The existence of the dwarf planet Pluto was proposed based on irregularities in Neptune's orbit. Pluto was subsequently discovered near its predicted position. But it now appears that the discovery was fortuitous, because Pluto is small and the irregularities in Neptune's orbit were not well known. To illustrate that Pluto has a minor effect on the orbit of Neptune compared with the closest planet to Neptune:

Required:
a. Calculate the acceleration due to gravity at Neptune due to Pluto when they are 4.50x10^12 m apart, as they are at present. The mass of Pluto is 1.4x10^22 kg.
b. Calculate the acceleration due to gravity at Neptune due to Uranus, presently about 2.50x10^12 m apart, and compare it with that due to Pluto. The mass of Uranus is 8.62x10^25 kg.

Answer:

[tex]F_4=\frac{4}{b}F_1[/tex]

Explanation:

Centripetal force is the net force acting on a body which makes it move along a curved path. This force is always towards the center of curvature.

The centripetal force is given by:

F = mv² / r

where m is the mass of the body, v is the velocity of the body, r is the radius, F is the centripetal force and v²/r is the centripetal acceleration.

Given that:

[tex]\frac{v_4}{v_1}=2\\\\v_4=2v_1\\\\ Also, radius\ of\ lane\ 4(r_4)=2*radius\ of\ lane\ 1\\\\Let\ r_1\ be\ radius\ of\ lane\ 1,m=mass\ of\ runner\ in\ lane\ 1=mass\ of\ runner\ in\ lane\ 4\ \\and\ v_4=velocity\ of\ runner\ in\ lane\ 4.\ Hence:\\\\r_4=b*r_1=br_1\\\\The\ centripetal\ force\ for\ lane\ 4(F_4)\ is:\\\\F_4=\frac{mv_4^2}{r_4}\\\\ F_4=\frac{m(2v_1)^2}{br_1}\\\\F_4= \frac{4mv_1^2}{br_1} \\\\But\ F_1=\frac{mv_1^2}{r_1}\\\\Hence\ F_4=\frac{4}{b}F_1[/tex]

F4 is equal to 4/b F1. A further explanation is provided below.

According to the question,

The net force of the object in uniform circular motion will be:

→ [tex]F = \frac{mv^2}{r}[/tex]

∴ [tex]F_1 = \frac{m_1 v_1^2}{r_1}[/tex]

  [tex]F_4 = \frac{m_4 v_4^2}{r_4}[/tex]

Now,

→ [tex]\frac{F_1}{F_4} = \frac{m_1}{m_4}\times (\frac{v_1}{v_4} )^2\times \frac{r_4}{r_1}[/tex]

   [tex]\frac{F_1}{F_4} = \frac{1}{4}\times b[/tex]

   [tex]F_1 = \frac{b}{4} F_4[/tex]

   [tex]F_4 = \frac{4}{b} F_1[/tex]

Thus the above response i.e., "option b" is correct.

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Answer:

T = 3.14 10⁻²  s

Explanation:

The general equation for a traveling transverse wave is

           y = A sin (k x - wt +Ф)

where w is the angular velocity that is related to the period and Ф is the phase of the oscillation

           w = 2π / T          (1)

In this case they indicate that the expression of the wave

         y = 0.003 cos (20 x + 200t)

if we use the relationship of the double angles

          a = kx - wt

          b = Ф

          sin (a + b) = sin a cos b + sin b cos a

for the case Ф = 90 we have

          sin (a + b) = cos b

we substitute

          y = A cos (kx -wt)

with an initial phase of fi = 90º

if we compare the terms of the two expressions

         A = 0.003 m  

         k = 20 m⁻¹

         w = -200  rad/s

the negative sign indicates that the wave goes to the left

if we clear from equation 1

          T = 2π / w

          T = 2π / 200

          T = 3.14 10⁻²  s

Answer:

C increase in potential energy

Answer:

B - the box pushing against the boy

Explanation:

Newton's third law of motion also known as the law of action and reaction  states that for every action there is equal and opposite reaction.

The action force is the force acting in one direction while the reaction force is  the force acting in the opposite direction. for example, when a person wants to jump, the person exerts a downward force on the ground known as action force and also, the ground exerts upward force on the person known as reaction force.

If the action force is the boy pushing the box, what is the reaction force is the box pushing against the boy.

