you are in a rocket ship in deep space, far away from any gravity. you decide to do an experiment to determine the mass of your rocket ship. initially your ship is traveling to the right at 800 m/s, then the engines begin to exert 300,000 n of constant force to the left and do so for 40 seconds. afterward, your rocket ship is traveling to the left at 200 m/s. what is the mass of your rocket ship?

The magnitude of Mars' gravitational field is 3.66 N/kg.

The approximate acceleration due to gravity experienced by the spacecraft is 3.66 m/s².

The gravitational fields of the Mars is calculated by applying the following equation;

E = F/m = GM/r²

where;

E = (6.626 x 10⁻¹¹ x 6.39 x 10²³) / (3.4 x 10⁶)²

E = 3.66 N/kg

The approximate acceleration due to gravity experienced by the spacecraft is calculated as follows;

F = mg = GmM/r²

g = GM/r²

where;

g = (6.626 x 10⁻¹¹ x 6.39 x 10²³) / (3.4 x 10⁶)²

g = 3.66 m/s²

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The frictional force where k is the unitary force of kinetic friction acting on an object and k is the coefficient of kinetic friction. For the vast majority of surfaces, K is less than S.

The weight of the object and the roughness of the surface in contact determine how much frictional force is generated. The friction force will grow as the roughness increases.

The weight of the object bearing normal to the surface times the coefficient of friction for the contacting surfaces gives the amount of the friction force. The force's direction is perpendicular to the surface and is in opposition to any forces acting on the box.

The amount of kinetic friction is inversely proportional to the amount of normal force and the degree of roughness between the sliding surfaces. The amount of static friction is inversely proportional to the amount of normal force and the degree of roughness between the sliding surfaces.

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Your power usage when pulling the box is 125 Watts. It takes 20 seconds to move a box 10 meter's along a rough surface when applying a continuous 250 n force.

Given: force = 250 N; distance = 10 m; speed = distance/time (10/20); speed = 0.5 m/s

W = work completed, where W = 250*10 = 2500 Joules.

Your labour of 2500 J by pulling the box

Thermal energy produced—considering that the box's surface and interior are both made of wood. Therefore, the kinematic friction coefficient is 0.3.

The thermal energy is therefore 75 N

thermal energy = 75*10 = 750 Joules, or thermal energy = force*d

force = mu

 force= 0.3*250.

So pulling the Box produces 750 Joules of thermal power.

Power exerted = force* v

= 250*0.5

=125 Watts

so, The power exerted by you while pulling box is 125 Watts.

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The atmosphere supports a column of mercury with a height of 760 mm. Supports a 32 m high water column. And, of course, that's why we fill the barometer with mercury instead of water or alcohol.

The vapor pressure of mercury is also minimal. Therefore, the pressure at the exit point is equal to atmospheric pressure. This pressure is therefore equal to 10 to the power of 5 times 1.1. The base area of ​​this water cube is 12" x 12" = 144 square inches. So, the pressure at the bottom of the water cube is 62.4 pounds / 144 square inches = 0.433 pounds per square inch (psi). The RCC column minimum size is 9" x 9" and incorporates four 12mm bars steel stiffeners and cleats of 8mm steel rings spaced 150mm center to center.

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A uniform circular motion is one in which the velocity of the object remains constant. This means that the object is moving with a constant speed and in a circle, without acceleration.

In this type of motion, the acceleration is zero. Acceleration is defined as a vector quantity, which means that it has both magnitude and direction. In this case, both magnitude and direction are zero, so there is no acceleration—the body moves in a straight line at constant speed in a circle.

A body has an acceleration when it is changing its velocity, either increasing or decreasing it. An example would be stopping on a highway, where your foot would push down harder on the gas pedal to increase your speed while going around a curve, then slowing down as you straightened out again.

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Changing the revolving mass and keeping the radial force same the Period will alter. According to variations in revolving mass.

