The magnitude of the magnetic force each exerts on the other is 4.41 N.
The magnitude of the magnetic force depends on the current through the wire, the length of the wire, and the radius of separation. It can be written as
F = μ₀ . I1 . I2 . L / (2π . a)
where F is a magnetic force, μ₀ is vacuum permeability (4π x 10¯⁷ H/m), I1 and I2 is current through the wire, L is the length of the wire and a is the radius of the wire.
From the question above, the given parameters are
L = 300 m
a = 23 cm = 0.23 m
I1 = I2 = 130 A
By substituting the parameters, we can calculate the magnetic force
F = μ₀ . I1 . I2 . L / (2π . a)
F = 4π x 10¯⁷ . 130 . 130 . 300 / (2π . 0.23)
F = 4.41 N
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HELP!
Emily is riding her skateboard down the sidewalk at 2 m/s when she suddenly hits a rock, causing the skateboard to stop. According to Newton's first law of motion, what happens to Emily?
a
Emily accelerates forward.
b
Emily moves forward at 2 m/s.
c
Emily moves forward at less than 2 m/s.
d
Emily stops with her skateboard.
Answer: (b)
Explanation:
According to the law of conservation of momentum.
B. Emily moves forward at 2 m/s.
a car has two headlights, and their power is derived from the car's battery. the filament in one burns out, but the other headlight stays on. are the headlights connected in series or in parallel?
It is necessary to collimate the light source before using the prisim to disperse the light so that the light rays entering the prisim are parallel series.
What is colimate?
collimator is a tool for converting a point source's divergent radiation into a parallel beam. To perform specific measurements in spectroscopy, geometrical optics, and physical optics, the light must be collimated.
An optical collimator is made up of a tube with a convex lens at one end and a variable aperture at the other end that is located in the lens' focal plane. To examine the image without parallax, radiation entering the aperture exits the collimator as a parallel beam.
Therefore collimation is needed for the light rays entering the prism to be parallel .
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If you are 16 miles from Charleston, how long will it take to get there if your average velocity is 42
miles per hour?
Answer:
22.9 minutes
Explanation:
Distance = Speed x Time
We want the time to go 16 miles at 42 miles/hour (mph).
16 miles = (42 mph)*T
T = 16 miles/(42 miles/hr)
Time = 0.381 hours
(60 minutes/hour)*(.381 hours)= 22.9 minutes
A cosmic-ray electron moves at 7. 5 × 10^6 m/s perpendicular to earth’s magnetic field at an altitude where the field strength is 1. 0 × 10 ^―5t. What is the radius of the circular path the electron follows?.
The separation between an orbit's center and its course is known as its radius. This separation is constant in all directions for an orbit that is entirely circular.
How does radius affect centripetal force?A particle travelling uniformly in a circle experiences a centripetal force, F, which is dependent on the mass (m), velocity (v), and radius (r) of the circle. the F formula using the dimensions method.
Where a, b, and c are the respective powers of m, v, and r and k is the dimensionless constant of proportionality.
Electric field
According to the query, the speed of an electron is 7.50 106 m/s.
1 105 T magnetic field, B
mass of an electron. m = 9.11 × 10⁻³¹
Electron charge, q = 1.6 1019
The relationship between radius of curvature,
r =( 9.11 × 10)-31 × 7.50 × (10)6/ 11.6 × (10) -19 ×1× (10) -5
= 4.266 m.
Therefore, the circular path's radius is 4.266 meters.
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a lighthouse is located on a small island 4 km away from the nearest point p on a straight shoreline and its light makes two revolutions per minute. how fast is the beam of light moving along the shoreline when it is 1 km from p? (round your answer to one decimal place.)
The speed of the beam of light moving along the shoreline when it is 1 km from p 62.83 km/min revolution.
