Houston, we have a problem


You are members of the crew of Earth’s first community development ship. On your way to the planet Proxima Centauri B your ship was damaged. You are not going to be able to land your ship on the planet as anticipated. You will have to take precautions when constructing your lander to arrive safely on the surface. Before you begin construction on your lander you will need to determine the gravitational acceleration between your ship and the planet.


Data:


Your spacecraft is equipped with advanced sensing equipment and you have measured the following information based on your current situation.


You are currently in a stable orbit 9 000 000 m from the center of planet Proxima Centauri B.

According to the calculations done by NASA, Planet Proxima Centauri B has a mass of approximately 6x10^24 kg.

Based on fuel consumption and expected material aboard the ship, your colony ship lander has a mass of approximately 1.1x105 kg.


1. Using Newton's Law of Universal Gravitation, determine what the force of gravity on your ship at that orbit be using the early measurements. Please show all work.


2.Using Newton’s second law determine the acceleration of your lander due to gravity. Please show your work.


3.Upon arrival, you measure the actual force of gravity to be 6x105 N,which is different from your calculated value in question 1. Identify a specific possible causes that would account for the difference in expected vs. actual values, and why they would affect the calculation.

Two units of measurement for energy are calories and joules. The measurement of 355 J is the same amount of energy as 84.84 calories.

Energy in physics is the ability to perform work. Different shapes, such as potential, kinetic, thermal, electrical, chemical, radioactive, etc., may be assumed by it. Other examples of energy being transferred from one body to another include heat and work. Energy is always distributed after it has been transported in accordance with its type. Thus, heat transfer could result in thermal energy, whereas work could result in mechanical energy.

Motion is a trait shared by all forms of energy. For instance, if a body is moving, it has kinetic energy. Due to the object's design, which incorporates potential energy, a tensioned object, like a spring or bow, has the ability to move even when at rest.

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The weight of the ball is the only force pushing down on a ball that has been tossed into the air approximately half its maximum height.

At this point, referring to a force as a push or a pull is perfectly appropriate. An object does not "have in it" or "contain" a factorOne thing experiences a force from another. The idea of a force encompasses both living and non-living things.

An illustration would be to push or forcefully shove a door. As a vector quantity, effort has both magnitude and a direction.. According to Newton's second law, force equals the "net of a body's natural mass and acceleration."

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A convex mirror can never provide more than one in magnification effect. This is so because a convex mirror's image of the thing is smaller than the object itself.

When an object is held 30 cm away from a convex mirror, the image it creates is half the size of the actual object. A convex mirror is a kind of spherical mirror in which the reflecting surface is the protruded portion of the sphere; in other words, the reflecting surface of these mirrors protrudes outward in the direction of the incident light source. Enlarging something's seeming size—rather than its actual size—is known as magnification. A calculated value known as "magnification" is used to measure this enlargement.

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The radius of the alpha particle's trajectory is 4.0 r.

An elastic collision is one in which the system does not experience a net loss of kinetic energy as a result of the collision.

Given:  the mass of the alpha particle is four times that of the proton, and its charge is twice that of the proton.

After elastic collision, the speed of the  proton and the alpha particle will be in a ratio of 2: 1.

Let, the speed of the proton be2 v then the speed of the alpha particle be v.

So, the proton's trajectory is = 2mv/qB = 4.0 r

Hence, alpha particle's trajectory is = (4m×v)/(2qB)

=2mv/qB  

=4.0 r

= 4.0r.

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The cross-sectional area decreases, so the resistance per unit length,  increases

The limitation of current flow in an electrical circuit is measured in terms of resistance. The ohm, or the Greek letter omega, stands for the unit of measurement for resistance.

According to the given information

We know that

Resistance of the wire is directly proportional to length of the wire and inversely proportional to the area of the wire

So,

R ∝ [tex]\frac{L}{A}[/tex]

Proportionality constant ρ = resistivity constant

R = ρ[tex]\frac{L}{A}[/tex]

So If the cross sectional area decreases , Resistance per unit length increases

The rate constant for radon-220, which has a half-life of 55. 6 seconds is 0.012.

We know that half life of first order reaction is : [tex]t_{1/2} = 0.693/k[/tex]

where k = rate of reaction.

Given half life = 55.6 sec

Putting this value in above equation we get k = 0.012

i.e. The rate constant for radon-220, which has a half-life of 55. 6 seconds                is 0.012.

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The resistance in a series rcl circuit is doubled.:

(a) The resonant frequency will decrease. The resonant frequency of an RLC circuit is inversely proportional to the total resistance. As the resistance increases, the total resistance increases and the resonant frequency decreases.

