First, for this problem, we will need to know the formula for time dilation
[tex]t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]Where t is the time in the reference frame on earth
t0 is the time on the ship
v is the velocity relative to lightspeed
and c is light speed in a vacuum
For this problem, we will need to convert .93x10^8 to a fraction of light speed.
.93x10^8 = .31c
Now, we can plug in the numbers we get from the given
t0 = 6 hours since the ship has been in the air for 6 hours
[tex]t=\frac{6}{\sqrt{1-\frac{(.31c)^2}{c^2}}}[/tex]t = 6.31089
For the answer to be valid, we will convert .31089 to minutes by multiplying it by 60 (60 minutes in a hour)
18.654 minutes
In a 92 s interval, 562 hailstones strike a glasswindow of area 1.216 m² at an angle 64° to thewindow surface. Each hailstone has a mass of2 g and speed of 5.8 m/s.If the collisions are elastic, find the averageforce on the window.Answer in units of N.
Given that the number of hailstones is n = 562
The mass of hailstone is m = 2 g = 0.002 kg
The speed of hailstone is v = 5.8 m/s
The time taken will be t = 92 s
The angle is
[tex]\theta=64^{\circ}[/tex]We have to calculate the force.
The force can be calculated by the formula
[tex]\begin{gathered} F=\text{ force due to one hailstone }\times numberofhailstones\text{ } \\ =m\frac{v}{t}\sin \theta\times n \end{gathered}[/tex]Substituting the values, the force will be
[tex]\begin{gathered} F=\text{ }\frac{\text{0.002}\times5.8\times\sin 64^{\circ}\times562}{92} \\ =0.063\text{ N} \end{gathered}[/tex]how would an increase in force affect the mechanical advantage of a simple machine
Mechanical advantage is a measure of the ratio of the output force produced to the input force applied in a system, mainly in the case of simple machines, such as levers and pulleys. It is a dimensionless quantity.
From the definition, the mechanical advantage of a simple machine is inversely proportional to the input force applied on the system. So, an increase in this force decreases the mechanical advantage of a simple machine.
For example, the mechanical advantage of a lever can be decreased by increasing the force on load arm or by reducing the force on the effort arm.
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There are two groups of earthworms on the sidewalk. One group is on a shady, moist area on the sidewalk, and they are moving. The other group is on a very sunny, dry area of the sidewalk, and none of the worms in this group are still living.
What question could be asked to investigate the reason for these observations?
A. What kind of living environment do earthworms need?
B. How do earthworms get on the sidewalk?
C. Why do earthworms crawl?
D. What kinds of birds eat earthworms?
A.
Smooth-skinned earthworms have a body made up of numerous tiny segments. The lines designating the segments are visible on the body. Each segment possesses tiny, stiff hairs that aid in the worm's movement; occasionally, the hairs are difficult to perceive. They lack a skeleton yet have a large number of muscles.
B.
Because they lack lungs, earthworms breathe through their skin. For dissolved oxygen to enter their bloodstream, their skin must be damp. The mucus-coated skin of earthworms makes them dependent on a wet, moist environment to survive.
C.
The earthworm's characteristic crawling movement is caused by the action of muscles in the body wall. These lengthen and shorten the body in wavelike motions. Four pairs of tiny hard bristles on each segment help the worm grip the ground and hold onto the side of the burrow.
D.
Blackbirds, robins, and song thrushes are ground feeders, and for them, a worm is the only food that compares to it in taste. Large eyes and powerful bills let all of them to see in the early morning light, when earthworms are most active close to the surface. Their strong bills also allow them to pull struggling earthworms from the soil.
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coherent light of frequency is shone through a single slit with a gap width equal to a. an interference pattern is observed on the screen a distance behind the slit. what effect will each of the following alterations have on the width of the central bright spot on the screen? a. decrease the gap width. b. decrease the frequency of the light. c. decrease the distance from the slit to the screen.
Coherent light at this frequency passes through a single slit with an interval width equal to the effect of each of the following changes on the width of the central bright spot on the screen. reduce gap width
Two wave sources are coherent if they have the same frequency and waveform. Interference is an ideal property of waves that allows for fixed interference. The central bright band of the single slit diffraction pattern is generated by constructive interference from all secondary sources.