A revolution is the motion of 1 object around a center or some other object, a forceful overthrow of a government by using the people, or any sudden or grand trade. An example of revolution is the movement of the earth around the solar.
dθ/dt = 3 rev/min
= 3×2π = 6π rad/min
tanθ = x/3
[tex]\frac{d}{dt}[/tex] tanθ = [tex]\frac{d}{dt}[/tex] (x/3)
sec²θ dθ/dt = 1/3 dx/dt
dx/dt = 3sec²θdθ/dt
At x = 1km; tanθ =x/3 =1/3
sec²θ = 1 + tan²θ = 1+(1/3)²
sec²θ =10/9
dx/dt = 3sec²θ dθ/dt
dx/dt = 3×10/9×6π
dx/dt = 62.83 km/min
Hence, the beam of light along the shoreline when it is 1 km away from point P is 62.83 km/min
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three solid, uniform, cylindrical flywheels, each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis. two of the flywheels rotate in one direction at the other rotates in the opposite direction at 3.42 rad/s. calculate the magnitude of the net angular momentum of the system.
Three solid, uniform, cylindrical flywheels with a radius of 1.47 m and a mass of 65.0 kg each rotate. The system's net angular momentum is 297.77 298 kg m2 / s in size.
I is the moment of inertia.
W = angular momentum L = angular velocity
I = 1/2 MR^2
I = 1/2 (65)(1.47^2)
I = 70.23
Moment of Inertia times Angular Velocity equals L.
In the same direction, two of the fly wheels turn.
L = 2I(W1) - I(W2) (W2)
L = 2*70.23(3.83) - 70.23(3.42) (3.42)
L = 297.77 ≈ 298 kg m^2 / s
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If net force acting on object is 0, then the force is considered to be..
a. balanced
b. equal in direction
c. unbalanced
d. distance/time
If net force acting on object is 0, then the force is considered to be balanced (option A).
What is net force?A net force refers to the sum of all the forces acting on an object.
The net force can accelerate a mass. Some other force acts on a body either at rest or motion. The net force is a term used in a system when there is a significant number of forces.
Fnet = F₁ + F₂ + F₃.............+ Fn
When the net force of an object is zero (0), this means that the sum of forces acting on the object is balanced. A balanced forces are forces that are opposite in direction and equal in size.
Therefore, a net force of 0 is a balanced force.
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There is a ball of fresh fruit at the top of a small cliff that is 45 m high. The fresh fruit baskets mass is 10kg's. Identify the energy (PE or KE) and calculate the it.
Given,
The mass of the fruit basket, m=10 kg
The height of the cliff, h=45 m
Kinetic energy is the energy possessed by an object due to its motion. Kinetic energy is directly proportional to the square of the velocity of the object.
Potential energy is the energy possessed by an object due to its position. The gravitational potential energy is directly proportional to the height at which the object is situated.
As the basket is at rest, its velocity is zero and hence it does not have kinetic energy.
Thus the energy possessed by the fruit basket is the potential energy.
The potential energy is given by,
[tex]E_P=\text{mgh}[/tex]Where g is the acceleration due to gravity.
On substituting the known values,
[tex]\begin{gathered} E_P=10\times9.8\times45 \\ =4410\text{ J} \end{gathered}[/tex]The potential energy of the fruit basket is 4410 J
which body has more internal energy - a piece of ice at a temperature of 0 degrees or from the melting of this ice at the same temperature?
The melting ice at the same temperature will have greater internal energy as compared to the ice at 0° C.
What is internal energy?
In thermodynamics, the internal energy is a quantity or state function that characterizes a substance's energy when capillary effects and other external fields, such as electric and magnetic forces, are absent. The value of the energy depends on the substance's state, not the nature of the processes that brought it to that condition, just like any other state function.
The melting ice at the same temperature will have more internal energy as compared to the ice at 0° C because during the melting of ice the intermolecular particles will absorb energy while breaking their bond and because of this, the melting ice has greater kinetic energy as well.
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Galileo’s pendulum theory stated that the time taken to swing through one complete cycle of a pendulum depends on what?
Italian astronomer, physicist, and engineer Galileo di Vincenzo Bonaiuti de' Galilei was sometimes referred to be a polymath.
Galileo asserted that the length of a pendulum affects how long it takes to swing through a full cycle.
A weight suspended from a pivot such that it can freely swing is called a pendulum. Gravity exerts a restoring force on a pendulum that causes it to accelerate back toward its equilibrium position when it is sideways from its resting position.
A pendulum is a tool for tracking periodic motion. It is made out of a string that is fastened to a sturdy structure. Typically, a pendulum swings from side to side when it is shifted through a tiny angle.