(b) The maximum current in the circuit will remain the same. The maximum current in an RLC circuit is determined by the magnitude of the source voltage and the total resistance. As the resistance increases, the total resistance increases, but the source voltage remains the same, so the maximum current remains the same.

What is resistance?
The opponents to current flowing through an electrical circuit is measured by resistance. The Greek letter omega (Ω) represents the unit of measurement for resistance, known as ohms. Georg Simon Ohm (1784–1854), a German physicist who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance. Ohm's Law is attributed to him as its creator.

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The speed  [tex]V_{i}[/tex] of the elevator at the beginning of the 8 m descent is nearly 4 m/s. Hence, option A is the correct answer.

We are given that-

the mass of the elevator (m) = 1000 kg ;

the distance the elevator decelerated to be y = 8m ;

the tension is T = 11000 N;

let us determine the acceleration 'a' by using Newton's second law of motion.

∑Fy = ma

W - T = ma

(1000kg x 9.8 m/s² ) - 11000N = 1000 kg x a

9800 - 11000 = 1000

a = - 1.2 m/s²

Using the equation of kinematics to determine the initial velocity.

[tex]V_{f}[/tex] ² = [tex]V_{i}[/tex]² + 2ay

[tex]V_{i}[/tex] = √ ( 2 x 1.2m/s² x 8 m )

[tex]V_{i}[/tex] = √19.2 m²/s²

[tex]V_{i}[/tex] = 4.38 m/s   ≈ 4 m/s

Hence, the initial velocity of the elevator is 4m/s.

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The electric power consumed by the household appliance is determined as 22 watts.

The electrical power consumed by the household appliance that is operating on 110 volts and whose electricity is flowing with a current of 0.2 amperes is calculated as follows;

P = IV

where;

P = 0.2 A  x  110 V

P = 22 W

Thus, the electric power consumed by the household appliance is a function of current and voltage.

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To find maximum spring compression we assume no energy losses due to friction.

Here, the initial and final kinetic energy of the car is zero.

We know that, Total Energy= kinetic energy+ Potential Energy

Since the initial and final kinetic energy of the car is zero, here initial potential energy of the car-spring-earth system completely converts to elastic potential energy.

By the law of conservation of energy,

K1 +U1 = K2 + U2

i.e, (KE+PE, + PE) = (KE + PEg+PES) =

Here KE=0 and Potential energy after reaching ground(PE, = 0) =  

0 + mgh + 0 = 0+0+1/2kx- 0

mgh = (1/2kx2) =

2= 2mgh/k

mg = 1325.(9.8) = mg = 1325.(9.8) = 12985N ) = =

We can round off 12985N to 13000N for easy calculation.

-2 2 = 2 * 13000 * 10 1.0 * 106 0.51m

(b) To find the maximum acceleration of the car after contact with the spring,

We apply Newton's 2nd law,

ma= (-kx = )

​​​​​​a = (-kx/n -m)  

Multiply the above equation with g/g

a = a= (-kug/mg) = (-kxg/u

a = -(1.0 * 10%) * (0.51) * (9.8)/13000 = -380m/s? = *

a = 380m/s

A level curve is a plane curve where f has a constant value. A plane is a surface in XYZ space where f has a constant value. A level curve or surface is sometimes called a level set. The plane is the equipotential surface of the Earth's gravitational field. It is a curved surface and all its elements are perpendicular to the vertical line.

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Work done by the gas during the process is -200J.

Work done can be defined as the product of force and distance travelled by the force.

For an isothermal process, temperature is constant and thus the heat transfer into and out of the system happens slowly so that the system is in thermal equilibrium.

Also, from the first law of thermodynamics, the change in internal energy (ΔU) of a closed system is equal to the sum of the heat transferred (Q) and the work done (W) by the system. i.e

ΔU = W + Q    

The internal energy is dependent on the temperature of the system and since this temperature is constant the change in internal energy is zero (0).

i.e

ΔU = 0

putting the values in the equation of FLOT

⇒ 0 = W + Q

⇒ W = -Q  

Therefore, for such process, the work done is the negative of the heat transferred (heat removed in this case).

Q = 200J

W = -200J

Therefore, the work done is -200 J

The value is negative to show that the process is a compression meaning that work is done by the surrounding on the gas.

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Maximum speed of the child as she swings is  2.23 m/s.

T=3.3 s is the oscillation's time period.

The swing's greatest angle is 25° (max).

