In a recent study of how mice negotiate turns, the mice ran around a circular 90∘ turn on a track with a radius of 0.10 m. The maximum speed measured for a mouse (mass = 18.5 g) running around this turn was 1.39 m/s. Part A What is the minimum coefficient of friction between the track and the mouse's feet that would allow a turn at this speed?

Answer:

Define universal gravitational constant. Why is newton's law of gravitation called universal law?

By using Newton's Second law of motion, the largest mass that can be lifted by this input force is equal to 2,244 kg.

Based on the information provided, we can logically deduce that the output to input force ratio is equal to 22:1. This ultimately implies that, the input force is equal to 1000 N, which would result in an output force of 22,000 N.

Next, we would calculate the largest mass by using Newton's Second law of motion:

Mass = Force/Acceleration

Mass = 22,000/9.8

Mass = 2,244 kg.

Note: Acceleration due to gravity is equal to 9.8 m/s².

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[tex]\large\boxed{Formula: I= \frac{Q}{t}}[/tex]

Let's solve!

The formula is given above.

Let's substitute the values according to the formula.

We'll have to divide the measure of charge by the given time.

[tex]I= \frac{40}{10}[/tex]

Final answer:

[tex]\large\boxed{= 4 \: Amps \: (A)}[/tex]

Hence, the current is 4 amps.

Answer:

See below....the question is unclear....pick the answer you think they want

Explanation:

Car goes from 30 m/s    to   24 m/s   in 10 seconds

acceleration = change in velocity/change in time

                     =   -6 m/s   / 10 s   =  - 3/5   m/s^2  

The wording of the question is not very good.....perhaps they meant to say that after the 5 seconds the velocity is now 24 m/s ?

a1 *10   +   a2 *5   = -6 m/s  

            ( 6 m/s is the change in velocity from 30 to 24 m/s)    

    a1/a2 = 1.5    so   a2 = a1/1.5   (substitute this in)

10 a1   + 5 ( a1/1.5)  =-6

15 a1 + 5 a1  = -9

a1 =  - .45 m/s^2

The velocity of the car at the end of the initial ten-second interval, given that the car further slows down for the next five seconds, is 25.5 m/s

From the first statement, we have:

v₁ = u₁ + a₁t₁

v₁ = 30 + (a₁ × 10)

v₁ = 30 + 10a₁ ......(1)

From the second statement, we have:

v₂ = u₂ + a₂t₂

24 = u₂ + (a₂ × 5)

24 = u₂ + 5a₂   .......(2)

But,

u₂ = v₁ = 30 + 10a₁

Thus, we have:

24 = 30 + 10a₁ + 5a₂

But,

a₁/a₂ = 1.5

a₁ = 1.5a₂ ..... (3)

Thus, we have:

24 = 30 + 10a₁ + 5a₂

24 = 30 + 10(1.5a₂) + 5a₂

24 = 30 + 15a₂ + 5a₂

24 = 30 + 20a₂

Collect like terms

24 - 30 = 20a₂

-6 = 20a₂

Divide both sides by 20

a₂ = -6 / 20

= -0.3 m/s²

Substituting the value of a₂ into equation 3, we have

a₁ = 1.5a₂

= 1.5 × -0.3

= -0.45 m/s²

Substitute the value of a₁ into equation 1 to obtain the velocity, v₁ at the end of the initial to 10 s

v₁ = 30 + 10a₁

= 30 + (10 × -0.45)

= 30 - 4.5

= 25.5 m/s

Thus, velocity of the car at the end of the initial ten-second interval is 25.5 m/s

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A. The average velocity of the particle in the time interval t₁=2sec and t₂=3sec is 4 i m/s.

B. The velocity and acceleration at any time t is  4t i +1 j and 4i.

C. The average acceleration in the time interval given in part (a) is 4

Acceleration can be defined as the rate change of velocity with time.

acceleration a = (Δv) / (Δt)

Given the following equation shows the position of a particle in time t, x=at² i + bt j

where t is in second and x is in meter. a=2m/s², b=1m/s.

