. Find the work done by the force mg⃗ on the cart.

Answer:

a and d

Explanation:

The ground's resistance is influenced by the form of substances under the earth. Other materials like metals have far less resistance and more electrical conductivity. Therefore more electrons will enter the detectors in the earth that has iron. Therefore, choice a and d is are correct.

Final answer:

Electrons passing through various materials to reach a detector are influenced by the resistance and resistivity of those materials. Iron ore, which has lower resistance, allows more electrons to reach the detector compared to dry soil or underground water. Thus, by measuring the charge reaching the detector per unit time, one can infer the type of material based on the known resistivity of different materials.

Explanation:

The question you've asked relates to how the measurement of electric current reaching a detector can be used to identify the type of material underground by considering the effect of materials' resistance on the flow of electrons. To answer the question, we need to understand some key principles:

Resistance is a measure of how much a material impedes the flow of charge.

The resistance to the flow of electrons through materials is in the decreasing order of dry soil, underground water, and iron ore, meaning iron ore has the lowest resistance among them.

Resistivity of materials affects the quantity of charge reaching the detector per unit time. The lower the resistivity, the higher the conductivity, and thus more charge will reach the detector because there is less opposition to the flow.

Now, evaluating the statements given:

(a) More electrons will reach the detector from iron than from dry soil. This is true because iron ore has a lower resistance compared to dry soil.

(b) The electrons reaching the detector are affected very little by what's under the surface. This is not true; the material significantly affects the electron flow.

(c) The detector will get more electric charge if the resistance to flow is less, and resistance is related to the type of material. This is a correct statement and aligns with the principles of conductivity.

(d) The electrons reaching the detector will carry water with them if water is under the surface. This statement is false, as electrons do not carry water with them.

Answer:

Explanation:

The efficiency of the heat engine is less than 100%. The heat engine converts the thermal energy from the burning of fuel to the mechanival energy. Thus, some of the energy gets lost as waste heat.

Hence, this waste heat is used up to heat up the interior of the car and person feels warmer in the car.

Thus, the waste heat generated in the engine is used for the heating of the car interior.

Final answer:

Running the heater in a car on a cold winter day doesn't cost much additional energy beyond running the fan because the heat generated by the engine is mostly released into the environment instead of being used for work in the car.

Explanation:

Heat engines convert thermal energy into work. In a car engine, heat is produced when fuel is burned, and this heat is converted into kinetic energy to move the car and power its systems. Running the heater in a car on a cold winter day doesn't cost much additional energy beyond running the fan because the heat generated by the engine is mostly released into the environment instead of being used for work in the car.

Answer:

Negative work

Explanation:

The work-energy theorem states that the work of the resultant forces acting on a particle modifies its kinetic energy:

[tex]W=\Delta K\\W=\frac{mv_f^2}{2}-\frac{mv_0^2}{2}\\W=\frac{m}{2}(v_f^2-v_0^2)\\W=\frac{m}{2}((7\frac{m}{s})^2-(15\frac{m}{s})^2)\\W=\frac{m}{2}(-178\frac{m^2}{s^2})[/tex]

Since the mass of the ball has to be positive, the work is negative.

The external force did negative work on the ball because the ball's speed decreased from 15 m/s to 7 m/s, indicating a decrease in kinetic energy.

To determine whether the force has done positive, negative, or zero work on the ball, we must consider the change in the ball's kinetic energy. Work done by a force is defined as the change in kinetic energy of an object. The formula for work done (W) is given by the change in kinetic energy:

W = ΔKE = ½mv2final - ½mv2initial

Since the speed of the ball decreased from 15 m/s to 7 m/s, the kinetic energy of the ball also decreased. A decrease in kinetic energy means that negative work was done on the ball by the external force.