The swing's bottom will have the following kinetic energy:

k=12mv2...........(1)

The mass in this situation is m, and the speed is v.

The potential energy change is expressed as,

∆U=mgL1-cosθmax...............(2)

Here, L is a string's length and g is the acceleration caused by gravity. L is given as,

L=gT24π2

Combine equation (1) with (2)

12mv2=mgL1-cos, maxv=2g, maxv=gT24, maxv=g2T22, maxv=9.8 m/s

22.33 m/s, 22.31 s22.31 cos25°

Therefore, the child's top speed is 2.23 m/s.

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The work done by a constant force f with arrow on a particle during a straight-line displacement d with arrow if the angle between f with arrow and d with arrow is 27° is positive.

Paintings done are elaborated in one way it consists of both forces exerted on the frame and the whole displacement of the frame. This block is preceded via a steady pressure F. The cause of this force is to move the frame a sure distance d in a direct route in the direction of the force.

To express this concept mathematically, the paintings W is identical to the pressure f times the gap d, or W = fd. If the force is being exerted at an attitude θ to the displacement, the paintings completed is W = FD cos θ.

The paintings accomplished through pressure are described to be the product of thing of the pressure inside the route of the displacement and the value of this displacement. formula. work can be calculated with the aid of multiplying force and Distance in the route of pressure as follows. W = F × d.

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The car can travel at 20.5 m/s (74 km/hr). Any faster, and it will leave the road.

What is speed?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object travels along a path. In other words, velocity is a vector, whereas speed is a scalar value.

According to the question:

Two forces—gravity and the normal force of the road—are acting on the car as it crests the hill. These combined exert a net centripetal force, which will cause the car to travel in a circular arc.

[tex]$$\vec{F}_c=\vec{F}_g+\vec{F}_N$$[/tex]

Next, realize that "without leaving the road" actually refers to "just at the point where the car is going to leave the road" and that this corresponds to the condition FN = 0.

This means that our equation becomes

[tex]$$F_c=F_g$$[/tex]

and that gravity alone will determine the radius of the path the car will follow.

Substituting [tex]$F_c=\frac{m v^2}{r}$[/tex] and [tex]$F_g=m g$[/tex], we get

[tex]$$\frac{m v^2}{r}=m g$$[/tex]

Since we don't observe small, light automobiles flying airborne more frequently than larger ones, we can cancel the mass, which means that all cars traveling at this speed will follow the same course regardless of mass.

[tex]$$\begin{aligned}& \frac{v^2}{r}=g \\& v=\sqrt{g r}\end{aligned}$$[/tex]

After Substituting the values:

[tex]$$v=\sqrt{(9.8)(43)}=20.5 m/s}$$[/tex]

So, the car can travel at 20.5 m/s (74 km/hr).

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A 4 kg ball is launched vertically into the air. The net force exerted on the ball at its highest point is 39.24N.

What is  net force?

In mechanics, the net force is the vector sum of forces acting on a particle or object. The net force is a single force that replaces the effect of the original forces on the particle's motion.

Given data

Ball mass m=4 kilogram

Gravitational acceleration is 9.81 m/s^2 , or g.

The location of the ball has no bearing on the net force applied to it in vertical projectile motion. As a result, the ball experiences a net downward force throughout its travel, and the size of this force is equal to the mass times the acceleration caused by gravity.

[tex]\begin{aligned}& F_{\text {net }}=m g \\& F=4 * 9.81 \\& F=39.24 N\end{aligned}[/tex]

Therefore, the ball is subject to a net force of 39.24 N.

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It reflects, inverts, and maintains the same velocity.

What is velocity?

The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar number. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.

"It reflects , reverts and maintains the same velocity" is the one among the following that describes what happens to the wave after it hits the fixed end. The correct option among all the options that are given in the question is the second option or option "b". I hope the answer has come to your help.

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Yes this information is correct about electrical resistance.

Electrical resistance is a force that counteracts the flow of current.

Sol- when two lamps are connected in parallel to a battery, the total electrical resistance that the battery senses is more than the resistance of either . Beacuse In a parallel circuit each bulb is in its own circuit. As bulbs are added the resistance in the circuit decreases since each circuit is another pathway for electrons to move from one end of the circuit to the other.when two lamps are connected in series to a all the  battery the electricals resistance that the battery's senses is the more than the resistence of either lamp.

As each bulb is connected in parallel to the battery of the , each has thatbsame potential difference across by to the it as the all of  voltage of across the battery of to the terminals. All of other to the potential by  differences are zero, as we know all the wires have to the zero resistance.