A. Velocity is time rate of change of displacement.

V = dx/dt

V = d/dt (2t² i + 1t j)

V = 4t i +1 j

Velocity in time interval,

At  t₁=2sec , V₂= 4x2 i + 1 j = 8 i + 1 j

At  t₂=3sec, V₃ = 4x3 i + 1 j = 12 i + 1 j

Average velocity in time interval t₁=2sec and t₂=3sec is

, V₃ - V₂ = (12 i + 1 j) - ( 8 i + 1 j )

Average velocity =  4 i

B. Velocity at time t, is

V(t) = V = 4t i +1 j

Acceleration a = dV/dt

a(t) = d/dt (4t i +1 j)

a(t) = 4 i +0 j

C. Average acceleration in time interval t₁=2sec and t₂=3sec is

a = 4 m/s²

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Answer:

1680 seconds

Explanation:

[tex]28 hrs * \frac{60 s}{1 hr} =1680s[/tex]

Answer:

See below

Explanation:

Alcohol first goes slightly down because of the expansion of the glass of thermometer before doing up.

[tex]\rule[225]{225}{2}[/tex]

The steel would expand by 4. 8 * 10^-3 cm

The change in length  ΔL is proportional to length  L. It is dependent on the temperature, substance, and length.

Using the formula:

ΔL= α LΔT

where  ΔL  is the change in length  L = 10cm

ΔT  is the change in temperature = 60° - 20° = 40° C

 α  is the coefficient of linear expansion = 1.2 x 10^-5 °C

Substitute into the formula

ΔL = [tex]1.2 * 10^-5 * 10 * 40[/tex]

ΔL = [tex]4.8 * 10 ^-3[/tex] cm

Therefore, the steel would expand by 4. 8 * 10^-3 cm

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This is an exercise of thermal scales.

T = 40 °C

T = °F ¿?

To convert degrees Celsius to degrees Fahrenheit, we have the formula:

[tex]\bf{^{\circ}F=\dfrac{9}{5} \ ^{\circ}C+32 \ \ \to \ \ \ Formula }[/tex]

We substitute our data into the formula.

[tex]\bf{^{\circ}F=\dfrac{9}{5} \times 40+32}[/tex]  

First we divide 9/5 multiplied by 40.

[tex]\bf{=75+32}[/tex]

Add 75 plus 32

[tex]\bf{=104 \ ^{\circ}F}[/tex]

Therefore, the temperature change of 40 °C on the °F scale is equal to 104.

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Piscis04}}}}}}[/tex]

Here, the calculated Magnitude of the load P is 2945.2 kN, the Longitudinal strain produced is 0.0005 and the decrease in length is 2 mm.

Given,

Length, L = 4 m

Outer diameter, D = 300mm, D= 0.3 m

Thickness, t = 50 mm, t = 0.05 m

Stress produced, σ = 75000 kN/m²

Young's modulus for cast iron, E = 1.5 x 10⁸ kN/m²

Calculating the diameter of the cylinder,

Diameter of cylinder, d = (D) – (2t) = 0.3 –( 2 × 0.05)

d= 0.2 m

(i) Magnitude of the load P:

Using the relation, σ =P/A

P = σ × A = 75000 × π /4 (D² – d² )

P= 75000 × π/4 (0.3² – 0.2²)

P= 75000 × π/4 (0.09 – 0.04)

P = 2945.2 kN

Hence, Magnitude of the load P is 2945.2 kN.

(ii) Longitudinal strain produced, e :

Using the relation, Strain, (e) = stress/E

e= 75000/(1.5 x 10⁸)= 0.0005

Hence, the Longitudinal strain produced is 0.0005.

(iii)Total decrease in length, dL:

The total decrease in length can be calculated using the strain as the ratio of change in length to the original length is known as Strain.

Strain = change in length/original length

e= dL/L

0.0005 = dL/4

dL = 0.0005 × 4m = 0.002m=2mm

Hence,the decrease in length is 2 mm.

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Answer: 1.32 x 10^-9 m

Explanation:

The formula for the radius of nth orbital is:

[tex]r_{n}=\frac{n^{2}}{Z} \times 0.528 \text { Angstorms }[/tex]

For hydrogen, Z= 1, so we have:

[tex]$$\begin{aligned}r_{n} &=5^{2} \times 0.528 \text { Angstorm } \\&=13.2 \text { Angstorms } \\&=13.2 \times 10^{-10} \mathrm{~m} \\&=1.32 \times 10^{-9} \mathrm{~m}\end{aligned}$$[/tex]

Answer: 1.32*10^-9

Explanation: I had the same question and here's what I got:

rn = n2(r1)

n = 5

r = 5.29*10^-11

rn = n^2(r1)

= 5^2(5.29*10^-11)

r = 1.32*10^-9

a) Mirrors

Mirror requires the high luster of metals in order to work.

When light shine on to the surface of a metal, its electrons absorb small amounts of energy and become excited into one of its many empty orbitals.