Answer:

 T₂ =602  °C

Explanation:

Given that

T₁ = 227°C =227+273 K

T₁ =500 k

Gauge pressure at condition 1 given = 100 KPa

The absolute pressure at condition 1 will be

P₁ = 100 + 100 KPa

P₁ =200 KPa

Gauge pressure at condition 2 given = 250 KPa

The absolute pressure at condition 2 will be

P₂ = 250 + 100 KPa

P₂ =350 KPa

The temperature at condition 2 = T₂

We know that

[tex]\dfrac{T_2}{T_1}=\dfrac{P_2}{P_1}\\T_2=T_1\times \dfrac{P_2}{P_1}\\T_2=500\times \dfrac{350}{200}\ K\\[/tex]

T₂ = 875 K

T₂ =875- 273 °C

T₂ =602  °C

The problem involves using Charles's Law, a form of the ideal gas law, to find the final temperature of nitrogen after heating, by converting all pressures to absolute pressures and applying the law to relate initial and final states.

The student's question involves determining the final temperature of nitrogen gas in a rigid tank after heating, given initial temperature and pressures, using the ideal gas law. To solve this problem, we assume the nitrogen behaves as an ideal gas and use the relation between pressure, volume, temperature, and the number of moles of gas, which is constant since the tank is rigid.

Firstly, convert all pressures into absolute pressures by adding atmospheric pressure to the gage pressures. Then, apply the ideal gas law in the form of Charles's Law (P1/T1 = P2/T2), which relates pressure and temperature at constant volume and number of moles. To find the final temperature (T2), rearrange the equation to T2 = (P2/P1) * T1, where P2 and P1 are the final and initial absolute pressures, respectively, and T1 is the initial temperature in Kelvin.

Answer:

The correct answer is option A.

Explanation:

The average kinetic energy of the gas particle only depends upon the temperature of the gas.

The formula for average kinetic energy is:

[tex]K.E=\frac{3}{2}kT[/tex]

where,

k = Boltzmann’s constant = [tex]1.38\times 10^{-23}J/K[/tex]

T = temperature

So, at standard temperature and pressure 0.50 moles of hydrogen and 1.0 mole of oxygen sample will have same value of average kinetic energy.

Where as in other option enlisted in question , molar masses of both gases will be involved which will give different answers for both the gases.

This question involves the concepts of the average kinetic energy of the molecules of a gas and temperature.

The gases will have the same "A. average molecular kinetic energy".

The average kinetic energy of gas molecules is given by the following formula:

[tex]K.E = \frac{3}{2}KT[/tex]

where,

K.E = average kinetic energy

K = Boltzmann constant

T = absolute temperature

Hence, the average kinetic energy depends upon the absolute temperature only. Since the temperature is the same for both gases. Hence, their average kinetic energy will also be the same.

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Final answer:

The force on the skier parallel to the slope is found by calculating the component of the skier's weight that acts along the slope. This force is the weight multiplied by the sine of the angle of the slope, which results in 534.8 Newtons for a 103 kg skier on a 32° slope.

Explanation:

To determine the force on the skier parallel to the slope, we can make use of the component of the gravitational force along the slope. Since we are neglecting friction, the only force acting on the skier in the direction parallel to the slope is the component of the skier's weight in that direction.

The weight of the skier can be calculated by multiplying the mass (m) by the acceleration due to gravity (g), which is W = m × g. The component of the weight parallel to the slope is Wparallel = W × sin(θ), where θ is the angle of the slope. Substituting the given values, we have W = 103 kg × 9.8 m/s² = 1009.4 N. The parallel component is then 1009.4 N × sin(32°).

To find the sine of 32°, we use a calculator and get sin(32°) ≈ 0.5299. Multiplying this by the weight gives the parallel force on the skier, which is 1009.4 N × 0.5299 ≈ 534.8 N. Therefore, the force on the skier parallel to the slope is 534.8 Newtons.

Answer:

The pendulum should be made longer by 0.194m in order to increase its period by 0.32s

Explanation:

using the formula T= 2π[tex]\sqrt{\frac{L}{g} }[/tex]

rearranging the equation and making L subject of formula we have;

L=T²g/4π²

lets calculate the length when T=1.06s

g=9.8m/s² , π=3.124

[tex]L=\frac{1.06^{2}*9.8 }{4*3.142^{2} }[/tex]

L=0.279m

the new period after its increased by  0.32s = 1.06+0.32 =1.38s

[tex]L_{2}=\frac{1.38^{2}*9.8 }{4 *3.142^{2} }[/tex]

[tex]L_{2}=0.473m[/tex]

increase in length = 0.473 -0.279

               =0.194m

The pendulum should be "0.194 m" longer.