The length of the pendulum determines how long it takes for it to swing through one full cycle. The "period of the pendulum" is when things happen.
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the combination of crumple zones and air bags and seat belts might increase the distance over which a person stops in a collision to as much as 1.00 mm . what is the force exerted on a 65.0- kgkg driver who decelerates from 18.0 m/sm/s to rest over a distance of 1.00 mm ?
From Newton's second law of motion,
F = ma
We know m = 65 kg. Next, we have to find a through this formula:
v² = v₀² + 2ad
0² = (18 m/s)² + 2(a)(1 m)
Solving for a,
a = -162 m/s²
So,
F = (65 kg)(-162 m/s²) = -10,530 Newtons.
A crumpled zone in the front of the car gradually slows the car down and increases the braking time. A safety cell is a rigid cage that prevents passengers from becoming trapped. Inside the car seat belts and airbags prevent the driver from hitting the windshield steering wheel and dashboard.
Crumple zones are typically found in the front and rear of a vehicle and are designed to crumple and crush under high-force impacts. The Crumple Zone transfers a portion of the vehicle's kinetic energy during impact to a controlled crash while maintaining the integrity of the occupant cell.
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a boy pushes his little sister on a sled. the sled accelerates from 0 to 3.2 m/s . if the combined mass of his sister and the sled is 40.0 kg and 18 w of power were generated, how long did the boy push the sled?
The boy pushed the sled for 15 seconds. The Work-Energy theorem can be applied in circumstances when a rigid body must move while being subjected to several forces.
What is Energy Theorem?The Work - Energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.
The Work-Energy theorem can be applied in circumstances when a rigid body must move while being subjected to several forces. A rigid body can only have kinetic energy because of its rigid structure, which prevents it from storing potential energy in its lattice.
The sled is initially at rest → initial velocity (u) = 0.
Final velocity (v) = 3.2 m/s
Mass of boy and sled (M) = 40 kg
Power developed (P) = 18 W = 18 Joules/sec
According to work - energy theorem -
Work done (W) = Δ E(K) = E(f) - E(i)
Therefore -
W=[tex](1/2*40*3.2*3.2-1/2*40*0)[/tex]=204 joule
Now, Power is defined as the rate of doing work -
P =[tex]pw/dt[/tex]= [tex]w/t[/tex]
18 = 204/t
t = 15 seconds
Hence, the boy pushed the sled for 15 seconds.
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The boy pushed the sled for 15 seconds.
What is Energy Theorem?The Work - Energy theorem states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.The Work-Energy theorem can be applied in circumstances when a rigid body must move while being subjected to several forces. A rigid body can only have kinetic energy because of its rigid structure, which prevents it from storing potential energy in its lattice.The sled is initially at rest → initial velocity (u) = 0.
Final velocity (v) = 3.2 m/s
Mass of boy and sled (M) = 40 kg
Power developed (P) = 18 W = 18 Joules/sec
According to work - energy theorem -
Work done (W) = Δ E(K) = E(f) - E(i)
Therefore -
[tex]$$\mathrm{W}=(1 / 2 * 40 * 3.2 * 3.2-1 / 2 * 40 * 0)=204 \text { joule }$$[/tex]
Now, Power is defined as the rate of doing work -
[tex]&\mathrm{P}=p w / d t=w / t \\[/tex]
[tex]&18=204 / \mathrm{t} \\[/tex]
[tex]&\mathbf{t}=15 \text { seconds }[/tex]
Hence, the boy pushed the sled for 15 seconds.
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Instructions:Draw a speed graph in the box that matches thefollowing scenario:A runner jogged 40m at a slow pace for 40seconds. She then stopped for 40 seconds to gea drink of water. After that, she sped up and ran60m more in 20 seconds.Tip:y axis - total of 100 mx axis - total of 100 s
Given data:
1) Runner jogged 40 m at a slow pace for 40 sec.
2) Stopped for 40 sec.
3) Again funs for 60 m in 20 sec.
As shown in the diagram below, a soccer player kicks a ball directly toward the goal along a displacement vector r, which has a length of 7.7 m and a direction 30 degrees east of south. Alternatively, she could have kicked it to a second player standing directly in front of the goal along a displacement ry, who could have then kicked it to the goal along a displacement vector rx, as shown. Find the magnitudes (in m) and directions of rx and ry
Given that, the soccer player makes a displacement r = 7.7 m from the goal.