The electrons immediately fall back down to lower energy levels and emit light.

This process is responsible for the high luster of metals.

Here,

Mirrors have metal coating on its back side, because of high reflective property , high lustrous mirror is preferred . When metal is more lustrous, the less light reflect into it and bounces back.

Coating one side of a piece of glass with shiny metals can turn it into a mirror, reflecting light coming toward it.

Window glass can reflect only eight percent of light hitting it, while mirrors can reflect 95 percent of light hitting them.

The glass in a mirror is usually coated with a layer of silver or aluminum.

Mirrors are shiny because when photons (rays of light) coming from an object , it strike the smooth surface of a mirror, then they bounce back at the same angle. Our eyes see these reflected photons as a mirror image.

Therefore,

Mirror requires the high luster of metals in order to work.

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Answer:A) mirrors

Explanation:

Weight is compared with the gravitational force exerted on each of them by the Earth.

Newton's law of gravity states that each particle having mass in the universe attracts each other particle with a force known as the gravitational force.

The gravitational force is proportional to the product of the masses of the two bodies and inversely proportional to the square of their distance.

When mass increases and distance reduces, gravity rises. Gravity also lowers when the distance between two points grows and the mass decreases.

The gravitational force is balanced by weight;

[tex]\rm F = W \\\\ G\frac{mM}{r^2} =mg[/tex]

Hence, weight is compared with the gravitational force exerted on each of them by the Earth.

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So, the complete sentence is If the mass of the sun is 2x, at least one planet will fall into the habitable zone if I place a planet in orbits 84, 1, and 5, and all planets will orbit the sun successfully for the best conditions.

When the mass of the sun is larger, Earth moves around the sun at a faster pace and When the mass of the sun is smaller, Earth moves around the sun at a slower pace.

When Earth is closer to the sun, its orbit becomes faster and When Earth is farther from the sun, its orbit becomes slower.

When Earth is closer to the sun, there will be a hotter climate. A little movement that takes one closer to the sun could lead to a huge impact, as the sun is very hot.

So, it can be concluded that If the mass of the sun is 2x, at least one planet will fall into the habitable zone if I place a planet in orbits 84, 1, and 5, and all planets will orbit the sun successfully for the best conditions.

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The value of x given the data from the question is 0.86 m

From the data given above, we can s determine the energy as follow:

E = mgh

E = 3 × 9.8 × 5

E = 147 J

E = ½Ke²

147 = ½ × 400 × x²

147 = 200 × x²

Divide both side by 200

x² = 147 / 200

Take the square root of both sides

x = √( 147 / 200)

x = 0.86 m

Since the block came to rest, there is no motion

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Answer:

Magnification= -image distance/object distance

.253=image distance/33.5

image distance= 8.48 cm

In the opposite figure, the work done by the force F to push the box upwards from the ground to the top of the inclined plane is 600 J.Option c is correct.

Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.

The displacement value from the triangle is;

[tex]\rm sin 30^0 = \frac{P}{H} \\\\ H=S =\frac{3 \ m}{sin 30^0} \\\\ S = 6\ m[/tex]

The work done is found as ;

[tex]\rm W= Fd \\\\ W = 100 \ N \times 6 \\\\ W= 600 \ J[/tex]

The force F in the opposing figure does 600 J of effort to lift the box from the ground to the top of the inclined plane.

Hence option c is correct.

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(a)  The charge stored in the 5.00-μF capacitor is 37.2  μC.

(b) The potential difference across the 10.0-μF capacitor is 3.72 V.

The capacitance of a capacitor is defined as the ratio of the charge stored and the potential difference between the capacitor.

The capacitance of a capacitor is denoted by C and expressed as

C = Q/V

Given, 5.00 μF, 10.0 μF, and 50.0 μF capacitors are connected in series across a 12.0-V battery.

(a) The equivalent capacitance is

1 / Ceq = 1 / C₁ +1 / C₂ + 1/ C₃

Substitute the values, we get

Ceq = 3.1  μF

The charge stored in 5.00-μF capacitor is

Q  = Ceq x V

Q = 3.1  μF x 12 V

Q = 37.2  μC

Thus, the charge stored in the 5.00-μF capacitor is 37.2  μC

(b) The potential difference across the 10.0-μF capacitor is given by

V = Q/C₂

Put the values, we get

V = 37.2 / 10

V = 3.72 V

Thus, the potential difference across the 10.0-μF capacitor is 3.72 V.

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The value of the electric current for the given conditions willl be  1939.02 A.