According to the question,

Time,

We know,

By using the formula,

→ [tex]T = 2 \pi \sqrt{\frac{L}{g} }[/tex]

or,

→ [tex]L = \frac{T^2g}{4 \pi^2}[/tex]

By substituting the values, we get

→     [tex]= \frac{1.06^2\times 9.8}{4\times 3.142^2}[/tex]

→     [tex]= 0.279 \ m[/tex]

Now,

The new period after it increased by 0.32 s, we get

= [tex]1.06+0.32[/tex]

= [tex]1.38 \ s[/tex]

then,

→ [tex]L_2 = \frac{1.38^2\times 9.8}{4\times 3.142^2}[/tex]

        [tex]= 0.473 \ m[/tex]

hence,

The increase in length will be:

= [tex]L_2-L[/tex]

= [tex]0.473-0.279[/tex]

= [tex]0.194 \ m[/tex]

Thus the answer above is right.

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Answer:

The runner's speed at the following times would remain 8.64 m/s.

Explanation:

Acceleration definition: Acceleration is rate of change in velocity of an object with respect to time.

In this case, after 3.6 seconds the acceleration is zero, it means that the velocity of the runner after 3.6 seconds is not changing and it will remain constant for the remainder of the race. Now, we have to find the velocity of the runner that he had after 3.6 seconds and that would be the runner's speed for the remainder of the race. For this we use first equation of motion.

First equation of motion:        Vf = Vi + a×t

Vf stands for final velocity

Vi stands for initial velocity

a stands for acceleration

t stands for time

In the question, it is mentioned that the runner starts from rest so its initial velocity (Vi) will be 0 m/s.

The acceleration (a) is given as 2.4 m/s²

The time (t) is given as 3.6 s

Now put the values of Vi, a and t in first equation of motion

                       Vf = Vi + a×t

                       Vf = 0 + 2.4×3.6

                       Vf = 2.4×3.6

                       Vf = 8.64 m/s

So,the runner's speed at the following times would remain 8.64 m/s.

Answer:

Explanation:

Given

Two baseballs are fired into a pile of hay such that one has twice the speed of the other.

suppose u is the velocity of first baseball

so velocity of second ball is 2u

suppose [tex]d_1[/tex] and [tex]d_2[/tex] are the penetration by first and second ball

using [tex]v^2-u^2=2 ad[/tex]

where v=final velocity

u=initial velocity

a=acceleration

d=displacement

here v=0 because ball finally stops

[tex]0-u^2=2ad_1----1[/tex]

for second ball

[tex]0-(2u)^2=2ad_2----2[/tex]

divide 1 and 2 we get

[tex]\frac{u^2}{4u^2}=\frac{d_1}{d_2}[/tex]

as deceleration provided by pile will be same

[tex]\frac{1}{4}=\frac{d_1}{d_2}[/tex]

[tex]d_2=4d_1[/tex]

thus faster ball penetrates 4 times of first ball

Final answer:

The faster baseball will penetrate farther into the pile of hay due to the greater change in kinetic energy caused by its higher speed.

Explanation:

In this scenario, we can analyze the problem using the concept of work and energy. When the slower baseball and the faster baseball are both fired into the pile of hay, the work done by air resistance on each baseball will be different. The work done by air resistance is equal to the change in kinetic energy of the baseball. Since the faster baseball has twice the speed of the slower baseball, it will experience a greater change in kinetic energy and therefore penetrate farther into the pile of hay.

Answer:

A,B,C,D,E

Explanation: Ranking the quantities from greatest to least, we have:

A.) Gravitational Force

B) Speed

C) KE

D) PE

E) momentum

The gravitational force is the greatest at periapsis and the least at apoapsis. The speed of the satellite orbits is greatest at periapsis and the least at apoapsis. The potential energy is highest at apoapsis and lowest at periapsis, while the kinetic energy is highest at periapsis and lowest at apoapsis.

The gravitational force is the greatest when the satellite is closest to the large mass (periapsis) and the force is the least when the satellite is farthest away (apoapsis).

The speed of the satellite is greatest at periapsis and least at apoapsis. This is because the gravitational force is strongest at periapsis, causing the satellite to accelerate and increase its speed.

