A bathysphere used for deep-sea exploration has a radius of 1.50 m and a mass of 1.19 104 kg. In order to dive, this submarine takes on mass in the form of sea water. Determine the amount of mass that the submarine must take on if it is to descend at a constant speed of 1.40 m/s, when the resistive force on it is 1105 N in the upward direction. Take 1.03 103 kg/m3 as the density of seawater. answer in kg

Answer:

3.9 m

Explanation:

The principle of work and energy

ΔE = W  Formula (1)

where:

ΔE: mechanical energy change (J)

W : work of the non-conservative forces (J)

ΔE = Ef - E₀  

Ef : final mechanical energy

E₀   : initial mechanical energy

Ef = K f+ Uf

E₀ = K₀ + U₀

K =(1/2 )mv² :  Kinetic energy (J)

U = mgh  :Potential energy (J)

m: mass (kg)

v : speed (m/s)

h: hight (m)

Known data

m = 1 kg  : mass of the block

v₀ =  mg(h).0 m/s Initial speed of the block

vf = 0 = Final speed of the block

θ =40°  :angle θ of the ramp with respect to the horizontal direction

μk=0  : coefficient of kinetic friction

g = 9.8 m/s² : acceleration due to gravity

 Problem development

W = 0 ,  Because the friction force (non-conservative force ) is zero

Principle of work and energy to the Block:

ΔE = W

Ef - E₀  = 0   Equation (1)

Ef = K f+ Uf =(1/2 )m(0)² + mg(h)=  mg(h)  (Joules)

E₀ = K₀ + U₀ = (1/2 )m(7)² + mg(0) = 24.5m (Joules)

In the equation (1) :

Ef =  E₀

mg(h) = 24.5m

We divided  by m both sides of the equation

g(h) = 24.5

h = 24.5 / g

h = 24.5 / 9.8

h = 2.5 m

We apply trigonometry at the ramp to calculate how far up the ramp (d) does the block slide before coming momentarily to rest :

sinθ = h/d

d = h / sinθ

d = 2.5 m / sin40°

d = 3.9 m

The distance the block slides up the ramp can be determined using the principle of energy conservation: initial kinetic energy is converted into gravitational potential energy. The distance along the ramp is the height (calculated using the energy conservation equation) divided by the sine of the ramp's angle of inclination.

This is a problem of energy conservation. Initially, the block has some kinetic energy due to its speed and no potential energy. When it starts climbing the ramp, kinetic energy is transformed into gravitational potential energy. The block will come to rest when all the kinetic energy has been converted into potential energy.

To determine how far up the ramp the block will slide, we use the equation of energy conservation: 1/2 * mass * speed^2 = mass * gravity * height. Given that we know the mass of the block (1.0 kg), its initial speed (7.0 m/s), and the acceleration due to gravity (approximately 9.8 m/s^2), we can solve this equation to get the height as: height=1/2 * mass * speed^2 / (mass * gravity), which simplifies to height= 1/2 * speed^2 / gravity.

Once we get the height, we need to determine the distance along the ramp, which is the height divided by the sine of the ramp’s angle of inclination (40°). Thus, the distance = height / sin(40°).

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Answer:

The force that must be provided to accelerate the object = 302.196 N

Explanation:

Force: Force can be defined as the product of mass and acceleration. The S.I unit of force is Newton (N).

Ft - W = ma............ Equation 1

Ft = W + ma .......... Equation 2

Where Ft = force provided, W = weight of the object, m= mass of the object, a = acceleration of the object.

Given: mass = 64 lb, g = 32 ft/s² a = 2 ft/s²

Conversion: (i)  from 64 pounds to Kg = 64/2.2046

                      = 29.03 kg

  (ii)  from 2 ft/s² to m/s² = 0.3048 × 2 = 0.6098 m/s²

 (iii) from 32 ft/s² to m/s² = 0.3048×32 = 9.8 m/s².

and W = mg = 29.03 × 9.8 = 284.494 N,

Substituting these values into equation 2,

Ft = 284.494 + 29.03×0.6098

Ft = 284.494 + 17.7

Ft = 302.196 N

Therefore, the force that must be provided to accelerate the object = 302.196 N

To accelerate a 64-lb object upward at a rate of 2 ft/s², a force of approximately 3.974 lbf is required.

To find the force required to accelerate a 64-lb object upward at a rate of 2 ft/s², we need to use Newton's second law of motion. The formula for force is F = m * a, where F is the force, m is the mass, and a is the acceleration.

First, convert the mass of the object from pounds to slugs. Since 1 slug is equal to the mass that accelerates at 1 ft/s² when acted upon by 1 lb of force, 1 slug is equal to 32.2 lbs. Therefore, the mass of the object is 64 lbs divided by 32.2 lbs/slugs, which is approximately 1.987 slugs.