The distance between this player and the second player is [tex]r_{y}[/tex], and the distance between the second player and the goal is [tex]r_{x}[/tex]. The angle made by the first player with the goal is θ = [tex]30^{0}[/tex] east of south.
The magnitudes of [tex]r_{x}[/tex] and [tex]r_{y}[/tex] can be determined using the trigonometric rules.
r is the hypotenuse of the triangle formed (as shown in figure in the question), and [tex]r_{x}[/tex] is the side of triangle which is opposite to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{x}[/tex] = r sinθ = 7.7m × sin(30°) = 3.85 m.
[tex]r_{y}[/tex] is the side of triangle adjacent to the angle θ = [tex]30^{0}[/tex]. So, [tex]r_{y}[/tex] = r cosθ = 7.7m × cos(30°) = 5.445 m.
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What is the magnitude of the velocity of the plane
We will have the following:
First, we are told that the wind accelerates directly northwest, that means that the angle of inclination is 45°, so the following is true:
[tex]\begin{gathered} \sum F_x=115-75cos(45) \\ \\ \sum F_y=75sin(45) \end{gathered}[/tex]Then:
[tex]\begin{gathered} v_f=\sqrt{(115-75cos(45))^2+(75sin(45))^2}\Rightarrow v_f=81.56229536... \\ \\ \Rightarrow v_f\approx81.6 \end{gathered}[/tex]So, the magnitude of the final velocity is approximately 81.6 m/s.
if an aircraft is in sluf and we know the weight of the aircraft, w, the wing area, s, the density and velocity, what else must we know to determine the coefficient of lift of the aircraft?
To determine the coefficient of lift of an aircraft in sluf, we must also know the angle of attack.
What is aircraft?
A vehicle that can fly by gaining support from of the air is called an aircraft. It uses either static lift, dynamic lift from an airfoil, or, in a few rare instances, the downward thrust from jet engines to counteract the force of gravity. Aeroplanes, helicopters, airships (including blimps), gliders, paramotors, as well as hot air balloons are a few examples of common types of aircraft. Aviation refers to the human activity which surrounds aircraft. Aeronautics is the study of aviation, which includes creating and building aircraft. Unmanned aerial vehicles may well be remotely controlled as well as self-controlled by onboard computers, unlike crewed aircraft that have an onboard pilot. Different factors, including lift type, aircraft propellant, usage, and others, can be used to categorise aircraft.
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Equal masses are suspended from two separate wires made of the same material. The wires have identical lengths. The first wire has a larger cross-sectional area than the second wire. Which wire will stretch the least?.
The original lengths of both wires are equal, the thicker wire will stretch less as a result since Young's Modulus predicts that its original length will change less.
Young's modulus is a measurement of a material's capacity to endure changes in length when subjected to compression or tension along its length. Young's modulus, also known as the modulus of elasticity, is determined by dividing the longitudinal stress by the strain. i.e.Young's modulus = stress/strain
We can assume that the thicker wire must have less strain if it suffers less stress than the thinner wire because strain is defined as the percentage change in length.
Therefore we can said that, For the Young's modulus to remain constant, which it does, it must also drop correspondingly as strain rises. The thicker wire will stretch less as a result since its original length will change less because both wires started off the same length.
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A student learns that a certain comet in the solar system is considered a short-period comet. Based on this knowledge, what is the student most justified in concluding?.
A student learns that a certain comet in the solar system is considered a short-period comet. Based on this knowledge, the student most justified in concluding The comet originates between the Sun and the asteroid belt.
The Solar System's asteroid belt is a torus-shaped area roughly midway between the orbits of Jupiter and Mars. Asteroids or minor planets are the names for the vast majority of solid, irregularly shaped entities that are far smaller than planets. The term "primary asteroid belt" also applies to this asteroid belt.
A comet is a tiny, frozen object in the Solar System that begins to outgas when it approaches the Sun. Outgassing is the process through which gases are released from the comet.
