A ship sets sail from Rotterdam, The Netherlands, intending to head due north at 6.5 m/s relative to the water. However, the local ocean current is 1.50 m/s in a direction 40.0º north of east and changes the ship's intended motion. What is the velocity of the ship relative to the Earth?

Answer:

[tex]0.76m/s^2[/tex]

Explanation:

We are given that

Final velocity, v=199 km/h=[tex]199\times \frac{5}{18}=55.3m/s[/tex]

1km/h=[tex]\frac{5}{18}m/s[/tex]

Initial velocity, u=0

S=2000 m

We know that

[tex]v^2-u^2=2as[/tex]

Using the formula

[tex](55.3)^2=2a(2000)[/tex]

[tex]a=\frac{(55.3)^2}{2\times 2000}[/tex]

[tex]a=0.76m/s^2[/tex]

Hence, the minimum acceleration necessary for the plane to take flight=[tex]0.76m/s^2[/tex]

Explanation:

Below is an attachment containing the solution.

Answer:

(a) I_A=1/12ML²

(b) I_B=1/3ML²

Explanation:

We know that the moment of inertia of a rod of mass M and lenght L about its center is 1/12ML².

(a) If the rod is bent exactly at its center, the distance from every point of the rod to the axis doesn't change. Since the moment of inertia depends on the distance of every mass to this axis, the moment of inertia remains the same. In other words, I_A=1/12ML².

(b) The two ends and the point where the two segments meet form an isorrectangle triangle. So the distance between the ends d can be calculated using the Pythagorean Theorem:

[tex]d=\sqrt{(\frac{1}{2}L) ^{2}+(\frac{1}{2}L) ^{2} } =\sqrt{\frac{1}{2}L^{2} } =\frac{1}{\sqrt{2} } L=\frac{\sqrt{2} }{2} L[/tex]

Next, the point where the two segments meet, the midpoint of the line connecting the two ends of the rod, and an end of the rod form another rectangle triangle, so we can calculate the distance between the two axis x using Pythagorean Theorem again:

[tex]x=\sqrt{(\frac{1}{2}L)^{2}-(\frac{\sqrt{2}}{4}L) ^{2} } =\sqrt{\frac{1}{8} L^{2} } =\frac{1}{2\sqrt{2}} L=\frac{\sqrt{2}}{4} L[/tex]

Finally, using the Parallel Axis Theorem, we calculate I_B:

[tex]I_B=I_A+Mx^{2} \\\\I_B=\frac{1}{12} ML^{2} +\frac{1}{4} ML^{2} =\frac{1}{3} ML^{2}[/tex]

A) Moment of inertia about an axis passing through the point where the two segments meet :   [tex]I_{A} = \frac{1}{12} ML^{2}[/tex]

B) Moment of inertia  passing through the point where the midpoint of the line connects  to its two ends :   [tex]Ix_{} = \frac{1}{3} ML^{2}[/tex]

A) The moment of inertia about an axis passing through the point where the two segments meet is [tex]I_{A} = \frac{1}{12} ML^{2}[/tex]  given that the rod is bent at the center and distance from all the points to the axis remains the same, the moment of inertia about the center will remain the same.

B) Determine the moment of inertia about an axis passing through the point midpoint of the line which connects the two ends

First step: determine the distance between the ends ( d )

  After applying  Pythagoras theorem

d = [tex]\frac{\sqrt{2} }{2} L[/tex]  

Next step :  determine distance between the two axis ( x )

After applying Pythagoras theorem

x = [tex]\frac{\sqrt{2} }{4} L[/tex]    

Final step : Calculate the value of  Iₓ

applying  Parallel Axis Theorem

Iₓ = Iₐ + Mx²

   = [tex]\frac{1}{12} ML^{2}[/tex]  + [tex]\frac{1}{4} ML^{2}[/tex]

∴  [tex]Ix_{} = \frac{1}{3} ML^{2}[/tex]

Hence we can conclude that Moment of inertia about an axis passing through the point where the two segments meet :   [tex]I_{A} = \frac{1}{12} ML^{2}[/tex],  Moment of inertia  passing through the point where the midpoint of the line connects its two ends :   [tex]Ix_{} = \frac{1}{3} ML^{2}[/tex]

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Explanation:

It is given that the number of electrons passing through the cross-sectional area in 1 s is [tex]3.4 \times 10^{18}[/tex]. Also, we know that charge on an electron is [tex]-1.60 \times 10^{-19} C[/tex], then negative charge crossing to the left per second is  as follows.