The potential energy (PE) is highest when the satellite is farthest away (apoapsis) and lowest when the satellite is closest to the large mass (periapsis). The kinetic energy (KE) is highest when the satellite is closest to the large mass (periapsis) and lowest when the satellite is farthest away (apoapsis).

The momentum of the satellite remains constant throughout the elliptical orbit.

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Answer:

V = 2.94cm³

The initial volume at 20°C is 2.94cm³

Explanation:

As the temperature of the iron sphere increases the volume of the sphere also increase.

Using the equation for volumetric expansion:

∆V = VαΔT

where ;

V is the initial volume

α is the volumetric expansion coefficient

∆V is the change in Volume

∆T is the change in temperature

After Expansion the final volume can be written as:

Vf = V + ∆V

Vf = V + VαΔT

Vf = V(1 + αΔT)

making V the subject of formula;

V = Vf/(1+αΔT) .....1

Given:

Vf = 3.00cm³

ΔT= 600-20 = 580

And from the test book.

α = 35.5 × 10⁻⁶K⁻¹

Substituting the values into eqn 1

V = 3.00/(1+580× 35.5×10^-6)

V = 3.00/(1+0.021) = 3.00/1.021

V = 2.94cm³

The initial volume at 20°C is 2.94cm³

Answer: 1cm3

Explanation:

V1 =?

V2 = 3cm3

T1 = 20°C = 20 + 273 = 293K

T2 = 600°C = 600 + 273 = 873K

V1 /T1 = V2 /T2

V1 / 293 = 3 / 873

V1 = 293 x ( 3 / 873)

V1 = 1 cm3

Answer:

Cerebral palsy

Explanation:

Cerebral palsy - it is referred to that disorder which is related to damages that caused permanent disorder in the functioning of body parts.  it affects the proper functioning of muscles thus cause the coordination problem.

it is caused due to abnormalities in the brain that result in the coordination of the body. As it is related to abnormalities in the brain thus it also causes a problem in vision, speaking, hearing, etc

Answer:

4.06 m/s

Explanation:

It's pretty easy

since it has no atmosphere, so there won't be air/wind resistance that will slow it down.

Distance = ut + (1/2) g t^2

Distance = 2.03

U = initial velocity = 0

t = time = 1sec

g = x

2.03 = x(1^2)/2

4.06 = x

x = g = 4.06.

Answer:

1.55 m

Explanation:

Momentum: This can be defined as the product of  mass of a body and it velocity. the S.I unit of momentum is kgm/s.

Mathematically,

Momentum can be represented as,

M = mv................................. Equation 1

Where m = mass of the body, v = velocity of the body, M = momentum.

Making v the subject of the equation,

v = M/m........................................... Equation 2

Given: M = 0.80 kg.m/s, m = 0.145 kg.

Substituting into equation 2,

v = 0.8/0.145

v = 5.52 m/s.

Using the equation of motion,

v² = u² + 2gs ....................... Equation 3.

Where v = final velocity of the rubber ball, u = initial velocity of the rubber ball, s = distance, g = acceleration due to gravity.

Given: v = 5.52 m/s, u = 0 m/s, g = 9.81 m/s².

Substituting into equation 2

5.52² = 0² + 2(9.81)s

30.47 = 19.62s

s = 30.47/19.62

s = 1.55 m.

Thus the ball was dropped from a height of 1.55 m

Answer:

Length of shadow cast by hand= 5.0 cm

Explanation:

With the hand inclined at an angle θ=30.0∘ above horizontal, it can be imagined to form part of a right angled triangle that has the following parts

vertical screen=vertical part of the triangle where we cast the shadow of the hand

The hand=the hypotenuse side

The horizontal = side to which the hand makes the 30.0° angle

By trigonometric relationship

Sin θ°= Opposite/hypotenuse

Sin θ° = (Shadow cast by hand)/(Length of hand)

Sin 30° = ( length of shadow cast by hand)/10cm

or 0.5 = (length of shadow cast by hand)/10cm

Length of shadow cast by hand= 0.5 × 10cm = 5.0 cm

The thickness of a silicon wafer can be found using the volume of a cylinder and the density formula. Given the diameter and the mass, rearranging to solve for height will give the thickness of the wafer in millimeters.