The orbital durations of comets differ widely, from a few years to possibly millions of years, and they often have very eccentric elliptical orbits. The Kuiper belt or its related scattered disc is the source of short-period comets.
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"That's just the tip of the iceberg" is a popular expression you may have heard. It means that what you can see is only a small part of the overall problem. As the diagram shows, most of an iceberg is actually out of sight, below the water level. Based on this diagram, what is the most likely density of the iceberg? (Assume a density of 1.03 g/mL for seawater.)
The possible density of the iceberg from the options that have been given in the question is 0.88 g/mL.
What is the iceberg?We know that the term density has to do with the ratio of the mass to the volume of an object. Now when we find that an object is denser than another, the denser object would tend to sink on the one that has a lesser density.
In accordance with the floatation principle which states that an object would displace only its own volume of the fluid. We can see that even if an object has an equal density as the other then it can float on the other liquid.
Here we have been shown the image of an iceberg which is close to what we have known as the "tip of the iceberg". We are now being asked to be able to obtain what should be the accurate density of the iceberg.
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a simple pendulum has a period t on the earth. if it were used on planet x, where the acceleration due to gravity is 3 times what it is on earth, its period would be
If a simple pendulum has a period t on the earth. if it were used on planet x, where the acceleration due to gravity is 3 times what it is on earth, the time period is 0.577 times the time period on earth.
What is the frequency?
It can be defined as the number of cycles completed per second. It is represented in hertz and inversely proportional to the wavelength.
As given in the problem a simple pendulum has a period t on the earth. if it were used on planet x, where the acceleration due to gravity is 3 times what it is on earth,
Time period of simple pendulum = 2π √( l / g)
= 2π √( l / 3g)
Thus, the time period is 0.577 times the time period on earth.
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The deepest section of ocean in the world is the Mariana Trench, located in the Pacific Ocean. Here,the ocean floor is as low as 10,918m below the surface. If the index of refraction of water is 1.33, howlong would it take a laser beam to reach the bottom of the treach?
Given:
The depth of the trench, d=10,918 m
The refractive index of the water, n=1.33
To find:
The time it takes for the laser beam to reach the bottom of the ocean.
Explanation:
The refractive index of water is given by,
[tex]n=\frac{c}{v}[/tex]Where c is the velocity of the laser in vacuum and v is the velocity of the laser in water.
On substituting the known values,
[tex]\begin{gathered} 1.33=\frac{3\times10^8}{v} \\ \implies v=\frac{3\times10^8}{1.33} \\ =2.3\times10^9\text{ m/s} \end{gathered}[/tex]The velocity is given by the equation,
[tex]v=\frac{d}{t}[/tex]Where t is the time it takes for the laser to reach the bottom of the trench.
On substituting the known values,
[tex]\begin{gathered} 2.3\times10^8=\frac{10,918}{t} \\ \implies t=\frac{10,918}{2.3\times10^8} \\ =47.5\times10^{-6}\text{ s} \\ =47.5\text{ }\mu\text{s} \end{gathered}[/tex]Final answer:
The laser beam would reach the bottom in 47.5 μs
a cherry pie in a 8.50 in diameter plate is placed upon a rotating tray. then, the tray is rotated such that the rim of the pie plate moves through a distance of 308 in. express the angular distance that the pie plate has moved through in revolutions, radians, and degrees.
The angular distance should be
In revolution, θ = 11.53 revolution.
In radian = θ = 72.40 rad.
In degree θ = 4150.8°.
Calculation of the angular distance:
Since
Pie diameter = 8.50 in
So, the circumference of the pie should be
P = πd = 8.50π in
And, rim of the pie rotates 308 in,
So,
1 Revolution of the pie is 8.50π in,
So, for 308 it should be
= 308 in / 8.50π in revolution
=11.53 revolution
Now in the case when when we have to find distance in radians:
1 revolution is 2πrad
So,
11.53 revolution = 11.53 × 2π = 72.40 rad.