Answer:

Explanation:

Work done by janitor = increase in potential energy of book

Potential energy = mgh , m is mass  , h is displacement in height and g is acceleration due to gravity .

here displacement in height of book = 2.6 - 1.3 = 1.3 m

so h = 1.3 m

m = mass of the box

increase in potential energy of box = m x 9.8 x 1.3

= 12.74 m

Work done by janitor = 12.74 m Joule .

Answer:

37.33m

Explanation:

Using the equation of motion

S = ut + 1/2gt^2

Time t = 2.76secs

g = 9.8m/s^2

S = 0 + 1/2(9.8)(2.76)^2

S = 4.9*7.6176

S = 37.33

Hence the window is 37.33m above the ground

Answer:

44.5s ; 22.64 m/s

Explanation:

The motion of the truck could be separated into 3 different phases :

First :

Time of motion :

Initial Velocity, u = 0 ; final velocity, v = 29 m/s

Acceleration, a = 2 m/s²

Recall: acceleration = change in velocity / time

Time = change in velocity / acceleration

Time = (29 - 0) / 2 = 14.5 second

Distance traveled = ((29 + 0) /2) * 14.5 = 210.25 m

Second :

Time = 25 seconds at constant speed

29 m/s for 25 seconds

v*t = 29 * 25 = 725 m

Third:

5 seconds before coming to rest

((29 + 0) /2) * 5

14.5 * 5 = 72.5 m

A.)

Length of journey = (14.5+ 25 + 5) = 44.5 seconds

B.)

Average velocity = total distance / total time taken

Average velocity = (210.25 + 725 + 72.5) / 44.5

= 1007.75 / 44.5

= 22.646067

= 22.64 m/s

Answer:

v = 5.7554 m/s

Explanation:

First of all we need to know if the angle of the vine is measured in the horizontal or vertical.

To do this easier, let's assume the angle is measured with the horizontal. In this case, the innitial height of the monkey will be:

h₀ = h sinα

h₀ = 5.32 sin43° = 3.6282 m

As the monkey is dropping from the innitial point which is the suspension point, is also dropping from 5.32. Then the actual height of the monkey will be:

Δh = 5.32 - 3.63 = 1.69 m

In order to calculate the speed of the monkey we need to understand that the monkey has a potential energy. This energy, because of the gravity, is converted in kinetic energy, and the value will be the same. Therefore we can say that:

Ep = Ek

From here, we can calculate the speed of the monkey.

Ep = mgΔH

Ek = 1/2 mv²

The potential energy is:

Ep = 16.9 * 9.8 * 1.69 = 279.9

Now with the kinetic energy:

1/2 * (16.9) * v² = 279.9

v² = (279.9) * 2 / 16.9

v² = 33.12

v = √33.12

Hope this helps

Answer:

d = 10.2 m

Explanation:

When the car travels up the inclined plane, its kinetic energy will be used to do the work in climbing up. So according to the law of conservation of energy, we can write that:

[tex]Kinetic\ Energy\ of\ the \ Car = Work\ Done\ while\ moving\ up\ the\ plane\\\frac{1}{2}mv^{2} = Fd[/tex]

where,

m = mass of car

v = speed of car at the start of plane = (36 km/h)(1000 m/1 km)(1 h/3600 s)

v = 10 m/s

F = force on the car in direction of inclination = W Sin θ

W = weight of car = mg

θ = Angle of inclinition = 30°

d = distance covered up the ramp = ?

Therefore,

[tex]\frac{1}{2}mv^{2} = mgdSin\theta\\\frac{1}{2}v^{2} = gdSin\theta\\\frac{1}{2}(10\ m/s)^{2} = d(9.81\ m/s^{2}) Sin\ 30^{0}[/tex]

d = 10.2 m

Answer: Change occurs when forces in one direction exceed forces in opposing direction

Explanation:

Force field analysis is the basic tool typically used in root cause analysis which enable an individual to take certain action after the identification of the root cause.

According to force-field analysis, there is a change when the forces in one direction exceed the forces in opposing direction.

If we compare the energy of visible light to the energy of X-rays, we find that X-rays have a much higher frequency. Usually, electromagnetic radiation with higher frequency (energy) have a higher degree of penetration than those with low frequency.

Answer:

5

Explanation:

Answer:

392 Nm or J

Explanation:

Work is equal to force times distance. The force required is the mass times acceleration - in this case F = 5kg x 9.81 ( gravity) = 49N. So work is 49N x 8m = 392 Nm or Joules.