The thickness of the silicon wafer can be found by using the formula for the volume of a cylinder (Volume = pi * radius2 * height) and the definition of density (Density = mass/volume). Given the silicon wafer has a diameter of 3 inches (or a radius of 1.5 inches), and a mass of 1.5g, we can determine the volume of the wafer from the given density. Rearranging the equation for the volume of a cylinder to solve for height (or thickness, in this case) gives: Thickness = Volume / (pi * radius2). Assuming measurements are converted correctly for consistent units, this calculation will give the thickness of the wafer in millimeters.

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Answer:

option C

Explanation:

given,

  [tex] \dfrac{v^3t}{A}[/tex]

where v is the speed

           t is the time

          A is the area

we know v = m/s  

     dimension of v = [LT⁻¹]

                            v³ = [L³ T⁻³]

                t  = s

      dimension of t = [T]

unit of area = m²

     dimension of A = [L²]

dimension of the given equation

  [tex]\dfrac{v^3t}{A}= \dfrac{[L^3T^{-3}][T]}{[L^2]}[/tex]

  [tex]\dfrac{v^3t}{A}= \dfrac{[L]}{[T^2]}[/tex]

                                 =[tex]\dfrac{Length}{time^2}[/tex]

hence, the correct answer is option C

Final answer:

In the equation [tex]v^3[/tex] * t / A, where v is speed, t is time, and A is the area, the result has the dimensions of length/time squared (L/[tex]T^2[/tex]), which represents an acceleration. The correct answer is c. [tex]length/time^2[/tex].

Explanation:

The equation given is [tex]v^3[/tex] * t / A. To determine the dimensions of the result, we need to assess each variable's dimensional formula. The velocity (v) has the dimension of length/time (L/T). Time (t) is already in the dimension of time (T). The area (A) has the dimension of length squared ([tex]L^2[/tex]).

Combining these, we have the dimensions for velocity cubed as [tex](L/T)^3[/tex], which gives us [tex]L^3/T^3[/tex]. This is multiplied by the time (T), resulting in [tex]L^3/T^2[/tex]. When we divide this by the area ([tex]L^2[/tex]), the result simplifies to L/T, which is the dimension of velocity. However, because we are dividing by area and not velocity, the final dimension is L/[tex]T^2[/tex], which is option c: [tex]length/time^2[/tex].

Answer:

F = -11199.63 N

Explanation:

given,

mass of the brick = 12 Kg

height of the fall, h = 1.9 m

thickness of the carpet = 2 cm = 0.02 m

average force = ?

velocity of brick just before hitting mat

[tex] v = \sqrt{2gh}[/tex]

[tex]v =\sqrt{2\times 9.81\times 1.9}[/tex]

      v = 6.11 m/s

velocity of brick just before hitting ground= 6.11 m/s

final velocity = 0 m/s

using equation of motion for acceleration calculation.

 v² = u² + 2 a s

 0² = 6.11² + 2x a x 0.02

 [tex]a = -\dfrac{6.11^2}{0.04}[/tex]

    a  =-933.3025 m/s²

now, average force is equal to

F = m a

F = 12 x (-933.3025)

F = -11199.63 N

negative sign represent the decelerating force.

Answer:

Explanation:

Given

Heat transfer [tex]Q=1.6\times 10^5\ J[/tex]

initial Temperature [tex]T_i=17.5^{\circ}\approx 290.5\ K[/tex]

Entropy change [tex]dS=485\ J/K[/tex]

The expression for entropy is given by

[tex]dQ=TdS[/tex]

[tex]T=\frac{dQ}{dS}[/tex]

[tex]T=\frac{1.6\times 10^5}{485}[/tex]

[tex]T=329.89\ K[/tex]

Temperature can be written as average of initial and final temperature

[tex]T=\frac{T_i+T_f}{2}[/tex]

[tex]329.89=\frac{T_f+290.5}{2}[/tex]

[tex]T_f=659.78-290.5[/tex]

[tex]T_f=369.28\ K[/tex]

Answer:

Purpose of family:

Basically main role of a family towards the society is its continuity by both reproduction and  interaction with each other. The main contribution of family to the society is society's continuation.