And also, 1 revolution is 360°
So,
11.53 revolution = 11.53 × 360 = 4150.8°
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an electron accelerated from rest through a voltage of 790 v enters a region of constant magnetic field. part a if the electron follows a circular path with a radius of 21 cm , what is the magnitude of the magnetic field? express your answer using two significant figures. b
The electron is accelerated through a potential difference of , so the kinetic energy gained by the electron is equal to its variation of electrical potential energy:
1/2mv²=eΔV
where
m is the electron mass
v is the final speed of the electron
e is the electron charge
is the potential difference
Re-arranging this equation, we can find the speed of the electron before entering the magnetic field:
v=√2eΔv/m=√2(1.6-10-19c)(790v)/9.1-10-31=1.66.10 m/s
Now the electron enters the magnetic field. The Lorentz force provides the centripetal force that keeps the electron in circular orbit:
evb=mv²/r
where B is the intensity of the magnetic field and r is the orbital radius. Since the radius is r=25 cm=0.25 m, we can re-arrange this equation to find B:
b=m/er =3.8.10 t
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in a simple electric circuit, ohm's law states that , where v is the voltage in volts, i is the current in amperes, and r is the resistance in ohms. assume that, as the battery wears out, the voltage decreases at 0.03 volts per second and, as the resistor heats up, the resistance is increasing at 0.03 ohms per second. when the resistance is 400 ohms and the current is 0.04 amperes, at what rate is the current changing?
Current is dwindling at 0.125 , where v is the voltage in volts, i is the current in amperes, and r is the resistance in ohms
Voltage = Current * Resistance ,
The Ohm's law is given by
V = IR eq. 1
Where V is the voltage across Resistance R and I is the current flowing through the Resistance R
Taking outgrowth of eq. 1 with respect to time t yields
dV/ dt = I * dR/ dt dI/ dt * R
dI/ dt * R = - I * dR/ dt dV/ dt
dI/ dt = (- I * dR/ dt dV/ dt)/ R eq. 2
Now substitute the given values into eq. 2
dI/ dt = (-0.02 *0.04(-0.02)) 300
dI/ dt = (-0.0008-0.02)/ 300
dI/ dt = -0.0208/ 300
Charge will go via the external circuit if the two conditions of an electrical circuit are satisfied. Flow of charge is appertained to as a current. In this case, the word" current" simply means that" charge is moving," indicating that commodity is taking place in the cables. The physical property of current, still, may be measured and quantified. The quantum of charge that moves past a point on a circuit at a given time is called current as a physical volume. The quantum of charge Q travelling through a line's cross section in a given quantum of time, as shown in the illustration below, can be measured to determine the current in a circuit.
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In the diagram below, two of the three rays used to find the image position are shown. Which of the following best describes the third (missing) ray?A.A ray incident parallel to the axis refracts outward, as if it came from the focus on the left hand side.B.A ray incident through the vertex continues through the lens without refracting.C.A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side.D.A ray incident on a path that would take it through the right focus refracts parallel to the axis.
Answer:
C. A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side
Explanation:
The third ray is the blue ray in the following figure
Therefore, the third ray is a ray parallel to the axis that refracts and passes through the focus of the right side.
So, the answer is:
C. A ray incident parallel to the axis refracts so that it passes through the focus on the right hand side
An electrified rod attracts pieces of paper. After a while these pieces fly away! Why?
Answer: The paper prices fall off due to repulsive forces.
Explanation: When an electrified or charged object is brought near an uncharged object, it causes the electrons of the uncharged object to move as electrons are free movable particles. The electron leave behind the atoms. The uncharged object becomes ionized.
Here the pieces of paper may fall off because it becomes de-ionized by surrounding air particles. While the pieces are attached to the rod, surrounding air particles may provide or take away electrons and make the pieces become neutral again
What is the speed of a rocket that starts with a speed of 120m/s and slows down at a rate of 22m/s2 for 4 seconds?
The final speed of the rocket, given it started with a speed of 120 m/s and slows down at a rate of 22 m/s² for 4 seconds is 208 m/s
How do I determine the final speed?From the question given above, the following parameters were obtained:
Initial speed (u) = 120 m/sAcceleration (a) = 22 m/s²Time (t) = 4 secondsFinal speed (v) =?The final speed of the rocket can be obtained as follow:
v = u + at
v = 120 + (22 × 4)
Clear bracket
v = 120 + 88
v = 208 m/s
Thus, we can conclude from the calculation above that the final speed of the rocket is 208 m/s
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The separation distance between two 2.0 kg masses is decreased by two-thirds. How is the gravitational force between them affected?