A force applied in a radial direction toward or away from the centre is referred to as a radial force. When a massed body or fluid element moves in a circular motion, an equilibrium between the centripetal force acting from the inside and the centrifugal force acting from the outside is created in the radial direction.

F = mv²/r

F = Force required to keep the mass in a circle

m = mass

v = velocity of the mass

r = radius of the circle.

Since, v = 2πr/t

Where t = period

π = pie

Substitute the value of v

We have, F = m(2πr/t)²/r

F = 4π²r²m/t²r

F = 4π²rm/t²

If the path radius and radial force are kept constant then mass is directly proportional to period

m ∝ t

Which means if mass increases period will increase as well.

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The wavelength of the electromagnetic radiation emitted by your phone is 1.578meters.

The name given to the recognized range of electromagnetic radiation is the electromagnetic spectrum (EMS). The frequency decreases from 3×10²⁶ Hz to 3×10³ Hz as wavelengths rise from around 10⁻¹⁸ m to 100 km.

The wavelength is the separation between two wave crests, while troughs have the same wavelength. Frequency, measured in cycles per second (Hz), is the number of vibrations that pass over a certain location in a second (Hertz).

Given,

Frequency  = 1900 mhz = 1900×10⁶,

velocity = 3×10⁸,

Wavelength = v/F

Wavelength = 3×10⁸/ 1900×10⁶

Wavelength = 1.578meters.

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The efficiency of a machine that requires 20 J of input work to do 10 J of output work. The efficiency of the machine η = 50 %

The engine efficiency  is defined as ratio of the useful work done to the heat provided.

By using the formula for efficiency of a machine and substituting the values in it, we get :

η = (Wo/Wi × 100)%

η = (10/20 × 100)%

η = 50 %

The efficiency of the machine will be η = 50 %

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Key observation that enabled Edwin Hubble to prove that the Andromeda galaxy laid far beyond the bounds of the Milky Way, thereby putting to rest the idea that it might have been a cloud within our own galaxy, was individual Cepheid variable stars.

The Andromeda galaxy was always thought to be a nebula within our own galaxy, the Milky Way. A Persian astronomer, Abd al-Rahman al-Sufi, was the first to formally describe the Andromeda as a nebulous smear (small cloud).

It wasn't until Edwin Hubble's discovery in 1925, when he identified extragalactic Cepheid variable stars for the first time on astronomical photos of Andromeda in 1925, that the Andromeda galaxy was eventually concluded to be an independent galaxy.

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Using the concepts of pressure, we find that 625m[tex]s^{-1}[/tex] is the speed of the stomp rocket rising at that moment when it is watched by students 500 meters away. after 2 seconds, when the angle of elevation is the angle is increasing at a rate of 0.4 radians per second.

We know that when an object is very far away, at the centre of that object there is an angle enclosed by the observer and that is given

angle=(length of arc)/radius of the arc.

θ=l/r

So, we are given that length of arc is 500 metres and angle is 0.4 radians/sec.

So,=>0.4=500/r

      =>r=500/0.4

       =>r=1250m

Now we are given the time when it is observed i.e. is 2 seconds.

So, we apply distance speed formula.,

which is Distance=Speed × Time

            =>1250=Speed×2

              =>Speed=1250/2

              =>Speed =625m[tex]s^{-1}[/tex].

Hence, when a stomp rocket is launched straight into the air and is being watched by students 500 meters away. after 2 seconds, and the angle of elevation is the angle is increasing at a rate of 0.4 radians per second, the speed of stomp rocket is 625m[tex]s^{-1}[/tex].

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40.47 m/s is the speed at which the arrow departs the bow.

Does velocity not depend on gravity?

An object's horizontal velocity is constant for small displacements and operates independently of the vertical force of gravity. The horizontal and vertical halves of an object that is projected at an angle to gravity can also be separated. The force of gravity has no impact on the horizontal velocity component either.