Answer:

a= 17.69 m/s^2

Explanation:

Step one:

given data

A car accelerates uniformly from rest to 23 m/s

u= 0m/s

v= 23m/s

distance= 30m

Step two:

We know that

acceleration= velocity/time

also,

velocity= distance/time

23= 30/t

t= 30/23

t= 1.30 seconds

hence

acceleration= 23/1.30

accelaration= 17.69 m/s^2

Answer:

The  velocity of the waves in the string is 30 m/s.

Explanation:

Given;

frequency of the wave, F = 60.0 Hz

number of loops, n = 5

length of the string, L = 1.25 m

1 loop, L  = λ/2

For 5 loops;

[tex]L = \frac{5\lambda}{2}[/tex]

where;

λ is the wavelength

[tex]L = \frac{5 \lambda}{2} \\\\5 \lambda = 2L\\\\\lambda = \frac{2L}{5} \\\\\lambda = \frac{2 \ \times \ 1.25}{5} \\\\\lambda = 0.5 \ m[/tex]

The velocity of the waves in the string is calculated as;

V = Fλ

V = (60)(0.5)

V = 30 m/s

Therefore, the  velocity of the waves in the string is 30 m/s.

Answer:

the frequency of the beats is 8.7687 kHz

Explanation:  

Given the data in the question;

The frequency for stationary source and moving observer is;

f' = f( 1 +( v_observer/v_sound))

we know that, speed of sound in dry air =  343 m/s

so we substitute

f' = 41.2 kHz( 1 + (33.0 m/s / 343 m/s) ) = 41.2kHz( 1 + 0.0962) = 41.2kHz(1.0962)

f' = 45.1634 kHz

Now the frequency for stationary observer and moving source with frequency f' will be

f" = f'( 1 / (1 - ( v_observer/v_sound)))

45.1634 kHz( 343 / 343 - 33)

we substitute

f" = 45.1634 kHz( 1 / (1 - (33.0 m/s / 343 m/s)))

f" = 45.1634 kHz( 1 / (1 - 0.0962))

f" = 45.1634 kHz( 1 / 0.9038 )

f" = 45.1634 kHz( 1.1064 )

f" = 49.9687 kHz

Now the beat frequency will be;

f_beat = f' - f

we substitute

f_beat = 49.9687 kHz - 41.2 kHz

f_beat = 8.7687 kHz

Therefore, the frequency of the beats is 8.7687 kHz

Answer:

50.97 m

Explanation:

m = Mass of truck

[tex]\mu_s[/tex] = Coefficient of static friction = 0.4

v = Final velocity = 0

u = Initial velocity = 72 km/h = [tex]\dfrac{72}{3.6}=20\ \text{m/s}[/tex]

s = Displacement

Force applied

[tex]F=ma[/tex]

Frictional force

[tex]f=\mu_s mg[/tex]

Now these forces act opposite to each other so are equal. This is valid for the case when the load does not slide

[tex]ma=\mu_s mg\\\Rightarrow a=\mu_s g\\\Rightarrow a=0.4\times 9.81\\\Rightarrow a=3.924\ \text{m/s}^2[/tex]

Since the obect will be decelerating the acceleration will be [tex]-3.924\ \text{m/s}^2[/tex]

From the kinematic equations we have

[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-20^2}{2\times -3.924}\\\Rightarrow s=50.97\ \text{m}[/tex]

So, the minimum distance at which the car will stop without making the load shift is 50.97 m.

Answer:

Positive charge is attracted to the neutral object.

Explanation:

Recall ; Like charges repel, unlike charges attract. This phrase simply means (positive (+) is attracted to negative (-ve) and vuc versa while both positive, positive and negative, negative charge repel.

For a neutral object. The quantity of positive charge equals the quantity of negative charges. This simply means a neutral object contains charges as well, which are usually scattered or randomly aligned.

Therefore, when a positive charge is brought near a neutral body, the order of alignment of the charges change, with the negative charge all moving towards the direction of the positively charged body and the positive charges in the neutral body aligning in the opposite direction.

The charge will be attracted.

As you may know, opposite charges attract (and equal charges repel).

So, when you put a positive charge near a neutral material, all the negative charges in the material will move towards the surface of the material closer to the positive charge (and the positive charges in the material will move away).

Now the charge in the material is not homogeneous, so the positive charge will see a negatively charged surface near it, and it will be attracted to that surface.