         I- = [tex]3.4 \times 10^{18} electrons \times -1.6 x 10^{-19} C/electrons[/tex]

         I- = 0.544 A

As it is given that the number of protons crossing per second is [tex]1.4 \times 10^{18}[/tex], as the charge on the proton is [tex]+1.60 \times 10^{-19} C[/tex], then positive charge crossing to the right per second is calculated as follows.

          I+ = [tex]1.4 \times 10^{18} electrons \times 1.6 \times 10^{-19} electrons/C[/tex]

            I+ = 0.224 A

          I = l I+ l + l I- l

So,    I = 0.544 + 0.224

            = 0.768 A

Thus, we can conclude that the current in given hydrogen discharge tube is 0.768 A.

Answer:

False. Field is non-zero

Explanation:

If you were moving along with the electrons, they would appear stationary to you. You would measure a current of zero. However, the fixed positive charges in the wire seem to move backwards relative to you, creating the equivalent current as if you weren't moving. You would measure the same field, but the field would be caused by the 'backward' motion of positive particles.

Moving at the same speed as the drift speed of electrons does not result in a zero magnetic field. The movement of electrons in a wire creates a magnetic field, and this field would still be present even if you were moving at the same speed as the electrons.

When moving along a wire at the same speed as the drift speed of the electrons, you will not measure a magnetic field of zero. The drift speed of electrons refers to the average velocity at which the electrons move in a conductor when an electric field is applied. This speed is generally very slow, but it does not mean that there is no magnetic field.

The movement of electrons in a wire creates a magnetic field around the wire, even if the drift speed is small. This is because the electric current generated by the movement of electrons is what produces the magnetic field.

So, even if you were to move at the same speed as the drift speed of the electrons in the wire, you would still measure a non-zero magnetic field because the movement of electrons in the wire is what generates the magnetic field.

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Answer:

True, check attachment for code

Explanation:

To convert java strings of text to upper or lower case, we can use and inbuilt methods To Uppercase and To lower case.

The first two lines of code will set up a String variable to hold the text "text to change", and then we print it out.

The third line sets of a second String variable called result.

The fourth line is where the conversion is done.

We can compare the string

We can compare one string to another. (When comparing, Java will use the hexadecimal values rather than the letters themselves.) For example, if we wanted to compare the word "Fat" with the word "App" to see which should come first, you can use an inbuilt string method called compareTo.

Check attachment for the code

Answer:

343/1500

Explanation:

Power: This can be defined as the product force and velocity. The S.I unit of power is Watt (w).

From the question,

P' = mg×v................. Equation 1

Where P' = power used to gain an altitude, m = mass of the engine, g = acceleration due to gravity of the engine, v = velocity of the engine.

Given: m = 700 kg, v = 2.5 m/s, g = 9.8 m/s²

Substitute into equation 1

P' = 700(2.5)(9.8)

P' = 17150 W.

If the full power generated by the engine = 75000 W

The fraction of the engine power used to make the climb = 17150/75000

= 343/1500

Answer: 4.3KN

Explanation:f=m(v-u)/t

m=0.77kg

t=0.0029s

s=16.2m/s

F= 0.77*16.2/0.0029

F=12.474/0.0029

F= 4301.38N

F=4.3KN

To find the magnitude of the average force acting on an object, one can use the derived form of the second law of motion, F = mΔv/Δt. Placing the given values into the equation, we calculate the force to be approximately 4307 N.

To solve this question, we can use the equation F = mΔv/Δt which is derived from the second law of motion (Force = mass × acceleration), where F is the average force, m is the mass of the object, Δv is the change in velocity, and Δt is the time interval.

Substituting the given values, m = 0.77 kg, Δv = 16.2 m/s (the final velocity) - 0 m/s (the initial velocity) = 16.2 m/s and Δt = 2.9 ms = 2.9 × 10⁻³ s (as time should be converted to seconds).

Therefore, F = (0.77 kg × 16.2 m/s) / 2.9 × 10⁻³ s = 4306.9 N. Therefore, the magnitude of the average force acting on the object during the 2.9 ms time interval is approximately 4307 N.