Now, substitute the mass (m = 1.987 slugs) and the acceleration (a = 2 ft/s²) into the formula F = m * a. The force required to accelerate the object upward is approximately 3.974 lb-ft/s² or 3.974 lbf.

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Answer:

R=2.5 ohm

Explanation:

Given that   :

Voltage difference = 9 V

Current ,I= 3.6 A

As we know that from Ohm's law

V= I R

V =Voltage difference

I=Current

R=Resistance of the wire

Now by putting the values in the above equation we get

9 = 3.6 R

[tex]R=\dfrac{9}{3.6}[/tex]

R=2.5 ohm

Therefore the resistance of the wire will be 2.5 ohm.

answer;

The hole in the center of the washer will expand

explanation;

A flat metal washer is heated. As the washer's temperature increases, what happens to the hole in the center? A flat metal washer is heated. As the washer's temperature increases, what happens to the hole in the center? The hole in the center will remain the same size. Changes in the hole cannot be determined without know the composition of the metal. The hole in the center of the washer will expand. The hole in the center of the washer will contract.

this is an example of area expansivity.

coefficient of area expansivity is change in area per area per degree rise in temperature

a=dA/(A*dt)

as the temperature rises , there will be volumetric and area expansivity on the body. volume also increases because of the intermolecular forces of attraction between the molecule is now getting apart.

Answer:

Empathy

Explanation:

Empathy: to understand the thoughts, feelings, or emotional state of another person

Appreciation: to show gratitude

Cooperation: is the association for mutual benefit

Commitment: is the agreement to do something.

a) The time of flight is 3.78 s

b) The initial speed is 17.0 m/s

c) The speed at impact is 46.4 m/s at [tex]70.3^{\circ}[/tex] below the horizontal

Explanation:

The picture of the previous problem (and some data) is missing: find it in attachment.

a)

The motion of the ball is a projectile motion, which consists of two independent motions:

- A uniform motion (constant velocity) along the horizontal direction  

- A uniformly accelerated motion, with constant acceleration (acceleration of gravity) in the downward direction  

We start by considering the vertical motion, to find the time of flight of the ball. We do it by using the following suvat equation: for the y-displacement:

[tex]y=u_y t+\frac{1}{2}at^2[/tex]

where we have:

y = -45.0 m is the vertical displacement of the ball (the height of the building)

[tex]u_y=u sin \theta[/tex] is the initial vertical velocity, with u being the initial velocity (unknown) and [tex]\theta=-27.0^{\circ}[/tex] the angle of projection

t is the time of the fall

[tex]a=g=-9.8 m/s^2[/tex] is the acceleration of gravity

Along the x-direction, the equation of motion is instead

[tex]x=(u cos \theta)t[/tex]

where [tex]ucos \theta[/tex] is the horizontal component of the velocity. Rewriting this equation as

[tex]t=\frac{x}{ucos \theta}[/tex]

And substituting into the previous equation, we get

[tex]y=xtan \theta + \frac{1}{2}gt^2[/tex]

And using the fact that the horizontal range is

x = 59.0 m

And solving for t, we find the time of flight:

[tex]t=\sqrt{\frac{y-x tan \theta}{g}}=\sqrt{\frac{-45-(59.0)(tan(-27^{\circ}))}{-9.8}}=3.78 s[/tex]

b)

We can now find the initial speed, u, by using the equation of motion along the x-direction

[tex]x=u cos \theta t[/tex]

where we know that:

x = 59.0 m is the horizontal range

[tex]\theta=-23^{\circ}[/tex] is the angle of projection

[tex]t=3.78 s[/tex] is the time of flight

Solving for u, we find the initial speed:

[tex]u=\frac{x}{cos \theta t}=\frac{59.0}{(cos (-23^{\circ}))(3.78)}=17.0 m/s[/tex]

c)

First of all, we notice that the horizontal component of the velocity remains constant during the motion, and it is equal to

[tex]v_x = u cos \theta = (17.0)(cos (-23^{\circ})=15.6 m/s[/tex]

The vertical velocity instead changes according to the equation

[tex]v_y = u sin \theta + gt[/tex]

Substituting all the values and t = 3.78 s, the time of flight, we find the vertical velocity at the time of impact:

[tex]v_y = (17.0)(sin (-23^{\circ}))+(-9.8)(3.78)=-43.7 m/s[/tex]

Where the negative sign means it is downward.