The arrow will start moving and accelerating as soon as it is let go from the bow. The arrow obeys the second law of motion, according to Newton. The method

m = mass of the arrow (kg) = 0.0850 kg

a = acceleration of the arrow (m/s²)

F = force (N) = 89.0 N

F=m*a

a = 1,047.059 m/s²

When an object accelerates, it will travel in a non-uniform manner. The method

[tex]v^{2} = v_{0} ^{2} +2*a*d[/tex]

= 40.47 m/s

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The cause of these bands is the interference between the waves reflected from the glass on the upper and lower surfaces of the air wedge.

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a) in the z direction  he should  proceed in order to decrease the temperature most rapidly

b) The temperature decrease in the rate of  −2√14e2 if he proceeds in that direction.

Taking the gradient of TT yields ∇T(x,y,z)=⟨−2xe(−x2−2y2−3z2),−4ye(−x2−2y2−3z2),−6ze(−x2−2y2−3z2)⟩, where we get the direction of maximum increase of any point (x,y,z). As   we're at (1,1,1) so  the appropriate vector in order for the  maximum decrease is

−∇T(1,1,1)=⟨2e6,4e6,6e6⟩≈⟨0.0049575,0.00991501,0.0148725⟩

we normalize the upper result  giving us  :

⃗ =−∇T(1,1,1)∥−∇T(1,1,1)∥=⟨−1/√14,−√2/7, −3/√14⟩, here  we are getting the direction of and along with an angle

Now,  if r(t)  is a parametrized path, then d/dtT(r(t))= change in T(r(t)).r ′(t)), in order for heading to the direction of maximum decrease,  so UV =∥u∥ ∥v∥cosθ in here θ=0. So, the rate of decrease is ∥∇T(1,1,1)∥e8=2/√14e2 or -2/√14e2

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The temperature of the ship's hull when he is at location (x,y,z) will be given by T(x,y,z)=e−x2−2y2−3z2, where x,y, and z is measured in meters. He is currently at (1,1,1).

(A) In what direction should he proceed in order to decrease the temperature most rapidly?

(B) If the ship travels at e8 meters per second, how fast will the temperature decrease if he proceeds in that direction?

The net force on the airplane is 420 N.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude. The application of force is the location at which force is applied, and the direction in which the force is applied is known as the direction of the force.

A spring balance can be used to calculate the Force. Newton is the SI unit of force.

Given parameters:

Force of the airplane, F = 800 N.

Force of air resistance, f₁ = 40 N.

Wind force, f₂ =  60 N.

Net force = ?

According to the question, wind force and force of air resistance are acting opposite direction. As, force of air resistance always acting opposite to the direction of plane flying, wind force is acting along the direction of plane flying.

Hence, net force = F - f₁  + f₂

= ( 800 -40 + 60) N.

= 820 N.

So, net force acting on the plane is 820 N.

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I = I° cos²∅

When ∅ is 0° then intensity is maximum

When ∅ is 90° then intensity is minimum.

When two polarizer are combined in such a way that their crystallographic axes are parallel, the resulting intensity is at its highest, and you can see the light's original color as it passed through intensity  the first polarizer. In this scenario, if the polarizer is colored and we are looking at the object through the polariser, the color that corresponds to the superposed wave that was created by the object's radiated wave (object's color) and the polariser's color will be the color of the object. On a beach, this is what happens when you wear polarized intensity sunglasses on a sunny day: the color of the objects appears differently than when you are wearing sunglasses.

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1.514 x 10⁴ N-m is the torque required to accelerate it.

Torque is the force that acts on the body causing it to turn about an axis.

It's given by

τ = I α ------- equation 1

Here I = moment of inertia of the disk

α  = angular acceleration of the disk

For disk, moment of inertia = ½ m r²

I = 1/2 x (31 x 10³ kg) x (7)²

= 1/2 x (1514 x 10³)

α = ω₂₋ω₁ / t

here ω = angular velocity of the rotating merry-go-round

Substituting the values

α = ( 0.68rad/s - 0rad/s ) / 34s => 0.02 rad/s²

Putting the values of I and α in equation 1

τ = 1/2 x (1514 x 10³) x 0.02

=> 1.514 x 10⁴ N-m

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The tension when the stick is at six o clock will be 17.96 N and when the stick will be on 12 o clock the tension will be 14.04 N.