The width of the center band is inversely proportional to the slot width. Coherence is a fixed ratio between wave phases in a beam of radiation of one frequency. The wavelengths of two rays are coherent when the phase difference is constant. Inconsistent if there are random or changing phase relationships. When two waves are monochromatic and in phase, they are said to be coherent. A coherent source is one that generates those waves. With the help of these waves, you can study the properties of the light path. For this purpose, one beam is transmitted along the intended track, and the other is transmitted to the control test.
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how does heat move from the inside to the outside in the outer 30% of the sun? through neutrinos released by nuclear fusion by convection: hot gas rises and cool gas sinks by radiation: photons bounce around heating up the gas by sound waves
Heat moves from the inside to the outside in the outer 30% of the sun by hot gas rises and cool gas sinks by radiation.
Radiation is the exchange of heat vitality through space by electromagnetic radiation. Most of the electromagnetic radiation that comes to the soil from the sun is imperceptible. As it were a little parcel comes as obvious light.
Energy from the sun is exchanged through space and the earth's climate to the earth's surface. Since this vitality warms the earth's surface and environment, a few of it is or gets to be heat vitality.
Even though you're encompassed by discussion, the discussion has nothing to do with this exchange of heat.
Heat lights, that keep food warm, work in the same way. Radiation is the exchange of warm vitality through space by electromagnetic radiation. Most of the electromagnetic radiation that comes to the soil from the sun is undetectable.
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While traveling, an airplane passenger placed a bag of potato chips in his checked luggage that was placed in the baggage compartment where the air was not regulated. When he opened the luggage after landing, the bag had exploded and potato chips were everywhere in his luggage. Which gas law does this describe?.
While traveling, an airplane passenger placed a bag of potato chips in his checked luggage that was placed in the baggage compartment where the air was not regulated. When he opened the luggage after landing, the bag exploded and potato chips were everywhere in his luggage. Boyle's law explains this phenomenon.
According to Boyle's law, the volume of a gas and its pressure are inversely proportional to each other.
In a bag of potato chips, nitrogen gas is filled to prevent breakage and keep the flavor intact.
At Earth, the pressure of the gas inside the package is less than the surrounding pressure and it prevents the potato pouch from bloating up. However, at higher altitudes, pressure decreases, and the volume of the gases inside the bag expands under lower pressure and ultimately the bag explodes.
In general, when the pressure of the potato bag becomes greater than the surrounding pressure, then it explodes.
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a wire having mass per unit length of 0.460 g/cm carries a 2.12 a current horizontally to the south. what are the direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward? magnitude
The direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward is clock wise direction and 0.245T.
What is a magnetic field?The magnetic field is the area that is affected by magnetism and is located around a magnet. The magnetic field is a valuable tool for explaining the distribution of the magnetic force within and around a magnetic object in nature.
The mass per unit length of the wire = 0.460 g/cm = 0.046 kg/m
Current in the wire, A = 2.12 A (due south)
To find,
The minimal magnetic field's magnitude as well as its direction.
F = ILB = mg
B = mg/IL
B = 0.046 × 9.8 /2
B = 0.225T
B = 0.245T.
The right hand rule specifies the magnetic field's direction, which is clockwise around the wire.
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The main engine of an ariane v rocket produces a thrust of 1015 kN and it’s booster rockets produce a total thrust of 13300 kN. If it has a launch mass of 780 tonnes, calculate its initial acceleration.
The initial acceleration of the rocket at the given thrust is 1.3 m/s².
What is the initial acceleration of the rocket?
The initial acceleration of the rocket is determined by Newton's second law of motion. This law states that the force applied to an object is directly proportional to the product of mass and acceleration of the object.
F = ma
where;
F is the applied forcem is the mass of the rocketa is the accelerationThe initial lunch force = 1015 kN = 1,015,000 N
The mass of the rocket = 780 tonnes = 780,000 kg
a = F/m
a = (1,015,000) / (780,000)
a = 1.3 m/s²
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b. A bus travelling in a straight seconds. road covers a distance of 220m in 20 between mass and weight. calculate its velocity
Answer:
11 m/s?
Explanation:
The question is not clear, but I am assuming that it is asking for the velocity of a bus traveling for 220 meters in 20 seconds.