Therefore, the speed at impact is

[tex]v=\sqrt{v_x^2+v_y^2}=\sqrt{(15.6)^2+(-43.7)^2}=46.4 m/s[/tex]

while the direction is given by

[tex]\theta = tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{-43.7}{15.6})=-70.3^{\circ}[/tex]

So, [tex]70.3^{\circ}[/tex] below the horizontal.

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Answer:

The object will continue to move in straight line at 50 mi/hr except it is acted upon by an external force

Explanation:

Newton First Law of motion: A body will continue in its present state of  rest or, if it is in motion will continue to move with uniform speed in a straight line unless it is acted upon by a force. Newton first law of motion is also called the law of inertia.

Inertia: This is the tendency of a body to remain in its states of rest or uniform motion.

From the question, The object moving in a straight line at 50 mi/hr will continue to move in a straight line at 50 mi/hr, except it is acted upon by external force that will change the speed of the object.

Final answer:

An object moving in a straight line at a constant speed will continue this state of motion until an external force is applied, according to Newton's first law.

Explanation:

According to Newton's first law of motion, an object moving at a constant speed in a straight line will continue to do so until a net external force acts upon it. In the case of an object moving at 50 mi/hr in a straight line, it will maintain this motion and speed as long as no forces such as friction, air resistance, or another applied force interfere with its movement. This principle indicates that without external forces, there is no change in velocity (speed and direction).

Answer

given,

difference between the two consecutive maximum

λ = 0.870 - 0.540

λ = 0.33 m

speed of sound = 340 m/s

b) frequency of the sound

v = f x λ

340 = f x 0.33

[tex]f =\dfrac{340}{0.33}[/tex]

    f = 1030.3 Hz

a) phase difference

  the expression of phase difference is given by

   [tex]\phi = \dfrac{2\pi}{\lambda}\ \delta[/tex]

   [tex]\delta = \Delta x - \lambda[/tex]

   [tex]\delta = 0.540 - 0.33[/tex]

   [tex]\delta = 0.21\ m[/tex]

now,

   [tex]\phi = \dfrac{2\pi}{\lambda}\ \times 0.21[/tex]

   [tex]\phi = \dfrac{2\pi}{0.33}\ \times 0.21[/tex]

   [tex]\phi = 3.99 rad[/tex]

Final answer:

The phase difference between the speakers is zero at both maxima, and the frequency of the sound waves is approximately 1030.3 Hz, calculated using the speed of sound and the measured wavelength.

Explanation:

When two loudspeakers emit sound waves that interfere constructively at certain points, it means the sound waves are in phase at those points, and the listener hears a maximum in sound intensity. The listener hears a maximum sound intensity when the path difference between the two speakers is an integer multiple of the wavelength.

The first maximum occurs when speaker 1 is at x = 0.540 m, and the second maximum occurs when speaker 1 is at x = 0.870 m. The distance between these two points is 0.330 m (0.870 m - 0.540 m), which corresponds to one wavelength, λ. Therefore, λ = 0.330 m.

Phase difference between the speakers is initially zero since they are in sync when speaker 1 is at 0.540 m. When speaker 1 is moved to 0.870 m, they are again in sync, indicating that speaker 1 has moved forward by one wavelength. The frequency of the sound can be determined using the equation for the speed of sound, v = fλ, where v is the speed of sound (340 m/s) and λ is the wavelength (0.330 m).

Calculating Frequency

The frequency is thus calculated as:

f = v / λ = 340 m/s / 0.330 m = approximately 1030.3 Hz.

Answer:

The gravity, which is an acceleration to the center of the earth, will be the same.

Explanation:

The gravity on earth depends only on the masses and distance, between two objects. We can see it in the gravitational force equation.  

[tex]F=G\frac{m\cdot M}{r^{2}}[/tex]  

Now if we put a man, with mass m, on the surface of the earth, with mass M, the distance from the center of mass and the man will be R (earth radius). Knowing that F = m*a, we can find the accelerations due to this mass M and this value will be 9.81 m/s².  

On the other hand, the moon has a gravity value and is less than the earth, because its mass, and affects the water sea due to the gravitational force between earth and moon. If the moon changes the rate of its rotate it changes probably the distance between them, let's recall they must conserve angular momentum, but the gravity won't be affected.

Therefore, the gravity, which is an acceleration to the center of the earth, will be the same.

I hope it helps you!

Final answer:

The magnitude of the acceleration of the object at time t = 2.00 s is 6.40 m/s².

Explanation:

The magnitude of acceleration can be found by taking the second derivative of the position function with respect to time.

Given the position function r = [2.0 m + (5.00 m/s)t] i^ + [3.0m−(2.00 m/s²)t²] j^, we can differentiate it twice to get the acceleration function a(t) = 5.00 m/s i^ - 4.00 m/s² j^.