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Answer:

Force, F = 44 N                

Explanation:

Given that,

Initial speed of the football, u = 0

Final speed, v = 15 m/s

The time of contact of the ball, t = 0.15 s

The mass of football, m = 0.44 kg

We need to find the average force exerted on the ball. It is given by the formula as :

[tex]F=ma\\\\F=\dfrac{mv}{t}\\\\F=\dfrac{0.44\times 15}{0.15}\\\\F=44\ N[/tex]

So, the average force exerted on the ball is 44 N. Hence, this is the required solution.

Answer:

[tex]\omega = 300 rad/s[/tex]

Explanation:

Given,

rotational acceleration = 30 rad/s²

initial angular speed = 0 m/s

time, t = 10 s

Final angular speed = ?

Using equation of rotation motion

[tex]\omega = \omega_o + \alpha t[/tex]

[tex]\omega =0+30\times 10[/tex]

[tex]\omega = 300 rad/s[/tex]

Rotational velocity after 10 s = 300 rad/s.

Final answer:

To calculate the initial temperature of the copper piece, use the principle of energy conservation and the equations for heat gained and heat lost. The final temperature of the system is approximately 24.8 °C.

Explanation:

To calculate the initial temperature of the copper piece, we can use the principle of energy conservation. The heat gained by the water is equal to the heat lost by the copper. The heat gained by the water can be calculated using the formula:

Q = m * c * ΔT

Where Q is the heat gained, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. The heat lost by the copper can be calculated using the formula:

Q = m * c * ΔT

Where Q is the heat lost, m is the mass of the copper, c is the specific heat capacity of copper, and ΔT is the change in temperature. Since the final temperature is known, we can rearrange the formulas to solve for the initial temperature of the copper:

Initial temperature of copper = (heat gained by water / (m * c)) + final temperature

Substituting the given values into the formulas, we get:

Heat gained by water = (159 g) * (4.18 J/g·°C) * (39.9 °C - 22.8 °C)

Heat lost by copper = (497 g) * (0.387 J/g·°C) * (final temperature - 89.5 °C)

Setting the two equations equal, we can solve for the final temperature:

(159 g) * (4.18 J/g·°C) * (39.9 °C - 22.8 °C) = (497 g) * (0.387 J/g·°C) * (final temperature - 89.5 °C)

Solving the equation, the final temperature of the system is approximately 24.8 °C.

Answer:

The correct frequenvy of the second fork is; ν2 = 566Hz

Explanation:

First of all, when two wave sources with slightly differing frequencies ν1 and ν2 generate waves at the same time and are superposed, then an interference effect will occur in time.

The intensity will be found to oscillate with time with a frequency (ν) called the beat frequency. It is depicted by:

ν = ± (ν1 −ν2).

In this question, there are two tuning forks, one with a frequency of let's say ν1=560Hz

The beat frequency is ν=6Hz

Therefore,

ν2=560 - 6 or ν2=560 + 6

i.e ν2=554 or ν2=566

For us to know the correct frequency, if the 560 Hz fork is loaded with wax, the increased inertia will lower its frequency.

Then it is found that the beat frequency increases. This can only mean that the other fork has a higher frequency. Hence the unkown frequency of the second fork must be,

ν2 = 566Hz

Answer:

11 m/s²

Explanation:

Deceleration: This can be defined as the rate of decrease of velocity. The S.I unit of deceleration is m/s².

From the question,

F = md ..................... Equation 1

Where F = Force acting on the dummy towards the rear of the car, m = mass of the dummy, d = deceleration of the dummy.

make d the subject of the equation

d = F/m............... Equation 2

Given: F = 825 N, m = 75 kg.

substitute into equation 2

d = 825/75

d = 11 m/s²

Answer:

11 m/s^2.

Explanation:

Given:

Mass = 75 kg

Force = 825 N

F = m × a

a = 825 ÷ 75

= 11 m/s^2.

Answer:

The answers to the questions are as follows;

(a) The rate of change of T at (1, 2, 2) in the direction toward the point (4, 1, 3) is  [tex]\frac{160\sqrt{11} }{33}[/tex]

(b) The direction of the gradient is in the direction of greatest increase and it is towards the origin.

Explanation:

To solve the question, we note that the shape of the ball is that of a sphere.