You are Given:
Displacement (d) : 220m (in this question, since there is no change in direction, the distance and displacement is the same)
Time (t) : 20 seconds
You want to Find:
Velocity: ???
Equation to use:
velocity = displacement/time
aka. v = d/t
Now just Solve:
v = d/t
v = 220m/20s
v = 11 m/s
You're driving home from the grocery store at 18 m/s with a 7. 0 kg bag of groceries on the front seat when the light ahead turns red. What is the shortest distance in which you can stop, after the brakes are applied, without the groceries sliding off the seat? the static and kinetic coefficients of friction are, respectively, 0. 65 and 0. 45. Assume that the surface of the seat is horizontal
The minimum distance such that the grocery bag does not slide off when the brake force applied is 25.43 m
The grocery bag will start to slide off if the force exerted by the brake is equal to the maximum static friction force.
Let:
Fs = static friction force
F = force exerted by the brake
m = mass of the grocery bag
v = velocity
μs = static coefficients of friction
g = gravitational acceleration = 9.8 m/s²
Then,
Fs = - μs . m. g
F = m . a
Fs = F
- μs . m. g = m . a
a = μs . g = 0.65 . 9.8 = - 6.37 m/s²
With this deceleration, the distance (s) will be:
v² = u² + 2 . a. s
Where v = 0 (since vehicle stops), u = 18 m/s
0 = 18² + 2 . (- 6.37 ) . s
s = 25.43 m
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a solenoid of radius 4.10 cm has 780 turns and a length of 25.0 cm. (a) find its inductance. mh (b) find the rate at which current must change through it to produce an emf of 70.0 mv. (enter the magnitude.) a/s
(a)- The Inductance of the given coil is 6.10mH.
(b)- The rate of the current for which the coil will produce an emf of 70mV is 11.47 A/s
Solution: -
Given
Radius of the coil = 4.10cm
Number of turns of the coil = 480 Turns
Length of the coil = 25 cm
(a)
Inductance of the coil = µ * (N^2) * (A/L)
Inductance = 4π x 10^-7 * (480)^2 * π *( 0.041m)^2 /0.25m
Inductance = 1.256 x 10^-6 * (480)^2 * π *(0.041)^2 /0.25m
Inductance= 1.52* 10^-3/0.25
Inductance= 6.10mH
(b)
Δi/Δt = emf/Inductance
Δi/Δt = 70 x10^-3/6.10mH
Δi/Δt= 11.47 A/s
Therefore the inductance of the coil is denoted as 6.10mH and the rate at which the current will flow the coil to give an emf of 70mV is 11.47 A/s.
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a 28 kg child is coasting at 2.0 m/s over flat ground in a 5.0 kg wagon. the child drops a 1.1 kg ball from the side of the wagon. what is the final speed (in m/s) of the child and wagon?
The final speed of the child and wagon is 2.1 m/s.
Momentum in a simple manner is an amount of motion. here amount is measurable due to the fact if an item is transferring and has mass, then it has momentum. If an object does not pass then it has no momentum. however, in normal lifestyles, it has a significance that many human beings failed to recognize it.
mass of child = 20 kg
mass of wagon = 5 kg
total mass m₁ = 25 kg
mass of ball dropped = 1.1 kg
new mass m₂ = 23.9
the initial speed of the child and wagon u₁ = 2 m/s
the final speed of the wagon = v₂
using conservation of momentum
m₁u₁ = m₂v₂
25×2 = 23.9 × v₂
final speed v₂ = 50/23.9
= 2.092 m/s
= 2.1 m/s
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10. What is the solution of the equation
-9x + 4 = -8- 5x?
A x = -3
B x=
2/7
x = 1
℗ x = 3
Answer:
x=3
-9x+4= -8-5x
+5x +5x
-4x+4= -8
-4 -4
-4x= -12
/-4. /-4
x=3
an engine flywheel initially rotates counterclockwise at 6.75 rotations/s. then, during 23.1 s, its rotation rate changes to 2.97 rotations/s clockwise. find the flywheel's average angular acceleration (including its sign) in radians per second squared. define counterclockwise rotation as positive
Flywheel's average angular acceleration is +0.42 radian per second square.
Angular acceleration is the rate of change of angular velocity and is denoted by "a".
Rate at which an object revolves or rotates about an axis is known as angular velocity and is denoted by "w".