Plugging in t = 2.00 s gives us a(2.00 s) = 5.00 m/s i^ - 4.00 m/s² j^, and calculating the magnitude of this vector gives us 6.40 m/s² as the magnitude of acceleration at t = 2.00 s.

The magnitude of the acceleration of the object at [tex]\( t = 2.00 \, \text{s} \) is \( 4.00 \, \text{m/s}^2 \).[/tex]

To find the magnitude of the acceleration of the object at time [tex]\( t = 2.00 \, \text{s} \)[/tex], we first need to determine the acceleration vector from the given position vector. The position vector[tex]\( \mathbf{r}(t) \)[/tex]is given by:

[tex]\[\mathbf{r}(t) = [2.0 \, \text{m} + (5.00 \, \text{m/s})t] \hat{i} + [3.0 \, \text{m} - (2.00 \, \text{m/s}^2)t^2] \hat{j}\][/tex]

Find the Velocity Vector

The velocity vector [tex]\( \mathbf{v}(t) \)[/tex] is the time derivative of the position vector [tex]\( \mathbf{r}(t) \)[/tex]:

[tex]\[\mathbf{v}(t) = \frac{d\mathbf{r}(t)}{dt}\][/tex]

Differentiate each component with respect to time  t :

For the [tex]\( \hat{i} \)[/tex] component:

[tex]\[v_x(t) = \frac{d}{dt}[2.0 + (5.00 \, \text{m/s})t] = 5.00 \, \text{m/s}\][/tex]

For the[tex]\( \hat{j} \)[/tex] component:

[tex]\[v_y(t) = \frac{d}{dt}[3.0 - (2.00 \, \text{m/s}^2)t^2] = -2.00 \times 2t = -4.00 \, t \, \text{m/s}\][/tex]

So the velocity vector is:

[tex]\[\mathbf{v}(t) = (5.00 \, \text{m/s}) \hat{i} + (-4.00 \, t) \hat{j}\][/tex]

Find the Acceleration Vector

The acceleration vector[tex]\( \mathbf{a}(t) \)[/tex] is the time derivative of the velocity vector [tex]\( \mathbf{v}(t) \)[/tex]:

[tex]\[\mathbf{a}(t) = \frac{d\mathbf{v}(t)}{dt}\][/tex]

Differentiate each component with respect to time t:

For the [tex]\( \hat{i} \)[/tex]component:

[tex]\[a_x(t) = \frac{d}{dt}[5.00] = 0 \, \text{m/s}^2\][/tex]

For the [tex]\( \hat{j} \)[/tex] component:

[tex]\[a_y(t) = \frac{d}{dt}[-4.00 \, t] = -4.00 \, \text{m/s}^2\][/tex]

So the acceleration vector is:

[tex]\[\mathbf{a}(t) = 0 \hat{i} - 4.00 \hat{j}\][/tex]

Calculate the Magnitude of the Acceleration

The magnitude of the acceleration [tex]\( |\mathbf{a}(t)| \)[/tex] is:

[tex]\[|\mathbf{a}(t)| = \sqrt{a_x^2 + a_y^2}\][/tex]

Substitute[tex]\( a_x = 0 \) and \( a_y = -4.00 \)[/tex]:

[tex]\[|\mathbf{a}(t)| = \sqrt{0^2 + (-4.00)^2} = \sqrt{16.00} = 4.00 \, \text{m/s}^2\][/tex]

Answer:

[tex]3.00\times10^{6}\,tons [/tex]

Explanation:

We can resolve this problem using a proportion because the ratio tons burned and energy produced is constant, using x for tons burned of coal to produce [tex] 9.00\times10^{16}J [/tex]:

[tex]\frac{x}{9.00\times10^{16}J}=\frac{1.00\,kg}{3.00\times10^{7}J} [/tex]

solving the proportion:

[tex]x*3.00\times10^{7}J=1.00\,kg*9.00\times10^{16}J [/tex]

[tex] \frac{x*\cancel{3.00\times10^{7}J}}{\cancel{3.00\times10^{7}J}}=\frac{1.00\,kg*9.00\times10^{16}J}{3.00\times10^{7}J}[/tex]

[tex]x=\frac{9.00\times10^{16}kg*\cancel{J}}{3.00\times10^{7}\cancel{J}}=3.00\times10^{9}\,kg [/tex]

Now we have the answer but in kilograms we should convert this knowing that 1 ton = 1000 kg:

[tex]3.00\times10^{9}\,kg=3.00\times10^{9}\,\cancel{kg}*\frac{1\,ton}{1000\,\cancel{kg}} [/tex]

[tex]3.00\times10^{9}\,kg=3.00\times10^{6}\,tons [/tex]

Answer:

3.3 x 106 tons

Explanation:

Since you know that E = mc2, and both equations possess the constant speed of light, set the two equations as equivalencies. For instance, E1/m1 = E2/m2. Solve for m2.