Therefore the distance of a point from the center is given by

f(x, y, z)  = [tex]\sqrt{x^2+y^2+z^2}[/tex]

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball

Therefore T ∝ [tex]\frac{1}{\sqrt{x^2+y^2+z^2}}[/tex] or T = [tex]\frac{C}{\sqrt{x^2+y^2+z^2}}[/tex]

Where

C = Constant of proportionality

x, y, and z are the x, y and z coordinates values

To find C, we note that at point (1, 2, 2), T = 160 °C.

Therefore 160 °C = [tex]\frac{C}{\sqrt{1^2+2^2+2^2}}[/tex] = [tex]\frac{C}{\sqrt{9}}[/tex] = [tex]\frac{C}{3}}[/tex]

Therefore C = 160 × 3 = 480 °C·(Unit length)

We therefore have the general equation as

T = [tex]\frac{480}{\sqrt{x^2+y^2+z^2}}[/tex]

The vector from points  (1, 2, 2) to point (4, 1, 3) is given by

1·i + 2·j +2·k - (4·i + 1·j +3·k) = -3·i + j -k

From which we find the unit vector given by

u = [tex]\frac{1}{\sqrt{(-3)^2+1^2+(-)^2} } (-3, 1, -1)= \frac{1}{\sqrt{11} } (-3, 1, -1)[/tex]  

From which we have the gradient equal to

∇T(x, y, z) = -480×(x²+y²+z²)[tex]^-{\frac{3}{2}}[/tex] in (x, y, z)

This gives D[tex]_u[/tex] = ∇T·u

                       = -480×(x²+y²+z²)[tex]^-{\frac{3}{2}}[/tex] in (x, y, z)·[tex]\frac{1}{\sqrt{11} } (-3, 1, -1)[/tex]

That is

[tex]-\frac{480}{\sqrt{11} }[/tex](x²+y²+z²)[tex]^-{\frac{3}{2}}[/tex] (-3·x + y - z)

From where D[tex]_u[/tex]Tat point (1, 2, 2) is  = [tex]\frac{160\sqrt{11} }{33}[/tex]  

(b) The direction of greatest increase in temperature is in the direction of the gradient and the direction of the gradient is opposite to the direction of {x, y, z}, which is away from the origin.

Hence the direction of the greatest increase in temperature is towards the origin.

Answer:

The value of total entropy change during the process

[tex]dS = 0.608 \frac{KJ}{K}[/tex]

Explanation:

mass of iron [tex]m_{iron}[/tex] = 25 kg

Initial temperature of iron [tex]T_{1}[/tex] = 350°c = 623 K

Mass of water [tex]m_{w}[/tex] = 100 kg

Initial temperature of water [tex]T_{2}[/tex] = 180°c = 453 K

When iron block is quenched inside the water the final temperature of both iron & water becomes equal. this is = [tex]T_{f}[/tex]

Thus heat lost by the iron block = heat gain by the water

⇒ [tex]m_{iron}[/tex] [tex]C_{iron}[/tex] ( [tex]T_{1}[/tex] -  [tex]T_{f}[/tex] ) = [tex]m_{w}[/tex] [tex]C_{w}[/tex] ( [tex]T_{f}[/tex] - [tex]T_{2}[/tex] )

⇒ 25 × 0.448 × ( [tex]T_{1}[/tex] -  [tex]T_{f}[/tex] ) = 100 × 4.2 × ( [tex]T_{f}[/tex] - [tex]T_{2}[/tex] )

⇒ [tex]( T_{1} - T_{f} ) = 37.5 ( T_{f} - T_{2} )[/tex]

⇒  [tex]( 623 - T_{f} ) = 37.5 ( T_{f} - 453 )[/tex]

⇒ [tex]( 623 - T_{f} ) = 37.5 T_{f} - 16987.5[/tex]

⇒ [tex]38.5 T_{f} = 17610.5[/tex]

⇒ [tex]T_{f} = 457.41 K[/tex]

This is the final temperature after quenching.

The total entropy change is given by,

[tex]dS = m_{iron}\ C_{iron} \ ln \frac{T_{f} }{T_{1} } + m_{w}\ C_{w} \ ln \frac{T_{f} }{T_{2} }[/tex]

Put all the values in above formula,

[tex]dS =[/tex] 25 × 0.448 × [tex]ln \frac{457.41}{623}[/tex] + 100 × 4.2 × [tex]ln \frac {457.41}{453}[/tex]

[tex]dS =[/tex] - 3.46 + 4.06

[tex]dS = 0.608 \frac{KJ}{K}[/tex]

This is the value of total entropy change.