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The maximum height attained by the projectile in terms of h is 12h/7.

The maximum height attained by the projectile is calculated by applying the following formula as shown below.

H = v² sin²θ / 2g

where;

H = ( v² ( sin 60 )² ) / 2g

H = ( v² x ³/₄ ) /2g

H = 3v² / 8g

To solve for the maximum height attained by the projectile in terms of h is calculated as follows;

vf² = vi² - 2gh

2gh = vi² - vf²

h = (vi² - vf²) /2g

where;

h = (v² - (3v/4)²) / 2g

h = (v² - 9v²/16) / 2g

h = (7v²/16) / 2g

h = 7v² / 32g

7v² = 32gh

v² = 32gh/7

The maximum height becomes;

H = 3v² / 8g

H = 3(32gh / 7) / 8g

H = (3 x 32 gh) / (7 x 8g)

H = 12 h / 7

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36.99N

Given

Maximum blood pressure  P = 150 mm

Effective area of the aneurysm a = 18.5 cm2.

Expression for the maximum force exerted by blood on an aneurysm is,

f =P * a = (150 mm Hg* (133.322 N/m²/ 1 mmHg)) * ( 18.5 cm² * (1 m² /10000cm²)) = 36.99N

The pressure is computed as the ratio of acting force on an object and the surface area of the object where the force is directed. The pressure is usually measured in terms of Pascal and blood pressure in mm of Hg.

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The stated statement states that the molecules' final maximum rate of translation is 270 m/s.

The rate at which the position of an object shifts in any direction. Speed is described as the ratio of the area traveled to the time required to cover that distance. Time is a scalar number since it just has a heading but no magnitude.

temperature at the start = T

v = √(3RT/M) = 467 m/s

temperature = T' later

note PV = mRT/M = NRT/NA

so NT = constant,

now N is tripled, T reduces to T' = T/3

so v will change to v' = √(3RT'/M) = v*√(T'/T) =v*√(1/3) = 270 m/s

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-0. 833m/s is the velocity of the centre-of-mass of this system, prior to the collision.

What is Centre-of-mass?

The unique location where the weighted relative position of the distributed mass accumulates to zero is known as the centre of mass of a distribution of mass in space (also known as the balance point). At this location, a force can be applied to produce a linear acceleration alone, not an angular acceleration.

What is Collision?

In physics, the abrupt, violent meeting of two bodies in direct contact is referred to as an impact. Examples of such bodies are two pool cues, a golf club and a ball, a hammer and a nail head, two railroad cars when linked, or a falling object and a floor. The force and the amount of time the objects are in touch, in addition to the materials the two objects are made of, have an impact on the outcome of the impact. It is generally knowledge that a hard steel ball dropped on a steel plate would rebound almost to the original position from where it was dropped, while a ball made of putty or lead will not.

What are the Calculations?

There are typically 3 masses named

m1= 3.38kg

m2= 0.702kg

m3= 7.80kg

Here m2 stays stationary hence its velocity (v2= 0)

Let the final velocity be V

Value of m1 + m2 + m3 = 3.38 + 0.702 + 7.8 = 11.882kg

A/Q V= m1v1/11.882 + m2v2/11.882 + m3v3/11.882

m1v1/11.882= 3.38 * 3.51/11.882= 0.998

m3v3/11.882= 7.8 * (-2.79) /11.882= -1. 831 ( here -ve sign is taken as the velocity of m3 is towards the left which is negative)

Hence, after simplifying V= m1v1/11.882 + m2v2/11.882 + m3v3/11.882 the final answer is -0. 833m/s

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The claim is refuted -rotation curve 1, -rotation curve 3, -rotation curve 2 -supports Rotation Curve 4, Rotation Curve 6, and Rotation Curve 5

You can work every significant muscle area with Curves since it combines stretching, cardio, and upper- and lower-body strength training routines. It may be done by people of all fitness levels and employs hydraulic resistance gym equipment created specifically for ladies.

Although males are permitted to join in some jurisdictions, Curves fitness and weight reduction facilities are focused solely on and built for women. Competitors of the clubs include Spa Lady and Lucille Roberts, two chains that cater only to women.

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The spacing between the lines is 3.33 X 10⁻³ mm and the estimated uncertainty in the line spacing is 3.33 X 10⁻⁵ mm.