Thus we can conclude that as a positive charge is brought near a neutral, insulating piece of material, the charge will be attracted towards it.

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Answer:

Heredity

Explanation:

Can't change the DNA you inherited the same way you can change eating habits+drug use or avoid stress

Answer:

[tex]\boxed {\boxed {\sf C. \ Heredity}}[/tex]

Explanation:

A risk factor is something that increases the chance of getting a disease. Some are controllable, but some are not.

Stress, eating habits, drug use, exercise, smoking, hygiene, and amount of sleep are all controllable or changeable risk factors. Anybody can change these things in their life.

On the other hand, uncontrollable risk factors, such as age, gender, ethnicity and heredity cannot be changed. Nobody has control over these factors.

So, heredity is the uncontrollable risk factor.

Answer:

Oppressors have a repressive attitude toward others. They have a need for power and dominance.

Explanation:

Oppression is the painful experience of deliberate arbitrariness, violence and abuse of power inflicted on an individual, society or group of people. The term repression is often used synonymously for this.  

Oppression arises from the general, also unconscious, assumption that a certain group of people is inferior or without rights. Oppression is seldom limited to governmental activities. Individuals can also be victims of oppression if they lack the solidarity of a social group.

Oppressive individuals, in turn, are those who exert repression on others. They are generally narcissistic and megalomaniacal people, who have a wrong self-perception of their virtues and negatively weigh the virtues of other people.

Answer:

10.44 liters of gasoline.

Explanation:

First, we need to convert the units of the car from mi/gal to km/L as follows:

[tex] mileage = 32.0 \frac{mi}{gal}*\frac{1.609 km}{1 mi}*\frac{1 gal}{3.785 L} = 13.60 km/L [/tex]

That means that for every liter of gasoline the car travels 13.60 kilometers.

So, to complete a 142-km trip in Europe the volume of gasoline needed is:

[tex] V = \frac{1 L}{13.60 km}*142 km = 10.44 L [/tex]

Therefore, to complete a 142-km trip in Europe we need to buy 10.44 liters of gasoline.

I hope it helps you!                

The work done by the given force should be -45 joules

Since force acts in the negative y direction

So,

F = -15j

here the displacement vector is d = 3i+3j-1k

Now

work done is W = dot product of force and displacement

                        = [-15j ] . [ 3i+3j-1k]

                        =-45 joules

Therefore, The work done by the given force should be -45 joules

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Given :

Mass, m = 68.05 kg.

To Find :

How much gravitational force would you experience on mars ?

Solution :

Acceleration due to gravity on mars is, g = 3.711 m/s²

( You can find it on internet )

Now, weight can be given as :

W = mg

W = 68.05 kg × 3.711 m/s²

W = 252.533 kg m/s² = 252.533 N

Hence, this is the required solution.

Answer:

If there is a large difference between the concentration of one fluid and the concentration of the other, then the particles will diffuse faster. In the experiment, the dye particles in the food coloring are very concentrated.

Explanation:

Answer:

5.67

Explanation:

force is = m x a

which will give us

0.63

x 9

= 5.67

Answer: I think this is the answer, In a collision, there is a force on both objects that causes an acceleration of both objects; the forces are equal in magnitude and opposite in direction. For collisions between equal-mass objects, each object experiences the same acceleration.

Explanation: I had a question similar to this, Hope this helps!

Answer:

[tex]Q'_H=1065kJ/min[/tex]

Explanation:

From the question we are told that

Heat Remove rate Q_o= 750 kJ/min

Power Draw P=5.25

a)Generally the coefficient of performance (COP) of an air conditioner is mathematically given  as

[tex]COP=\frac{Q_o}{P}[/tex]

[tex]COP=\frac{750kJ/min}{5.25kw}[/tex]

Where

[tex]750kJ/min=12.5kJ/sec[/tex]

[tex]COP=\frac{12.5kJ/sec}{5.25kw}[/tex]

[tex]COP=2.38[/tex]

b)Generally the equation for power is mathematically represented as

[tex]P=Q_H-Q_o[/tex]

[tex]P+Q_o=Q_H[/tex]

[tex]Q_H=P+Q_o[/tex]

[tex]Q_H=5.25+12.5[/tex]

[tex]Q_H=17.75kW[/tex]

Generally rate of heat transfer to the outside air is mathematically given as

[tex]Q'_H=17.75*60[/tex]

[tex]Q'_H=1065kJ/min[/tex]