Given:
The mass of two objects is: m1 = m2 = m = 2 kg
The distance between the object is decreased by two-thirds
To find:
How on reducing the distance, the gravitational force between them affects them.
Explanation:
Let the distance between two objects each having mass "m" be "r". The gravitational force between them is given as:
[tex]F_1=G\frac{m_1\times m_2}{r^2}[/tex]Here, G is the universal gravitational constant.
Substituting the values in the above equation, we get:
[tex]\begin{gathered} F_1=G\times\frac{2\text{ kg}\times2\text{ kg}}{r^2} \\ \\ F_1=G\times\frac{4\text{ kg}^2}{r^2}..........(1) \end{gathered}[/tex]Now, the distance between the mass is reduced by two-thirds. Thus, the new distance between them will be "R" which is given as:
[tex]R=r-\frac{2}{3}r=r(1-\frac{2}{3})=\frac{r}{3}[/tex]Now, the gravitational force between two masses with their distance of separation reduced by two-thirds is given as:
[tex]F_2=G\frac{m_1\times m_2}{R^2}[/tex]Substituting the values in the above equation, we get:
[tex]\begin{gathered} F_2=G\times\frac{2\text{ kg}\times2\text{ kg}}{(\frac{r}{3})^2} \\ \\ F_2=G\times\frac{4\text{ kg}^2}{\frac{r^2}{9}} \\ \\ \begin{equation*} F_2=G\times\frac{9\times4\text{ kg}^2}{r^2} \end{equation*} \\ \\ F_2=9\times(G\times\frac{4\text{ kg}^2}{r^2})..........(2) \end{gathered}[/tex]Substituting equation (1) in equation (2), we get:
[tex]\begin{gathered} F_2=9\times(G\times\frac{4\text{ kg}^2}{r^2}) \\ \\ F_2=9F_1 \end{gathered}[/tex]From the above equation, we observe that the new gravitational force F2 between two masses when their distance of separation is reduced by two-thirds will be nine times that of the original value of gravitational force F1.
Final answer:
The new gravitational force F2 between two masses when their distance of separation is reduced by two-thirds will be nine times that of the original value of gravitational force F1.
an 81-kg baseball player slides into second base. the coefficient of kinetic friction between the player and the ground is 0.49. (a) what is the magnitude of the frictional force? (b) if the player comes to rest after 1.6 s, what was his initial velocity?
a) The magnitude of the frictional force= -µ mg = 0.49*81*9.8 = 389 N
b)The player comes to rest after 1.6 s, his initial velocity Vi = 7.68 m/s
Acceleration due to friction = - µ g = - 4.80 m/s^2.
V = V0 + at
V = 0
a = - 4.802 m/s^2
t = 1.6 s
V0 = V - at = 0 + 4.8*1.6 = 7.68 m/s
the acceleration of the player due to frictional force is given as
a = f/m = 388.96 /81 = 4.8 m/s2
final velocity = Vf = 0
time = t = 1.6 sec
using the formula
Vf = Vi + at (Vi = initial velocity)
Vi = Vf - at
Vi = 0 - (-4.8) (1.6) (a = -4.8 since player is slowing down)
Vi = 7.68 m/s
A force known as friction exists between two surfaces that are sliding or attempting to glide over one another. Friction, for instance, makes it challenging to push a book across the floor. The direction in which an object moves or attempts to move is always the direction in which friction operates. When anything moves faster or slower in a straight line, it is said to have been acceleration. Because the direction is constantly changing, even motion on a circle accelerates at a constant pace.
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From the bob’s frame while it is in uniform circular motion what is the direction and magnitude of the inertial force it feels?.
Radially outward is both the direction and magnitude of the inertial force. as it is moving uniformly in a circle, from the bob's frame. Radially emanating from the source of the charge is an electric field that is positively charged.
Radially outward means This is so because an electric field is produced when a positive charge is forced by the field. The electric field pulls the positive charge with a force that is directed away from the charge's origin. It is called Radially outward.
In physics, magnitude is referred to as an object's maximal size and direction. Both vector and scalar values use magnitude as a common factor. We know that scalar quantities are those that have magnitude and nothing else by definition.
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