Types of families:

The family further divided into six types nowadays. Namely,

Defining each Family and their pros and cons :

1). Nuclear Family: The most basic kind of family is nuclear family based on two parents and their biological or adopted children. Number of children is variable, some have one and others have more than one. The main aim of the nuclear family is to up bring their kids and teach them how to socialize in the society.

Pros of nuclear family:

Cons of nuclear family:

2). Single Parent: Consists of either a mother or a father living with one or more than one child. Parents may initially married, separated or departed, or passed away (one of them). Like other family structures single parents also have some pros and cons.

Pros of single parent:

Cons of single parent:

3). Extended Family: Basically extended families are joint families, in which grandparents, parents and children live together to support each other both financially and socially.

Pros of extended family:

Cons of extended family:

4).Childless Family: Partners who have no any children either by choice or due to infertility.

Pros of childless family:

Cons of childless family:

5). Step family:

When two families start living to gather, like two divorced people get married and living together with their children (from 1st partner).

Pros of step family:

Cons of step family:

6) Grandparent Family: In which grandchildren are raised by their grandparents.

Pros of grandparent family:

Cons of grandparent family:

Similarities and Differences:

By considering the pros and cons of different family structure we come to the point that many of them have some similarities like financial stability, strong bonding, and more socialization. Likewise there are few differences as well as some families share strong bond while other suffers from isolation. Some are more financially stable and others are less. Some have children while other are childless. Some children have both parents while other have single or step patent. Some of them have high tolerance while other has less. Some live quality life whiles other compromise on their needs and wants.

Explanation:

Force is given by rate of change of momentum.

Mass of soccer ball = 430 g = 0.43 kg

Initial velocity = 0 m/s

Final velocity = 25 m/s

Change in momentum = 0.43 x 25 - 0.43 x 0

Change in momentum = 10.75 kg m/s

Time taken = 0.01 s

Rate of change of momentum = Change in momentum ÷ Time

Rate of change of momentum = 10.75 ÷ 0.01

Rate of change of momentum = 1075 N

Force = 1075 N

The average force acting on the ball is 1075 N in the direction of travel of ball.

Answer:

9.97sec

Explanation:

To solve for the period we can derive the formula as follows

ω=2πf

ω=2π/T

v=rω

v=2πr/T

T=2πr/v

[tex]T=\frac{2*3.142*10}{6.3}[/tex]

T=9.97sec

Answer:

Preventive Maintenance.

Explanation:

Preventive maintenance is nothing but The removal, installation, and repair of landing gear tires by the holder of a private pilot certificate on an aircraft owned or operated. Preventive maintenance in an aircraft is performed by any person with holding at least a private pilot certificate. Only he/she can approve an aircraft to return to service after performing Preventive maintenance tests.

Answer: The specific heat of the unknown solid is [tex]4.00J/g^0C[/tex]

Explanation:

As we know that,  

[tex]q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]    (1)

where,

q = heat absorbed  = 32.0 kJ = [tex]32.0\times 10^3J[/tex] J      (1kg=1000g)

[tex]m[/tex] = mass of unknown solid= 2.00 kg  = [tex]2.00\times 10^3g[/tex] (1kg=1000g)

[tex]T_{final}[/tex] = final temperature

[tex]T_{initial}[/tex] = initial temperature

[tex]\Delta T[/tex] =[tex]4.00^0C[/tex]

[tex]c[/tex] = specific heat of unknown solid = ?

Now put all the given values in equation (1), we get

[tex]32.0\times 10^3J=2.00\times 10^3g\times c\times (4.00^0C)][/tex]

[tex]c=4.00J/g^0C[/tex]

Therefore, the specific heat of the unknown solid is [tex]4.00J/g^0C[/tex]

The scientific heat of the unknown solid will be "4.00 J/g°C".

Given values are:

Heat absorbed, q = 32.0 kJ or, [tex]32.0\times 10^3[/tex] J

Mass, m = 2.00 kg or, [tex]2.00\times 10^3[/tex] g

Rise in temperature, ΔT = 4.00°C

We know the relation,

→ q = m×c×ΔT

or,

→    = m×c×([tex]T_{final} - T_{initial}[/tex])

By substituting the values,

[tex]32.0\times 10^3=2.00\times 10^3\times c\times 4.00[/tex]

             [tex]c = 4.00[/tex] J/g°C    

Thus the above answer is appropriate.