Answer:

= 4.96cm

Explanation:

distance between objects of moon = 5.20km = 5.2 × 10³ m

Wavelength of light, λ = 550nm = 5.50 × 10⁻⁷m

distance of moon, L = 384000 km = 3.84 × 10⁸m

formula for resolving power of two objects

d = (1.22 × λ ×L) / D

D = (1.22 × λ ×L) / d

D = (1.22 × 5.50 × 10⁻⁷ ×3.84 × 10⁸) / 5.2 × 10³

D = 4.96cm

These objects would be classified as extreme trans Neptunian object (ETNO).

Explanation:

ETNO’s are the objects lying beyond the planet Neptune and orbiting the Sun. They follow a highly eccentric path which is tilted. ETNO has been grouped into three major according to their respective perihelia.  

Within this region (beyond Neptune’s orbit), a hypothetical planet has been discovered. It was discovered following its gravitational effect on the other objects of Kuiper Belt (region beyond the orbit of the Neptune- the last planet of our Solar system)

The Planet is assumed to be around 2 times the Earth’s size and around 10 times heavier than Earth.  

Planet X, if it exists, would likely be classified as a planet rather than a dwarf planet because it is much larger and more massive, suggesting it could clear its orbital neighborhood, which is one of the criteria that differentiate planets from dwarf planets.

The hypothetical object proposed by the astronomer beyond the Kuiper Belt, nicknamed Planet X, would be classified differently from Eris and other dwarf planets like Pluto, Makemake, and Haumea. Since it is speculated to be about 10 times the mass of Earth and 2-3 times its size, placing it within the ice giant category, it would resemble Uranus or Neptune rather than the smaller dwarf planets in the solar system.

Dwarf planets are generally smaller bodies that, while orbiting the Sun and having sufficient mass for their self-gravity to overcome rigid body forces, have not cleared their neighboring region of other objects. In contrast, Planet X, being significantly larger and more massive, would likely be considered a full-fledged planet if its existence were confirmed, primarily because of its mass, size, and potential to clear its orbit, aligning closer with the current criteria for a planet.

Answer:

Explanation:

Potential energy Is given as.

U=kq1q2/r

Where k is a constant

q1 is charge

And q2 is also a charge

r is the distant between the two charges

When distance between the two charges is infinity then, the potential energy will b zero

U=kq1q2/∞

Therefore

U=0

Thus, the potential energy is zero when charged particles are separated by an infinite distance.

Let considered that both charges are positive.

Then U becomes

U=k(+q1)(+q2)/r

This shows that the energy is positive when the charges are positively charge. Also if the charges are also both negative charged the total energy will also be positive

U=k(-q1)(-q2)/r.

Both when their are opposite charges, the energy will be negative

U=k(-q1)(+q2)/r

U will be negative

Answer:

The magnitude of air = 392N

Explanation:

We use Newton's 2nd law. The sum of the vertical forces must be equal to zero because at terminal speed , the acceleration is zero. Solving for the air resistance force,F(air ) gives:

EFvertical = mg - F(air)= ma

F(air) = mg = 40 × 9.8 = 392N

Answer: 392N

Explanation:

Newton's second law of motion states that "The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object."

the sum of vertical forces has to be equal to zero because by the time the terminal speed has been attained, the acceleration is zero. Now, we solve for air resistance force.

summation of F(vertical) = mg - F(air) = ma

a = 0 m/s²

thus, F(air) = mg

F(air) = 40kg*9.8m/s²

F(air) = 392N

Answer:

The direction of the magnetic field is also reversed.