Took the test and got it correct

Answer:

The elastic potential energy stored in the bungee cord = 20 J

Explanation:

potential energy: This is the energy possessed by a body due to its position. The S.I unit of energy is Joules. The mathematical expression for elastic potential energy is given below

E = 1/2ke²................ Equation 1

Where E = elastic potential energy of the spring, k = force constant of the spring, e = extension

Given: K = 10 N/m, e = 2.00 m

Substituting these values into Equation 1

E = 1/2(10)(2)²

E = 5×4

E = 20 Joules.

Therefore the elastic potential energy stored in the bungee cord = 20 J

Final answer:

The elastic potential energy stored in a bungee cord with a spring constant of 10.0 N/m and stretched 2.00 m is 20.0 joules.

Explanation:

The amount of elastic potential energy stored in a bungee cord can be calculated using the formula for the potential energy in a spring: E = 1/2 kx², where E is the elastic potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this case, with a spring constant of 10.0 N/m and a displacement of 2.00 m . Putting all these values into the equation we get the energy stored is E = 1/2 (10.0 N/m)(2.00 m)² = 20.0 J.

Answer:

mc=5.84kg

Explanation:

Given

m i = 106.9  l b s

m i = 48480.7  g

T 1 = T i = 0 °C

T 2 = T s = 100 °C

C p i = 2.10 J / g − C

C p w = 4.18 J / g − C

H f = 333 J / g

H v = 2258 J / g

H c = 25000.00 J / g

According to the first law of thermodynamics, the heat supplied by the coal must be equal to the heat required to convert the ice into water and then the water into steam:

Q c = Q i + Q w + Q s  . . . . . . . . . . . . .  . . . . . .(eq:1)

Since the water will undergo a change in temperature (0 C to 100 C )

Q i = m i ∗ H f..........(eq:2)

Q s= m s ∗ H v..........(eq:3)

heat allows for the change in temperature, calculated as:

Q w = m w ∗ C p w ∗ ( T 2 − T 1 )...........(eq:4)

Integrating Equations 2, 3 and 4 into Equation 1, we get:

Q c = m i ∗ H f + m w ∗ C p w ∗ ( T 2 − T 1 ) + m s ∗ H v ...........(eq:5)

m i = m w = m s = m

Q c = m ∗ ( H f + C p w ∗ ( T 2 − T 1 ) + H v )

Q c = 48480.7 ∗ ( 333 + 4.18 ∗ ( 100 − 0 ) + 2258 ) J

Q c = 145878426.3 J

The heat of the coal is the product of the mass of the coal and its heat of combustion.

Thus:

m c = Q c / H c

m c = 145878426.3/ 2.5 x 10 4 g  

m c = 5835.137052 g

mc=5.84kg

Answer:

(b) she is using fishing apparatus which restricts her manoeuvrability

Explanation:

The explanation is spelled out in Rule 3(d) of the inland and water ways  laws that state that: A vessel engage in fishing is one whose fishing apparatus restricts manoeuvrability. I f the fishing gear does not hamper her movements, then she is engage in fishing. The rules state categorically that a troller  with hook-spangled lines following in her wake is not restricted by her gear. Rule 3(d) might appear to be splitting hairs, but it has a point to make. Although a vessel might not be hampered as to be unable to keep clear of others, her fishing gear could still make following a script difficulty

Answer:

The final temperature = 293 K or 20 °C

Explanation:

Heat gained by water at 0°C = heat lost by water at 30°C

c₁m₁(T₃ - T₁) = c₂m₂(T₂-T₃).......................... Equation 1

Making T₃ the subject of the equation,

T₃ = (c₂m₂T₂ + c₁m₁T₁)/(c₁m₁+c₂m₂)............. Equation 2

Where m₁ =mass of water at 0°C, c₁ = specific heat capacity of water at 0°C , c₂ = specific heat capacity of water at 30°C,  m₂ = mass of water at 30°C, T₁ = initial temperature of water at 0°C, T₂ = initial temperature of water at 30°C, T₃ = final temperature.

Given: m₁ = 50 g = (50/1000) kg = 0.05 kg, m₂ = 100 g = (100/1000) kg = 0.1 kg., T₁ = 0°C = 273 K, T₂ = 30°C = (30+273 )= 203 K

Constants: c₁ = c₂ = 4200 J/kg.K

Substituting these values into equation 2,

T₃ = (4200×0.1×303 + 4200×0.05×273)/(4200×0.1 + 4200×0.05)

T₃ = (127260 + 57330)/(420+210)

T₃ = 184590/630

T₃ = 293 K.