Initial Angular velocity is denoted as w1 and final angular velocity is denoted as w2.
So, according to the equation of rotational motion,
w2= w1+at
Where t is the time
When we put the values given in this equation
= +2.97= -6.75+ a×23.1
= +2.97+6.75=a×23.1
= 9.72= 23.1×a
So, a= +0.42
Rate of change of angular velocity of flywheel is +0.42.
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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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A student is pulling a wagon and records the force vs time values in the table, which of the following will also remain constant for the wagon
A student is pulling a wagon and records the force vs time values in the table, then the acceleration of the wagon would remain constant, therefore the correct answer is option D.
What is Newton's second law?
Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.
As given in the problem if a student is pulling a wagon and records the force vs time values in the table,
As the Force of the pulling is constant and assuming the mass of the wagon to be constant the acceleration of the wagon would not change.
Thus, the correct answer is option D.
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The question is incomplete, the complete question is,
A student is pulling a wagon and records the force vs time values in the table, which of the following will also remain constant for the wagon
A. Displacement
B. velocity
C. Momentum
D. Acceleration
what fluid property is responsible for the development of the velocity boundary layer? for what kinds of fluids will there be no velocity boundary layer in a pipe?
Fluid viscosity is the property of the fluid that is responsible for the development of the velocity boundary layer. Non-viscous fluids do not exhibit the property of velocity boundary layer in a pipe.
What is fluid viscosity?
Thickness of a fluid is called its viscosity. In liquids, velocity boundary layer is formed due to viscosity.
Viscosity is also termed as the flow rate of a liquid. If a liquid has a high flow rate then its viscosity is low and vice versa.
The fluid viscosity can be measured by using viscometer. The formula to measure viscosity is F = μA. u/y
Here F is force, μ is fluid viscosity, A is the area and u/y sheer deformation rate.
On the contrary, a non-viscous fluid is one that has less thickness and can flow easily.
For example, water is a non-viscous fluid.
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A runner is initially going 5 m/s to the right when she slows down at to 2 m/s over 10
seconds.
a) What is her acceleration?
b) How far does she travel in these 10 seconds?
Answer:
acceleration =-0.3
distance =0.16m
Explanation:
the runner was initially moving with a velocity of 5mls and attained a final velocity of 2mls because it decelerated. therefore to find its acceleration you can go by the formula a=v-u÷t
the distance can be found by the formula v²=u²+2as
Just before Sarah started her laboratory work, she made a hot cup of tea. She left the tea on her desk while she worked because she never takes food or drink into the lab area. When she finished collecting data, Sarah's cup of tea was cool. What energy transfer caused her tea to cool?
The energy transfer between cup tea and surrounding caused her tea to cool according to newtons law of cooling.
The pace at which a body is exposed to radiation alters its temperature is roughly proportional to the temperature difference between the item and its surroundings, and the provided difference is small. The cooling law of Newton is this.
Heat is transported more quickly and a person's body temperature changes more quickly the higher the temperature difference between a system and its surroundings. When the temperature difference between the body and its surroundings is small, the rate of cooling of a body is directly related to the temperature difference and the surface area exposed.
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a woman stands near the edge of a cliff and drops a stone over the edge. exactly one second later she drops another stone. one second after that, how fast is the distance between the two stones changing?
The two stones will fall at the different time. But the difference between the time is just of one second.
The distance of the cliff is also considered. Here, the speed or velocity is asked. To calculate this we have to use the equation of motion.
There are three equations of motion.
We have;
The kinematic equation of motion that can be used is s = ut - (1/2)·gt²
For the first stone, we have, s₁ = ut₁ - (1/2)·gt₁²
For the second stone, we get; s₂ = ut₂ - (1/2)·gt₂²
g = The acceleration due to gravity ≈ 9.81 m/s²
s = The distance below the cliff top
The initial velocity of the stones, u = 0
To calculate the change of distance between the two stones,
we will subtract the two equation of motions are
s₁-s₂
With all the values kept together in the equation of motion, we can easily find the change of distance between the two stones.
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gravity always tries to collapse the mass of a star toward its center. what mechanism can oppose this gravitational collapse for a star? question 5 options: solar wind pressure convective movement of gases magnetic field pressure radiation pressure
Answer: The correct option is D radiation pressure.