Ohm's law claims that the voltage across a conductor is directly proportional to the current flowing through it.

Ohm's law claims that the voltage across a conductor is direct to the current flowing through it. This current-voltage connection may be expressed mathematically as,

V=IR

15.9 V = I × 8.2 × 10³ Ω

I = 1939.02 A

Hence, the value of the electric current for the given conditions willl be  1939.02 A.

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a. The spring is compressed  by  0.174 m.

b.  The vertical distance the dart travels from its position when the spring is compressed to its highest position is 9.6 m.

c. The horizontal velocity of the dart at that time is  13.74 m/s.

d. The horizontal distance from the equilibrium position at which the dart hits the ground is 19.236 m.

The energy by virtue of its position is called the potential energy.

a. Given is the potential energy stored in the compressed spring of a dart gun, with a spring constant of 62.00 N/m, is 0.940 J.

PE  of spring = 1/2 kx²

Put the values, we get

P.E = 0.940 = 1/2 x 62 x²

x = 0.174 m

Thus, the spring is compressed by 0.174 m.

b. Given is a 0.010 kg dart is fired straight up.

The vertical height is find out by

0.940 J = (0.010 kg) (9.8 m/s²) h

h = 9.6 m

Thus, the vertical distance the dart travels from its position is 9.6 m

c. From the conservation of energy principle, total mechanical energy is conserved.

1/2 mv² =mgh

v = √2gh

Plug the values, we get

v = √2 x 9.8x 9.6

v = 13.74 m/s

Thus, the horizontal velocity is  13.74 m/s.

d.  Time that dart spends in air, t = √2h/g

t = √(2x9.6)/9.81

t = 1.4 s

The horizontal distance from the equilibrium position at which the dart hits the ground.

Horizontal distance = (Velocity on x direction) x time

Horizontal distance = 13.74 m/s x 1.4s

Horizontal distance = 19.236 m

Thus, the horizontal distance is 19.236 m.

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This is a uniform rectilinear motion (MRU) exercise.

To start solving this exercise, we obtain the following data:

To calculate distance, speed is multiplied by time.

We apply the following formula: d = v * t.

We substitute the data in the formula: the speed is equal to 4.6 m/s, the time is equal to 10 s, which is left as follows:

[tex]\bf{d=4.6\dfrac{m}{\not{s}}*10\not{s} }[/tex]

[tex]\bf{d=46 \ m}[/tex]

Therefore, the speed at 10 seconds is 46 meters.

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

a. The magnitude of the impulse which the player must impart to the ball is 17.25 kg.m/s.

b. The magnitude of average acceleration of the player's head during the impact is   195.66 m/s².

The change in momentum is equal to the product of impact force applied while colliding and time for that impact.

Impulse F. t = m (Vf -Vi)

where, Vf is the final velocity and Vi is the initial velocity.

Given, a soccer player 'heads' a size 3 ball deflecting it by 40.0°, and keeps its speed of 13.20 m/s constant. A size 3 ball has a mass of approximately 2.000 kg.

a. Substitute the values into the expression, we get

Impulse (x) = 2 x (13.20 - 13.20cos40°)

Impulse  (x) = 3.088 kg.m/s

Impulse in y direction, is

Impulse (y) = 2 x  13.20sin40°

Impulse (y)  = 16.97 kg.m/s

so, the magnitude of impulse is

I = sq rt(Ix² + Iy²)

Put the values, we get

I = 17.25 kg.m/s

Thus, the magnitude of the impulse which the player must impart to the ball is 17.25 kg.m/s

b. The player's head has a mass of 2.90 kg. The brief time of the impact, 30.40 ms,

F.t = I

Put the given values, we have

F = 17.25 / 30.40 x 10⁻³

F = 567.434 N

From the Newtons second law of motion,

F = ma

Plug the values from the question, we have

567.434 N =  2.90 x a

a = 195.66 m/s²

Thus the magnitude of average acceleration of the player's head during the impact is  195.66 m/s².

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The term temperature has to do with the  measure of an object's "hotness".

The term temperature has to do with how hot or cold a body is. In other words, the word temperature brings us to call to mind the degree of hotness or coldness of a body.

Succinctly put, the term temperature has to do with the  measure of an object's "hotness".

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The estimated density of the golf ball is  170  kg/m³

What is density?

Density is the ratio as Mass per unit Volume.

In displacement method,  

First , we measuring the volume of water displaced by an object which tell us the volume of the object then we will use the physical balance to determine its mass.

Then calculate the density by dividing the mass by the volume.