Explanation:

Answer:

a)T = 8.63  × 10 ⁴ N, b)T = -3.239 × 10 ⁴ N

Explanation:

Given:

W = 27.8 KN = 27.8 × 10 ³ N,

For upward motion: Fnet is upward, Tension T is upward and weight W is downward so

a) a=21.22 m/s² ( not written clearly the unit. if it is acceleration?) then

Fnet = T - W

⇒ T = F + W = ma + W

T = (W/g)a + W                           (W=mg ⇒m=W/g)

T = (27.8 × 10 ³ N / 9.8 ) 21.22 m/s² + 27.8 × 10 ³ N

T = 86,263.265 N

T = 8.63  × 10 ⁴ N

b) For Declaration in upward direction a = -21.22 m/s²

Fnet = T - W

⇒ T = F + W = ma + W

T = (W/g)a + W                        

T = (27.8 × 10 ³ N / 9.8 ) (-21.22 m/s²) + 27.8 × 10 ³ N

T = -32395.5 N

T = -3.239 × 10 ⁴ N

as Tension can not be negative I hope the value of acceleration and deceleration is correct.

Explanation:

Below is an attachment containing the solution.

Answer:

[tex]P_{C} = 3.2\, atm[/tex]

Explanation:

Let assume that gases inside bulbs behave as an ideal gas and have the same temperature. Then, conditions of gases before and after valve opened are now modelled:

Bulb A (2 L, 2 atm) - Before opening:

[tex]P_{A} \cdot V_{A} = n_{A} \cdot R_{u} \cdot T[/tex]

Bulb B (3 L, 4 atm) - Before opening:

[tex]P_{B} \cdot V_{B} = n_{B} \cdot R_{u} \cdot T[/tex]

Bulbs A & B (5 L) - After opening:

[tex]P_{C} \cdot (V_{A} + V_{B}) = (n_{A} + n_{B})\cdot R_{u} \cdot T[/tex]

After some algebraic manipulation, a formula for final pressure is derived:

[tex]P_{C} = \frac{P_{A}\cdot V_{A} + P_{B}\cdot V_{B}}{V_{A}+V_{B}}[/tex]

And final pressure is obtained:

[tex]P_{C} = \frac{(2\,atm)\cdot (2\,L)+(4\,atm)\cdot(3\,L)}{5\,L}[/tex]

[tex]P_{C} = 3.2\, atm[/tex]

Answer:

[tex] W = 5.94 \cdot 10^{15} N [/tex]      

Explanation:  

To calculate the weight on the surface of a neutron star we can use the following equation:

[tex] W = m*g [/tex]

Where:

W: is the weight of the person

m: is the mass of the person

g: is the gravity of the neutron star

Hence, first we need to find m and g. The mass is equal to:

[tex]m = \frac{W}{g} = \frac{685 N}{9.81 m/s^{2}} = 69.83 kg[/tex]

Now, the gravity of the neutron star can be found using the followig equation:    

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

Where:

G: is the gravitational constant = 6.67x10⁻¹¹ m³ kg⁻¹ s⁻²    

M: is the mass of the neutron star = 1.99x10³⁰ kg

r : is the distance between the person and the surface of the neutron star = 25/2 = 12.5 km  

[tex] g = \frac{6.67 \cdot 10^{-11} m^{3}kg^{-1}s^{-2}*1.99 \cdot 10^{30} kg}{(12.5 \cdot 10^{3} m)^{2}} = 8.50 \cdot 10^{13} m/s^{2} [/tex]  

Now, we can find the weight on the surface of the neutron star:

[tex]W = m*g = 69.83 kg * 8.50 \cdot 10^{13} m/s^{2} = 5.94 \cdot 10^{15} N[/tex]      

I hope it helps you!

Your weight on a neutron star with the same mass as the Sun and a diameter of 25.0 km would be approximately 5.95 × 10¹⁴ N. This is due to the extremely high gravitational acceleration on the neutron star's surface. Such high gravity results from the star's compactness and mass.

To determine your weight on the surface of a neutron star, we need to calculate the gravitational acceleration on its surface and then use this to find the weight force.

Step-by-Step Solution:

Summary: Your weight on a neutron star with the same mass as the Sun and a diameter of 25.0 km would be approximately 5.95 × 10¹⁴N, which is significantly more than your weight on Earth.

Answer:

Carrier Wave

Explanation:

A carrier wave is described or known as the continuous electromagnetic radiation, of constant amplitude and frequency, which is being given out or released by a transmitter. It is modulated in direct proportion to the signal,that is voice or music, which is meant to be transmitted or broadcasted.

It is mostly used for the transmission of information such as speech and music which can be seen in radio communication.