Explanation: When gravitational force tries to collapse the star in itself, the radiation pressure coming from the gamma rays creates a force in the outward direction. This outward force hence creates equilibrium and as a result, the star remains in a stable condition.
The radiation pressure is due to the gamma rays. These rays are produced through the fusion reaction, taking place in the core of the star.
Hypothetically considering, if this radiation pressure is not present the star will eventually collapse due to its own gravity. This phenomenon is termed Gravitational Collapse.
If the force of gravity acting on an object is 40N and the object has a mass of 2.8k, what is the acceleration due to gravity?
Answer:
0.07
Explanation:
2.8/40 = 0.07
a thin rod of length 3.15 m and mass 12.7 kg is rotated at an angular speed of 3.60 rad/s around an axis perpendicular to the rod and through one of its ends. find the magnitude of the rod's angular momentum.
The magnitude of the rod's angular momentum is 165.92 [tex]Kg m^{2} s^{-1}[/tex].
The moment of inertia for the rod through an axis 'perpendicular' to one of its ends is given by :
[tex]I=\frac{Ml^{2} }{3}[/tex] (where M = mass of rod , l = length of rod)
Now, the angular momentum of the rod is given by;
L= Iω
= [tex]\frac{Ml^{2} }{3}[/tex]×ω
=[tex]\frac{12.7Kg * (3.15 m^{2})}{3}[/tex]* [tex]3.95 rad s^{-1}[/tex]
= 165.92 [tex]Kg m^{2} s^{-1}[/tex]
∴ The required angular momentum is: 165.92 [tex]Kg m^{2} s^{-1}[/tex]
As the rotating equivalent of linear momentum in physics, angular momentum (rarely a moment of momentum or rotational momentum) is used. It is a conserved quantity, meaning that in a closed system, the total angular momentum stays constant, making it a significant physical quantity. The magnitude and direction of angular momentum are both conserved. The conservation of angular momentum is responsible for the useful characteristics of bicycles, motorcycles, frisbee-lead bullets, and gyroscopes. Hurricanes develop spiral structures and neutron stars rotate rapidly due to the conservation of angular momentum. Conservation generally sets a limit on a system's potential motion but does not determine it in any way.
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A school bus moves 200 meters in 20 seconds, and another 100 meters in the next 10 seconds.
Calculate its average speed in m/s.
Answer: 300 m/s
Explanation:
So If it moves 200 metres in 20 seconds and then another 100 metres this is changing the total distance travelled to 300 metres. Also, it moves this distance extra distance in 10 seconds therefore the total time is 30 seconds.
speed = distance / time
speed = 300 / 30
speed = 10 m/s
After travelling a total of 300 metres and spending a total of 30 seconds in motion, the school bus travels at an average speed of 10 metres per second (m/s).
To figure out how fast the school bus was going on average, we need to know how far it went and how long it took to get there.
First, we add up the two lengths the school bus travelled: 200 metres plus 100 metres equals 300 metres.
Next, we add up how long it took to go both distances: 20 seconds plus 10 seconds equals 30 seconds.
Here's how to figure out the average speed:
Average Speed = Total Distance Travelled / Total Time Spent
Putting the numbers in:
Average Speed = 300 metres in 30 seconds
10 metres per second (m/s) is the average speed.
So, the school bus's usual speed is 10 m/s.
Average speed is the general rate of movement over a certain amount of time, no matter how it changes during the trip. In this case, the bus went 300 metres in 30 seconds, which means it went 10 m/s on average.
It's important to know that instantaneous speed is not the same as usual speed. Instantaneous speed is the speed of the bus at any given time during its trip. This speed could change as the bus speeds up, slows down, or stays at the same speed.
Calculating the average speed is helpful for figuring out how well something works generally, figuring out how efficient it is, and comparing different trips or types of transportation. But it might not take into account all the details of a given trip, such as different speeds or stops along the way. For a full picture of how the bus moves, it may be necessary to think about other things.
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a large truck with mass 30m crashes into a small sedan with mass m. if the truck exerts a force f on the sedan, what force will the sedan exert on the truck? f30 f 2f 30f
If the truck exerts a force f on the sedan then Force f will exert on the truck.
According to newtons third law ,"every action have an equal and opposite
reaction".