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Kinetic energy of Corvette with a mass of 1,054 kg and a velocity of 48m/s is 12,14,208 J

Kinetic energy is a type of power that an item or particle possesses as a result of motion. An object accelerates and acquires kinetic energy when it undertakes work—the transfer of energy—by being subjected to a net force. Kinetic energy is one of the properties of a moving object or particle, which depends on both mass and speed. The type of motion can be any combination of vibration, rotation on an axis, and translation (or transit along a path from one spot to another).

A body's translational kinetic energy is equal to 1/2mv2, or one-half of the product of its mass, m, and square of its velocity, v.

Here,

m = 1,054 kg

v = 48 m/s

KE = ?

KE = 1/2 mv²

KE = [tex]\frac{1}{2}[/tex] × 1054 × 48²

KE = 0.5 × 1054 × 2304

KE = 12,14,208 J

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you get the same acceleration.

we know that:

   F = ma
   a = F/m
    a = 2F/2m
     a = F/m

so if we double the force and the mass, you get the same acceleration.

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The initial velocity of the skateboard will be greater than its final velocity.

The correct option is C.

Acceleration is the rate at which the speed and direction of velocity vary over time. A point or object going straight ahead gets accelerated when it accelerates or decelerates. Even if the speed decreases, movement on a circle accelerates because the direction is always shifting.

We refer to a change in an object's speed or direction as acceleration. The rate at which speed varies is known as acceleration. Keep in mind that velocity has two parts: speed and direction.

Our theory says that an object accelerates in the reverse direction from the velocity when it slows down. As a result, the object is moving backwards.

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The complete question is-

For a skateboard with a negative acceleration, which of the following statements is always true?

A. The skateboard is losing speed

B. The final velocity of the scooter will be negative

C. The initial velocity of the skateboard will be greater than its final velocity

D. The skateboard will have a negative displacement

1000 kg is the mass of the ball.

To find the volume of a substance, divide its mass by its density (mass/density = volume). Consistent measurement units should always be used. If the density is specified in grams per cubic centimeter, for instance, then calculate the mass in grams and provide the volume in cubic centimeters.

From mass and volume measurements, the densities of brass and aluminum will be determined. Three different methods will be used to calculate volumes: geometrically (by measuring lengths); via water displacement; and via pycnometry.

The density calculation formula is p = m/V.

m = p*v

m = 100kg

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The length of the cable that connects the pendulum ball to the ceiling with a period of 5.5 s is 7.5 m

T = 2 π √ ( L / g )

T = Time period

L = Length of the pendulum

g = Acceleration due to gravity

T = 5.5 s

g = 9.8 m / s²

5.5 = 2 * 3.14 √ ( L / 9.8 )

√ L = 0.88 * √ 9.8

L = 0.77 * 9.8

L = 7.5 m

A simple pendulum consists of a mass suspended in air by a massless and unstretchable string that is fixed to a rigid support on the other end. The time taken to complete on oscillation is the time period of a simple pendulum.

Therefore, the length of the cable is 7.5 m

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For a charged particle, a constant magnetic field can be used to change for a charged particle, only the direction of the particle's velocity .

magnetic force = q(VxB)  

which is perpendicular to V and B

so it can't change magnitude only can change direction.

A magnetic field is a vector field near a magnet, an electric current, or an alternating electric field where the observed magnetic forces exist. A magnetic field consists of moving electric charges and the internal magnetic moments of elementary particles associated with a fundamental quantum property called spin. The magnetic field and the electric field are both related and are components of the electromagnetic force, which is one of the four  forces of nature.

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Flame length is used to describe the fireline intensity.

The sum of the heat released during a given period of time for each unit length of the fire's edge and the rate at which the fire spreads per unit of ground area is called the heat availability of combustion per unit of ground. Btu/sec/ft of fire front is the fundamental unit of measurement.