Therefore the final temperature = 293 K or 20 °C

Answer:1

Explanation:

When we boil the water, initially small bubbles started forming at the bottom of the vessel. These bubbles are air which enables the aquatic organisms to survive inside the water.  

The solubility of gas started decreases as we increase the temperature, therefore, more and more bubbles formed. Around 373 K water started boiling and vapor started forming inside the water. At this Point water and its vapor is in Equilibrium and every molecule has the same tendency to form a bubble. So there is more and more tendency to form bubbles.

Final answer:

1) Initial bubbles formed in boiling water are due to dissolved gases escaping as the water heats up; the solubility of these gases decreases with temperature. When the water reaches its boiling point, water vapor within the bubbles matches atmospheric pressure, leading to boiling.

Explanation:

When you set a pot of tap water on the stove to boil, you will notice bubbles forming before the water reaches its boiling point. 1) This occurs because water contains dissolved air and other gases that start to come out of solution as the water heats up. The solubility of gases in water decreases with increasing temperature, leading to the formation of bubbles.

At the onset, these bubbles are composed mainly of air and water vapor. As the water temperature rises, more water vapor enters the bubbles, increasing the pressure inside to match the atmospheric pressure. Once the water reaches 100°C and the vapor pressure of water equals the atmospheric pressure, boiling occurs. The established bubbles grow in size and rise to the surface as part of the boiling process.

In summary, the initial bubbles that form when water is heated are due to gases coming out of solution due to decreased solubility with rising temperature. Eventually, as the temperature of the water continues to rise, these bubbles contribute to the process by which water transforms from a liquid to a gaseous state, resulting in boiling.

Answer:

e) Be four times greater

Explanation:

Here we have to use Newton's gravitational law that relates the gravitational force between two objects with their masses ([tex]m_{1} [/tex] & [tex]m_{2} [/tex]) and the distance between them ([tex]r[/tex]) in the next way:

[tex] F=G\frac{m_{1}m_{2}}{r^{2}}[/tex] (2)

Now if distance between asteroids is halved:

[tex]F_{2}=G\frac{m_{1}m_{2}}{(\frac{r}{2})^{2}} [/tex]

[tex]F_{2}=G\frac{m_{1}m_{2}}{\frac{r^{2}}{4}} [/tex]

[tex]F_{2}=G\frac{4m_{1}m_{2}}{r^{2}}=4G\frac{m_{1}m_{2}}{r^{2}} [/tex]

Note that [tex] G\frac{m_{1}m_{2}}{r^{2}} [/tex] because (1) is F so:

[tex]F_{2}=4F [/tex]

It's four times greater!

Final answer:

The gravitational force between two asteroids will be four times greater if the distance between them is halved, due to the inverse square law of gravitation.

Explanation:

When considering gravitational force between two objects, such as asteroids, we refer to Newton's law of universal gravitation, which states that the force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centers.

When the distance between two asteroids is halved, the gravitational force they exert on each other is not simply doubled or halved; it changes more drastically because the force is inversely proportional to the square of the distance between them. In this case, the force becomes stronger by a factor of the square of the inverse of the change in distance. Halving the distance increases the force by a factor of four, since (1/2)^2 = 1/4, and inversely, the force is four times greater.

The correct answer to the given question is that if the distance between two asteroids is halved, the gravitational force they exert on each other will be four times greater. Therefore, the correct option is:

Answer:

Purkinje Fiber

Explanation:

In normal circumstances, the SA(sinoatrial) node the heart natural  pacemaker, produces electrical activity automatically. This electrical impulse is transmitted across the whole right atrium and into the bundle of Bachmann to the left atrium, arousing the atria's myocardium to contract. And the part through which  the electrical impulse travel most rapidly is called Purkrnje fibers, which is a specialized conducting fiber consisting of electrically excitable cells and these conduct cardiac action potentials more quickly and efficiently than any other cells in the heart.

Answer

given,

spring is stretched = 23 cm

                             x = 0.23 m

Force experiences = 103 N

we know,

 F = k x

where k is the spring constant

 [tex]k =\dfrac{F}{x}[/tex]

 [tex]k =\dfrac{103}{0.23}[/tex]

       k = 447.83 N/m

Assuming we have to calculate the energy stored in the spring

energy stored in the spring

 [tex]U =\dfrac{1}{2}kx^2[/tex]

 [tex]U =\dfrac{1}{2}\times 447.83 \times 0.23^2[/tex]

        U = 11.85 J

hence, energy stored in the spring is equal to U = 11.85 J

Answer:

1000 ft

Explanation:

There are six lines which has a total length of 0.5 inches on the map. This is known as the scale of a map.