Diffraction grating = 300 lines/mm

Thus,

The spacing between the lines = d =

= d = 1/300 lines/mm

= d = 3.33 X 10⁻³ mm

A grating consists of many slits, or lines, close together. In a grating, the spacing between adjacent lines is constant. Gratings are also used to produce interference patterns. When waves are incident on a grating all of the lines act as coherent sources of the waves.

Now, the uncertainty in the lines spacing is = Δ d =

= Δd = d (tolerance)

= Δd =  3.33 X 10⁻³ X 1%

= Δd = 3.33 X 10⁻⁵ mm

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There are 10 identical machines could you add to the factory without exceeding the 85 dB limit.

Calculation:-

sound leve in decibel is:

β dB = 10 log ( I / Io )

where I is the intensity of sound

It is the relative intensity

72 = 10 logs ( I /10⁻¹²)

8  = log ( I /10⁻¹²)

10⁸  =  I / 10⁻¹²

I  =  10⁸ . 10⁻¹² =  10⁻⁴  W /m2

If the sound level is 85 dB, the number of identical machines is n.

85 = 10 logs ( n I / Io )

=  10 logs ( n . 10⁻⁴ / 10⁻¹² )

9  =  log ( n . 108 )

10⁹ = n. 10 8

n = 10.

so  n  = 10 .

Sounds below 70 dB are considered safe for hearing. This is the sound of a normal conversation between two people. A noise level of 80 or 85 dB will damage your hearing over time. 70 decibels is as loud as a washing machine or dishwasher. Medium noise level. 70 dB of noise is not considered harmful to human hearing.

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The Light Intensity that passes through the set of polarizers is 9.99939871 W/m

[tex]I=icos\alpha[/tex]

I=10 cos 0.62832

=9.99939871 W/m

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The definition of moment of inertia allows for the following results for the moment of inertia with respect to each axis:

1-Iₓ = m r²

2-Iy=9m r²

3-Iz=10m r².

What exactly is moment interia?

The expression yields the moment of interia as a scalar quantity.

Sol-

I =∫ r² dm

Where I is the moment of inertia, m is the body's mass, and r is the distance from the axis of rotation.

In the case of point particles, the expression is as follows:

I = m r²

In this case, we calculate along each coordinate axis.

a) The distance is x = r with respect to the x axis, and the moment of inertia is

Iₓ = m r²

indicate the distance in relation to the y-axis

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Throughout the process, from a finite time before the collision to a finite time after the collision, the angular momentum of the rod and puck system is constant about any fixed point in space.

The condition of conservation of angular momentum of a system about a point is that net torque about that point of the system must be zero. The point that has zero net torque is any fixed point in space.

τ = I α

I = L / ω

τ = L ω / ω t

τ = L / t

Since L is constant, τ = 0

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If this glass is heated ice will turn into water

Explain forms of water.

Ice, water, and gas are all forms of water that can exist (vapour or gas). Ice, a solid, can melt into water with the addition of heat (a liquid). Ice forms when heat is removed from water, a liquid (a solid). We refer to a shift in a substance's state as occurring when liquid water becomes a solid or a gas. The molecules of the water don't change, even when its physical appearance does.

Solid water is what an ice block is. The ice turns into liquid water when heat (an energy source) is introduced. It's melted since it's at 0 degrees Celsius. If you keep heating the water, it will transform into water vapour, which is water that has turned gaseous.

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The kinetic energy of the two particles will be equal if they are travelling at the same speed in a vacuum. The equation: gives the particle's kinetic energy.

KE = (1/2)mv^2

m is the particle's mass, v is its speed, and KE is its kinetic energy.

In this instance, the particle with mass m will have the following kinetic energy:

KE = (1/2)m*v^2

And the kinetic energy of the particle with mass 3m will be:

KE = (1/2)3mv^2

     = (3/2)mv^2

The two equations may be made to equal one another and we can solve for v because the particles have the same kinetic energy.

(1/2)mv^2 = (3/2)mv^2

(1/2)*v^2 = (3/2)*v^2

1/2 = 3/2

Since there is no solution to this equation, two particles travelling in a vacuum cannot be moving at the same speed if one of them has a mass.

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The overall momentum of the system can be thought of as being conserved because the total momentum before and after the collision is the same. As a result, the system receives no net external impulse.

Momentum is a vector quantity that is influenced by the object's direction. During collisions between objects, momentum is a relevant concept. The total momentum before a collision between two objects equals the total momentum after the impact (in the absence of external forces).

The law of conservation of momentum is this. It holds true in every collision. According to the principle of momentum conservation, momentum is only modified by the action of forces as they are outlined by Newton's equations of motion; momentum is never created nor destroyed inside a problem domain.

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