The rate of energy or heat emission per unit time per unit length of the fire front is called the fireline intensity (kW/m). From a mathematical perspective, it is equal to the product of the fuel's low heat of combustion (kJ/kg), the amount of fuel used in the flame front (kg/m2), and the linear rate of fire

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The law that explains after energy conversions, the total amount of energy has the same amount as the original amount of energy is the Law of conservation of energy.

The state law of conservation of energy is that energy cannot be created, the energy cannot be destroyed, and the energy can be converted from one form of energy to another form of energy. Examples like mechanical energy. Mechanical energy is the sum of potential energy and kinetic energy.

If an apple fell from a branch of a tree

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125.06⁰angle is the axis of the polarizer oriented, with respect to the vertical

given,

Only 67.0% of the intensity of the light passes through the sheet and strikes a second sheet of polarizing material. No light passes through the second sheet.

for the first sheet we have malus law as

         I =I₀cos²θ₁

    here(given)

    I/I₀ = 0.67

   so cos²θ₁ =0.67

        θ₁ = cos⁻¹√(0.67)

               = 35.06⁰

which is the angle the first sheet makes with transmission axis

here  given no light passes through the second sheet i.e. both the sheets are in crossed position

so the angle the transmission axis of the second sheet makes with the vertical is

   θ₂ = θ₁ +90⁰

        =35.06 + 90⁰

         =125.06⁰

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The time it takes for the energy stored in the capacitor to be reduced to half its initial value is 0.00693 seconds.

A capacitor is a device that stores electrical energy in an electric field by accumulating electric charges on two insulated surfaces. It is a two-terminal passive electronic component. Capacitance is the effect of a capacitor.

The time it takes for the energy stored in the capacitor to be reduced to half its initial value is calculated as follows.

Q=Q₀[tex]e^{-t/RC}[/tex]

the time constant, RC = 10 ms = 0.01 s

Q₀ is the initial charged stored

Q is the final charge of the capacitor

Q₀/2=Q₀[tex]e^{-t/RC}[/tex]

Q₀/2Q₀=[tex]e^{-t/RC}[/tex]

1/2=[tex]e^{-t/RC}[/tex]

㏑(1/2)=-t/RC

㏑(1/2)=-t/0.01

-0.693=-t/0.01

t=o.00693 s

Thus, the time at which the energy stored in the capacitor will reduce to half of its initial value is 0.00693 s.

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The complete question is:

"The capacitor in an RC circuit is discharged with a time constant of 10.0ms. At what time after the discharge begins is the charge on the capacitor reduced to half its initial value."

The magnitude of the force that the garbage exert on the floor of the service elevator is equal to 238.05 Newtons.

The mass of the garbage in the elevator is 20.7 kg. The elevator is accelerated downward at a rate of 1.7 m/s².

The acceleration due to gravity is g.

As the elevator accelerator downward then the total net acceleration of the elevator in the download direction is

A =  (1.7 + 9.8) m/s².

A = 11.5 m/s².

The force that the garbage exert on the floor of the service elevator will be equal to the product of the mass of the garbage and the net acceleration with which the elevator is going downward,

F = 20.7 × 11.5

F = 238.05 N.

So, the force exerted by the garbage on the floor is 238.09 Newton.

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The radius of the new orbit should be 4 times larger to increase the satellite period 8 times.

Calculation:-

Using the formula for the satellite period.

T = 2π [tex]\sqrt{\frac{R^{3} }{GM} }[/tex]

In which R is the average radius of orbit for the satellite G is the gravitational constant, and M is the mass of the planet.

Therefore the radius of the new orbit ought to be four instances large to increase the satellite period 8 instances.

The orbital length is without delay associated with the common distance among the planet and the sun. This regulation means that planetary orbital velocity decreases with increasing distance from the sun.

The orbital length will increase if the orbital distance is multiplied. As the distance of the planet from the solar increases, the length of revolution decreases. you could calculate the space in more than one methods. One way is to multiply the calculated rate by the length.

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