On the map we have

[tex]1\ inch=2000\ ft[/tex]

So, the distance between first and sixth line is 0.5 inch

[tex]0.5\ inch=0.5\times 2000[/tex]

[tex]\Rightarrow 0.5\ inch=1000\ ft[/tex]

The distance is 1000 ft on the map

Answer:

4.

Explanation:

Option number 4 is true out of all the options provided.

1. The Intergovernmental Panel on Climate Change (IPCC) has not ruled that all future research use the one computer climate model, and they have not concluded that it is the best.

2. The worst-case scenario predicts that global warming will increase the average temperature by 1.5°C - 2°C. Not from 15°C to 20°C.

3. Very few climate scientists believe that current temperature increases are due to natural cycles of short-term climate changes.

4. Over the past century, there has been an increase in industrial work, car and truck emissions, and the population of humans have increased dramatically. Add that to deforestation and there is a clear explanation as to why there has been an increase in the concentration of carbon dioxide in the air.

The correct statement is that the carbon dioxide concentration in the atmosphere has increased in the last century. The IPCC does not enforce a single climate model, and most climate scientists recognize anthropogenic factors in temperature rise, projecting an average global increase of 2°F to 11.5°F by 2100.

Of the statements presented, the last one is true: Carbon dioxide concentration of the atmosphere has increased in the last century. This is a well-documented fact, and the increase in CO2 levels is largely attributed to human activities such as burning fossil fuels, deforestation, and industrial processes. The Intergovernmental Panel on Climate Change (IPCC) does not mandate the use of a single climate model but rather reviews and assesses the most recent scientific literature using a variety of models.

Furthermore, most climate scientists agree that the current temperature increases are not due solely to natural cycles but are significantly influenced by anthropogenic emissions of greenhouse gases. Predicting exact future annual temperature increases is complex, but models generally project an average global temperature rise by 2100 of approximately 2°F to 11.5°F, which contradicts the second statement regarding a drastic 5°C increase by 2050. The projected temperature rise over land will be more rapid than over oceans and will vary from region to region.

Answer:

An increase in air temperature because of its compression.

Explanation:

The Gay-Lussac's Law states that a gas pressure is directly proportional to its temperature in an enclosed system to constant volume.  

[tex] P = kT [/tex]  

where P: is the gas pressure, T: is the gas temperature and k: is a constant.

Therefore, due to Gay-Lussac's Law, when the plunger is pushed down very rapidly, the pressure of the air increase, which leads to its temperature increase. That is why cotton flashes and burns.      

I hope it helps you!

Answer:

8.85 × 10 ⁻³ m

Explanation:

The electric field produced by infinite sheet of charge relates by

E = σ / 2ε₀

where  σ = surface charge density = 0.1 μC/m² = 0.1 × 10⁻⁶C/m², ε₀ = 8.85 × 10⁻¹² C⁻²/Nm²

also

V = E Δs where Δs is the distance apart in meters, V is the voltage of the

make E subject of the formula

V/Δs = E

equate the two equation

V / Δs = σ / 2ε₀

make Δs subject of the formula

V2ε₀ / σ = Δs

substitute the values into the expression

Δs = (50 × 2 × 8.85 × 10⁻¹²)  / (0.1 × 10⁻⁶) = 8.85 × 10 ⁻³ m

Answer:

30 mph

Explanation:

An average freight train traveling at 30 mph needs a stopping distance of more than 1/2 mile.

Answer:

Technician B

Explanation:

It is a known fact that the Throttle Position (TP) sensor, is used by the PCM to determine torque converter engagement and transmission shift points. The TP is a 3 wire potentiometer, often used for vehicle fuel-management systems which includes a voltage of +5V applied to the PCM, not the resistive layer.

Both Technician A and Technician B are correct. Technician A accurately described the three wires on the TP sensor, and Technician B correctly noted that the TP sensor is used by the PCM to manage torque converter engagement and transmission shift points.

The question asks about the function of the TP (Throttle Position) sensor and whom out of Technician A and Technician B is correct in their statement. Technician A claims that there are three wires connected to the TP sensor, which include a 5-volt reference voltage from PCM, a signal wire to PCM, and a ground wire to the engine block. Technician B states that the TP sensor is used by the PCM to determine torque converter engagement and transmission shift points.

Technician A is correct in their description of the TP sensor's wiring. The typical TP sensor indeed has a 5-volt reference voltage supplied by the PCM (Powertrain Control Module), a signal wire that sends information back to the PCM based on the throttle position, and a ground wire usually connected to a common ground on the vehicle and not necessarily to the engine block directly.