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Answer:

13520 N

Explanation:

Pascal's Principle: The principle states that the pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

The operation of hydraulic press and car brake system is based on pascal's principle.

From pascal's principle,

F/A = f/a ........................... Equation 1

Where F = force exerted by the large piston, A = area of the large piston, f = force applied to the small piston, area of the small piston.

Making F the subject of the equation

F = A(f/a)......................... Equation 2

Given: A = 0.13 m², a = 0.0075 m², f = 780 N

Substituting into equation 2

F = 0.13(780/0.0075)

F = 13520 N.

Thus the force exerted by the large piston = 13520 N

Answer:

You need at least 2.8 s to slow down your car to 100 km/h. If we add reaction time (≅0.3 s), you will need 3.1 s.

Explanation:

Hi there!

The equation of velocity for an object moving in a straight line is the following:

v = v0 + a · t

Where:

v = velocity at time t.

v0 = initial velocity.

a = acceleration.

t = time.

We have to find the time at which the velocity is 100 km/h with a decceleration of 4.9 m/s² and an initial velocity of 149 km/h. Let´s first convert km/h into m/s:

149 km/h · (1000 m / 1 km) · ( 1 h / 3600 s) = 41.4 m/s

100 km/h · (1000 m / 1 km) · ( 1 h / 3600 s) = 27.8 m/s

Now, let´s solve the equation of velocity for the time:

v = v0 + a · t

(v - v0) / a = t

Replacing with the data:

(27.8 m/s - 41.4 m/s) / -4.9 m/s² = t

Notice that the acceleration is negative because you are slowing down.

t = 2.8 s

You need at least 2.8 s to slow down your car to 100 km/h. If we add reaction time (≅0.3 s), you will need 3.1 s.

To get the car under the speed limit, it would take approximately 4.34 seconds.

To calculate the minimum time it takes for the car to get under the 100 km/h speed limit, we need to find the deceleration required to slow down from 149 km/h to 100 km/h.

First, let's convert the speeds to m/s. 149 km/h is equal to 41.4 m/s and 100 km/h is equal to 27.8 m/s.

Using the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the distance, we can rearrange the equation to solve for acceleration:

a = (v² - u²) / (2s)

Plugging in the values, we get a = (27.8² - 41.4²) / (2(-30.5)).

Solving this equation, we find that the minimum deceleration required is approximately -3.13 m/s².

Finally, we can use the formula a = Δv / t to find the minimum time:

t = Δv / a = (41.4 - 27.8) / 3.13 = 4.34 seconds.

Answer:

Bio psychology

Explanation:

Since, Dr. Wolski does research on the potential relationship between neurotransmitter deficiencies and mood states. His psychological specialty must be biological psychology.

Biological psychology, or bio psychology, is a discipline in which scientific investigation and clinical practice investigates the relation between brain and body. In this area scholars evaluate the biological basis of feelings, impulses and behaviors.

Answer:

Explanation:

A continuous spectrum shows all colors of the rainbow with no gaps, produced by a solid or very dense gas emitting radiation. In contrast, a line spectrum consists of only certain discrete wavelengths - either as an absorption spectrum with dark lines representing absorbed wavelengths, or as an emission spectrum showing bright lines for emitted wavelengths from excited gas atoms.

The difference between a continuous spectrum and a line spectrum mainly lies in the type of light they represent. A continuous spectrum is formed when a solid or a very dense gas gives off radiation, showing an array of all wavelengths or colors of the rainbow. This can be seen when white light is passed through a prism as represented in Figure 5.10. It's like viewing a rainbow where all the colours blend into each other without any gaps.

On the other hand, a line spectrum, which could either be an absorption or an emission spectrum, consists of light in which only certain discrete wavelengths are present. Absorption spectrum appears as a pattern of dark lines or missing colors superimposed on the continuous spectrum, created when a cloud of gas absorbs certain wavelengths from the continuous spectrum behind it. Meanwhile, an emission spectrum appears as a series of bright lines when we examine an excited gas cloud, demonstrating that the gas is emitting light at only certain wavelengths, as showcased in Figure 5.12.