Answer:

height of tower= 78.48 meters

Explanation:

So here are your givens:

time(t)= 4 s.

initial velocity(u) = 0 m/s

acceleration due to gravity (g)= 9.81 m/s^2

distance(s)=s meters

using one of Newton's equation of motion ;

[tex]s=ut+\frac{1}{2} gt^{2} \\s=0(4)+\frac{1}{2}(9.81)(4)^{2} \\s=\frac{1}{2} (9.81)(16)\\s=\frac{156.96}{2} \\s=78.48[/tex]

height of the tower from the ground=total distance covered by bearing

height of tower= 78.48 meters

Final answer:

The shot tower needs to be at least 78.4 meters tall for a ball bearing to solidify in 4.0 seconds given the acceleration due to gravity.

Explanation:

Calculating the Height of the Shot Tower

To determine how high the tower must be for a ball bearing to solidify in 4.0 seconds, we can use the kinematic equation for free-fall motion without initial velocity, which is h = 1/2gt², where h is the height, g is the acceleration due to gravity (9.8 m/s² on Earth), and t is the time in seconds. For t = 4.0 seconds, we get:

h = 1/2 * 9.8 m/s² * (4.0 s)²

h = 1/2 * 9.8 * 16

h = 4.9 * 16

h = 78.4 meters

Therefore, the shot tower must be at least 78.4 meters tall to allow a ball bearing to solidify in mid-air within 4.0 seconds before impact.

Answer:

The initial velocity is 0.5114 m/s or 511.4 mm/s

Explanation:

Let the initial velocity be 'v'.

Given:

Mass of the ball (m) = 130 g = 0.130 kg   [ 1 g = 0.001 kg]

Initial height of the ball (h₁) = 1.4 mm = 0.0014 m   [ 1 mm = 0.001 m]

Final height of the ball (h₂) = 15 mm = 0.015 m

Now, from conservation of energy principle, energy can neither be created nor be destroyed but converted from one form to another.

Here, the kinetic energy of the ball is converted to gravitational potential energy of the ball after reaching the final height.

Change in kinetic energy is given as:

[tex]\Delta KE=\frac{1}{2}m(v_f^2-v_i^2)\\Where\ v_f\to Final\ velocity\\v_i\to Initial\ velocity[/tex]

As it just touches the 15 mm high roof, the final velocity will be zero. So,

[tex]v_f=0\ m/s[/tex].

Now, the change in kinetic energy is equal to:

[tex]\Delta KE = \frac{1}{2}\times 0.130\times v^2\\\\\Delta KE = 0.065v^2[/tex]

Change in gravitational potential energy = Final PE - Initial PE

So,

[tex]\Delta U=mg(h_f-h_i)\\\\\Delta U=0.130\times 9.8\times (0.015-0.0014)\\\\\Delta U=0.017\ J[/tex]                    [ g = 9.8 m/s²]

Now, Change in KE = Change in PE

[tex]0.065v^2=0.017\\\\v=\sqrt{\frac{0.017}{0.065}}\\\\v=0.5114\ m/s\\\\1\ m=1000\ mm\\\\So,0.5114\ m=511.4\ mm\\\\\therefore v=511.4\ mm/s[/tex]

Therefore, the initial velocity is 0.5114 m/s or 511.4 mm/s

Answer:

4.0 cm

Explanation:

For the compression of the spring, the kinetic energy of the mass equals the elastic potential energy of the spring.

So, 1/2mv² = 1/2kx² ⇒ x = (√m/k)v

Since m and k are constant since its the same spring x ∝ v

If our speed is now v₁ = 2v, our compression is x₁

x₁ = (√m/k)v₁ = (√m/k)2v = 2(√m/k)v = 2x

x₁ = 2x

Since x = 2.0 cm, our compression for speed = 2v is

x₁ = 2(2.0) = 4.0 cm

If the same block collides with the spring at a speed of 2v, the compression will be 4.0cm.

Given the data in the question;

Using conservation of energy:

Kinetic energy of the mass = Elastic potential energy of the spring

We have:

[tex]\frac{1}{2}kx^2 = \frac{1}{2}mv^2\\\\kx^2 = mv^2[/tex]

"v" is directly proportional to "x"

Hence,

[tex]\frac{x_1}{x_2} = \frac{v_1}{v_2}[/tex]

We substitute in our given values

[tex]\frac{2.0cm}{x_2} = \frac{v}{2v}\\\\x_2 = \frac{v(2.0cm*2)}{v} \\\\x_2 = (2.0cm*2)\\\\x_2 = 4.0cm[/tex]

Therefore, if the same block collides with the spring at a speed of 2v, the compression will be 4.0cm.