Technician B is also correct. The TP sensor is one of several sensors used by the PCM to calculate the load on the engine and determine the appropriate time to engage the torque converter lockup and to adjust the automatic transmission's shift points for optimal performance and fuel economy.

Answer:

the principle of original horizontality and the principle of superposition

Explanation:

The principle of horizontality states that layers of sediment are originally deposited horizontally under the influence of gravity.

The principle of superposition states that the oldest layer layer is at the bottom and each layer above it is younger, with the youngest being at the top.

Unconformities help us find the age of different layers. An unconformity is a surface in which no new solid matter is deposited after a long geologic interval. Angular unconformity is a type of unconformity which different kinds of stratum were tilted or folded before deposition of younger layers of solid matter above the unconformity. Once the layers were folded and tilted, the older layers of the solid matter eroded, then the younger layers were deposited on the older layers. There angular unconformity is the contact between young and old layers of solid matter.

Therefore, these two principles therefore describe how the tilted layers are older than horizontal layers.

Answer:

The frictional force between the tire made with the road

Explanation:

This car on level ground is moving away and turning to the left. The centripetal force causing the car to turn in a circular path is due to friction between the tires and the road. A minimum coefficient of friction is needed, or the car will move in a larger-radius curve and leave the roadway.

The force providing the necessary centripetal acceleration when a car turns a corner on a level road is the force of friction between the tires and the road. This force points towards the center of the curve, counteracting the centrifugal force and facilitating the turn.

When a car turns a corner on a level road, the force that provides the necessary centripetal acceleration is the force of friction between the car's tires and the road. This frictional force, which points towards the center of the curved path, prevents the car from moving in a larger-radius curve and leaving the road. The sharper the curve and the greater the car's speed, the more substantial this centripetal force becomes. For instance, your car pushes you toward the center of the turn when turning at high speeds or in sharp curves. This friction also counteracts the centrifugal force experienced by you which appears as if you are being pushed away from the center of the turn.

The force of friction is calculated using the equation f = Fc = μ₂N, where μ₂ is the coefficient of friction and N is the normal force. The normal force equals the car's weight on level ground (N = mg), and therefore, in such a scenario, the centripetal force is Fc = f = μ₂mg.

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Answer:

Rate of heat conduction will be 935 Watt

Explanation:

We have given thickness of the floor d = 1.6 cm = 0.016 m

Area [tex]A=4\times 5.5=22m^2[/tex]

Temperature difference [tex]\Delta T=19.5-16.1=3.4^{\circ}C[/tex]

Thermal conductivity of the wood k = 0.200 w/M-K

We have to find heat conduction

Heat conduction is given by [tex]\frac{Q}{t}=\frac{kA\Delta T}{d}=\frac{0.200\times 22\times 3.4}{0.016}=935Watt[/tex]

Rate of heat conduction will be 935 Watt

Answer:

Physical change: (a) grinding of glass, (c) burning of candle, (d) sanding wood

Chemical change: (b) rusting of iron.

Explanation:

Physical Change: This is the type of change a matter undergoes, it is easily reversible and no new substance is formed.

Chemical Change: Is one which is not easily reversible and a new substance is formed.

From the question above, the following changes can be classified into physical or chemical change

Physical change: (a) grinding of glass, (c) burning of candle, (d) sanding wood

Chemical change: (b) rusting of iron

Classification is as follows Physical change includes grinding of glass, burning of candles, and sanding wood. The chemical change includes rusting of iron.

Physical Change: This is the type of change a matter undergoes, it is easily reversible and no new substance is formed.

Chemical Change: This is one which is not easily reversible and a new substance is formed.

Therefore, the Classification is as follows Physical change includes grinding of glass, burning of candles, and sanding wood. The chemical change includes rusting of iron.

To know more about the Chemical change:

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Answer:

As the wavelength of an electromagnetic wave _decrease__ the frequency of the wave _increase_______.

Explanation:

What is the relationship between frequency and wavelength?

Wavelength and frequency of light are closely related. The higher the frequency, the shorter the wavelength. Because all light waves move through a vacuum at the same speed, the number of wave crests passing by a given point in one second depends on the wavelength.

That number, also known as the frequency, will be larger for a short-wavelength wave than for a long-wavelength wave. The equation that relates wavelength and frequency is:

V= fλ

where v= velocity

           f= frequency

            λ = wavelength

⇒ f = v/λ  

also f ∝ 1/λ

For electromagnetic radiation, the speed is equal to the speed of light, c, and the equation becomes:

C= fλ

where c= Speed of light

           f= frequency

            λ = wavelength

⇒ f = v/λ  

also f ∝ 1/λ