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Answer:

Explanation:

a)Magnitude = [tex]\sqrt{(x1-y2)^{2} + (x1-x2)^{2} }[/tex]

84=[tex]\sqrt{(0- (-67))^{2} + (x-0)^{2} }[/tex]

x= +50.67 or -50.67 units

b) We are given that the resultant is entirely in the -ve x direction which means that the y-component of the resultant is 0; It means that the y-component of the next vector = -ve of the y component of the initial vector i.e 67.

To make the magnitude 80 units in the negative x direction where the y component is 0, the x component must be -130.67(-50.67 - 80) as the x component is + 50.67units.

Magnitude = [tex]\sqrt{(0- (67))^{2} + (-130.67)^{2} }[/tex] = 146.85 units

c) The direction vector = 67/146.85 i  - 130.67/146.85 j where i corresponds to the vector in y direction and j corresponds to the vector in x direction. Or this vector is at an angle of 180 - [tex]Tan^{-1}(67/130.67)degrees[/tex] i.e 152.85 degrees from the +ve x-axis.

A) The two possibilities for the x-component are; +50.67 units or -50.67 units

B) The magnitude of the vector added to the original one is; 146.85 units

C) The direction of the vector is; θ = 207.15°

A) We are given;

Magnitude of vector = 84 units

Y-component of the vector = -67 units

We know that the formula for for 2 vectors like this in x and y direction is;

A = xi^ + yj^

Where A is the magnitude of the resultant

x is the value of the x-component

y is the value of the y-component

Thus;

A = √(x² + y²)

84 = √(x² + (-67)²)

84² = x² + 4489

7056 = x² + 4489

x = ±√(7056 - 4489)

x = ±50.67 units

B) From A above, let us take the positive value of the x-component and as such our original vector will be;

A = 50.67i^ - 67j^

We want to add another vector to this that would make the resultant to be -80 units in the x direction. Thus, A = -80i and if the new additional vector is V^, then we have;

-80i^ = (50.67i^ - 67j^) + V^

V^ = -(80 + 50.67)i^ + 67j^

V = -130.67i^ + 67j^

The magnitude of vector V is;

V = √(x² + y²)

V = √(-130.67)² + 67²)

V = 146.85 units

C) The direction of the vector V is;

θ = tan^(-1) (y/x)

θ = tan^(-1) (67/-130.67)

θ = -27.15°

Since it points entirely in the negative x axis, then the angle is;

180 - (-27.15) = 207.15°

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Answer:

composite track

Explanation:

To travel an incredible circular track, the guide must constantly change course because the extraordinary circular track is a turn when plotted on a Mercator map. It is ridiculous to try to navigate an incredible circular route. All things considered, to make the best use of the shorter cruise separation from the extraordinary circular runway, pilots generally divide an incredible hover runway between the underlying position and the target into many much smaller sections ( for trajectory purposes) of approximately one to several days of cruising time (based clearly on the specialty and conditions) and making course changes every day simultaneously, generally in the early afternoon. Absolute separation is thus the set of separations of these fragments determined by the methods of Mercator Sailing. A potential problem with the incredible circular track, however, is the most limited route between two areas, similarly for most tracks closer to the well (or at a higher range) than the two points, starting point or goal. The high areas are often in danger due to the terrible climate and icing. A protected thought of a veteran sailor is to set a range limit for the long voyage plan. This arrangement is called an extraordinary composite circle course arrangement, terminated with way points. This minicomputer soothes the monotonous procedure for deciding these way points for travel.

Answer:

The answer is composite track.

Explanation:

For ships to cover the shortest distance between two points on the surface of the earth, navigators base their calculations using great circles. A great circle is circular line drawn on a globe that follows the circumference of the earth ( thereby dividing the globe into equal halves ).  As the ship moves from one point to the other, the navigator adjusts its course because the earth is on a constant rotation. Great circles, because they usually cover distances of about 40,000km are broken down into smaller lines called Rhumb so as to provide a steady course. The one common great circle is the equator and the ship's heading does not change on this line.