Here,  D = m/V

By displacement method , the estimated volume of golf ball is 100 cm³  and estimated mass is 600 g

Then ,

Density =  100 cm³ / 600 g = 0. 17 g/ cm³ = 170  kg/m³

So the estimated density of golf ball is  170  kg/m³

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At 11.3°C the rod will just come into contact

Coefficient of linear expansion of aluminium [tex]\alpha_{Al}[/tex] = [tex]23*10^-^6[/tex] °[tex]C[/tex]

Coefficient of linear expansion of Brass [tex]\alpha_{B} =19*10^-^6[/tex] °[tex]C[/tex]

[tex]\alpha = \Delta{L}/Lo(T2-T1)[/tex]

For aluminium

[tex]\alpha_{Al} = \Delta{L}/Lo(T-0)[/tex]

[tex]\Delta{L_{1}} = (23*10^-^6*50*T)[/tex]

For Brass

[tex]\alphaB = \Delta{L_{2}/Lo(T-0)[/tex]

[tex]\Delta{L_{1} +\Delta{L_{2} =0.024cm(23*10^-^6*50*T)+(19*10-6*50*T) =0.024[/tex]

T =11.43 °C

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The first law states that the internal energy change of that system is given by Q − W . Since added heat increases the internal energy of a system, Q is positive when added to the system and negative when removed from the system.

R=√20²+40²+2.20.40 cos 50

R=55 N

R/sin β = F/sin α

55/sin 50 = 40/sin α

α = 33°

Physical science explains the physical world and not supernatural events and an idea is considered true by science if it can be observed, explained and reproduced by others.

Physical science is a systematic study of the of the physical world and phenomena based on observation and experiments.

The scientific method involves:

Science explains the physical world and not supernatural events.

Science studies physical phenomena such as the stars, the planets, living things, etc.

Science do not study about angels or demons or supernatural events.

An idea is considered true by science if it can be observed, explained and reproduced by others.

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The loops must the coil have to generate a maximum emf of 2500 will be 439.

According to  Faraday's law of electromagnetic induction, the rate of change of magnetic flux linked with the coil is responsible for generating emf in the coil resulting in the flow of amount of current.

Given data;

Area,A = 0.239 m²

Angular velocity,ω=373 rad/sec

Magnetic field,B=0.0639 T

Maximum emf,E= 2500V

The formula for the maximum induced voltage is;

E{max} = N ×  B × A × ω

2500 = N × 0.639 × 0.0239 × 373

N = 438.66

N = 439 \ turns

Hence, loops must the coil have to generate a maximum emf of 2500  will be 439.

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Answer: 11392.99

Explanation: I had the same problem and here are the steps:

Values:

N (Number of loops) = 2000

A (area) = 0.239

ω (angular velocity) = 373

B (magnitude) = 0.0639

ε = NABω

= (2000)(0.239)(373)(0.0639)

ε = 11392.99 (FINAL ANSWER)

We will use the design process to meet the requirements of the competition by the given explained in the main answer.

The initiative was taken by two or more parties operating independently to win the business of a third party by competing to hire contractors on the best terms possible.

The complete question is

"A local businessperson placed an advert in the local newspaper for a competition for girls only from different schools to participate in the competition. The competition is about drawing ideas for a shopping complex for the local community. Girls from the different schools are excited about the competition. you are a group of boys in the local schools who saw the advert and feel it is unfair for you to be excluded from the competition.

consider yourself as one of the learners in the local schools.

Explain why the project should be given to boys also who have better skills for this project than the girls do.

1.2 think about the design process skills, investigates, design, make, evaluate and communicate."

Explain how you will use the design process to meet the requirements of the competition.

[ 1.1 ]Boys should also be given the project because some of them have more artistic talent than girls do when it comes to sketching designs for local shopping centers.

Boys can also present a clear picture of how local communities can expand their shopping options.

For instance, they can encourage local merchants to offer seasonal items because doing so will benefit their businesses.

They can also suggest that retailers encourage customers to bring a friend to participate in competitions, which will be highly regarded.

[1.2] In order to fulfill the needs of the competition, I would make sure to explore how a shopping center for the neighborhood functions, for instance, by making sure I am aware of the strategies one may use to enhance his or her firm in the neighborhood.

In order to win the competition, I would make sure that I was confident in what I was saying and that I was audible enough to be heard during the competition.

Finally, I would make sure I met the competition's conditions by staying on-topic and solely addressing the issues raised in the advertisement

Hence will use the design process to meet the requirements of the competition.

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