Learn more; https://brainly.com/question/18723512

Answer:

8 seconds

Explanation:

Given:

The velocity of the sky diver 't' seconds after jumping is given as:

[tex]v(t)=80(1-e^{-0.2t})[/tex]

The velocity is given as, [tex]v=65\ ft/s[/tex]

So, in order to find the time required to reach the above given velocity, we plug in 65 for 'v' in the above equation and solve for time 't'. This gives,

[tex]65=80(1-e^{-0.2t})\\\\\frac{65}{80}=1-e^{-0.2t}\\\\0.8125=1-e^{-0.2t}\\\\e^{-0.2t}=1-0.8125\\\\\textrm{Taking natural log on both sides, we get:}\\\\-0.2t=\ln(0.1875)\\\\t=\frac{\ln(0.1875)}{-0.2}\\\\t=8.4\ s\approx 8\ s(Nearest\ whole\ number)[/tex]

Therefore, the time taken to reach a velocity of 65 ft/s is nearly 8 seconds.

The velocity of the skydiver is 65 ft/s after approximately 9 seconds. This is found by solving the provided velocity function for the given speed.

To determine after how many seconds the velocity of the skydiver is 65 ft/s, we need to solve the equation

[tex]v(t) = 80(1 - e^-^0^.^2^t).[/tex]

Given v(t) = 65, we set up the equation:

[tex]65 = 80(1 - e^-^0^.^2^t)[/tex]

First, isolate the exponential term:

[tex]65/80 = 1 - e^-^0^.^2^t\\0.8125 = 1 - e^-^0^.^2^t[/tex]

Subtract 1 from both sides:

[tex]-0.1875 = -e^-^0^.^2^t[/tex]

Divide by -1:

[tex]0.1875 = e^-^0^.^2^t[/tex]

Take the natural logarithm (ln) of both sides to solve for t:

[tex]ln(0.1875) = -0.2t[/tex]

Solve for t:

[tex]t = ln(0.1875) / -0.2[/tex]

Using a calculator, we get:

[tex]t = 8.6 seconds[/tex]

Rounding to the nearest whole number, the velocity is 65 ft/s after about 9 seconds.

Answer:

Horizontal velocity is 14 m/s

Vertical velocity is 28.3 m/s

Explanation:

Hello dear friend, you have not mentioned the type of speed that you require for this problem.

In this case, there are three possibilities with which the slingshot can be fired i.e. Horizontally, Vertically straight up and vertically straight down. Below is the explanation / answer to all three possibilities

Fired horizontally:

initial conditions:  

Vertical Velocity = 0 ; Horizontal Velocity = 14m/s

final conditions:

Vertical Velocity  (v²  = u² + 2gs) but initial vertical velocity is zero

v²  =  2gs so v²  = 2(9.8)(31) = 607

v = 24.6m/s

but Horizontal Velocity is still  = 14m/s

Resultant velocity from these two velocity components (Pythagoras theorem)

V² = (v horizontal)² + (v vertical)² = 14² + 24.6²

V = 28.3m/s

angle = tan ⁻¹(24.3/14) = 60.1⁰

V = 28.3m/s at angle of 60.1⁰ to the horizontal

Fired Vertically  Straight Up

distance before the pebble reaches maximum height from top of building

v²  = u² + 2gs

where, v is zero at maximum height

g is minus for upward motion.

v²  = u² + 2gs

0  = 14² -  2(9.8)s

s = 196/19.6 = 10.0m

totals distance from maximum height to the ground = 10.0 m + 31.0 m = 41.0m

v²  = u² + 2gs

now u from maximum height is 0 and g is positive for downward motion

v²  =  2gs

v²  =  2(9.8)(41.0)

v = 28.3m/s

v = 28.3m/s vertically straight up

Fired Vertically Straight Down

v²  = u² + 2gs

u = 14m/s, g = 9.8m/s², s = 31.0m

v²  = 14² + 2(9.8)(31.0)

v = 28.3m/s

v = 28.3m/s vertically straight down