If truck exerts a Force [tex]F_{ts}[/tex] on sedan then sedan will exert a force [tex]F_{st}[/tex] on truck and [tex]F_{ts}[/tex] = - [tex]F_{st}[/tex]
so, we can say that vehicle experiences a force of same magnitude.
given the truck exerts force on the sedan, so the sedan also exerts Force F on the truck.
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Use the velocity vs time graph below for objects A and B to answer the given question.If A has the greater value pick answer choice AIf B has the greater value pick answer choice Bif A = B pick answer choice =.Which object has the greater Instantaneous Velocity at t = 5s?
Given the velocity versus time graph of an object.
From the graph, the velocity of object A is constant as the line representing its velocity is horizontal. The velocity of object a is decreasing with time. That is, object B is decelerating.
From the graph, at t=5 s the value of the instantaneous velocity of object A is 0 m/s.
And the value of the instantaneous velocity of object B is the same throughout the graph. And the value is 4 m/s.
Thus the value of the instantaneous velocity of object B is greater than that of object A.
Thus the correct answer is B has the greater value
in which reference frame is the translational (nonconvertible) kinetic energy greater: the reference frame in which the bat is at rest immediately before the collision or the reference frame in which the ball is at rest immediately before the collision?
The reference frame in which the bat is at rest immediately before the collision is the reference frame in which translational (nonconvertible) kinetic energy is greater.
As translational (nonconvertible) kinetic energy is greater when the bat is at rest because when it will be at rest the mass will be more. The translational dynamic energy of a body is rise to one-half the item of its mass and the square of its speed.
The translational kinetic energy depends on movement through space, and for an inflexible body of consistent mass, it rises to the item of half the mass times the square of the speed.
The movement of an unreservedly falling body could be a translational active vitality. Kinetic rangy at a pivoting fan is rotational kinetic energy.
In material science, the dynamic energy of a protest is the vitality that it has due to its movement. It is characterized as the work required to quicken a body of a given mass from rest to its expressed speed.
Having picked up this vitality amid its speeding up, the body keeps up this motor vitality unless its speed changes. The same sum of work is done by the body when decelerating from its current speed to a state of rest.
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what is the momentum of an 7.2- kg bowling ball rolling at 3.0 m/sm/s ? express your answer to two significant figures and include the appropriate units.
The momentum of an 7.2 kg bowling ball rolling at 3 m/s is 21.6 kgm/s.
What is momentum and how the momentum of bowling ball calculated out to be 21.6 kgms?Momentum is defined simply as the quantity of motion of the body , but it is the product of mass and velocity.There are several kind of momentum like linear momentum, translational momentum.Here is given the mass of the object 7.2 kg and the velocity is 3 m/s of the ball.Now to calculate the momentum we will simply apply the formula momentum = mass x velocity.7.2 x 3 = 21.6 kg-m/s is the momentum of the bowling ball rolling at 3 m/s .To know more about momentum visit:
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a certain amount of work w is required to accelerate a motorcycle from rest to a speed v. how much work is required to accelerate the same motorcycle from rest up to a speed v/4?
The work required to move the motorcycle from rest to a speed of v/4 is 1/16 times of the initial work w.
As we already know, from the work energy theorem,
That work done by all the conservative forces and all the none conservative forces on the body is equal to the change in kinetic energy of that body.
So, in formula form, it can be written as,
W = ∆K
Where w is work done on the body and ∆K is the change in kinetic energy of the body.
So, if now we assume, that the work done to increase the velocity of the body from zero to V is w, then we can write,
w = 1/2mv² ..... Equation 1
m is the mass of the body.
Now, as per the question,
Let us say the work done needed to increase the speed of the body from rest to v/4 is w', then we can write,
w' = 1/2m(v/4)² ..... Equation 2
Now,
Dividing equation 2 by 1,
We get,
w'/w = 1/16
So, the value of w' is w/16.
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a soccer ball is kicked from the ground with an initial speed of 19.5 m/s at an upward angle of 45o. a player 55m away in the direction of the kick starts running to meet the ball at that instant. what must be his average speed if he is to meet the ball just before it hits the ground?
Answer:
R = V^2 sin 2θ / g range formula
R = 19.5^2 * 1 / 9.80 = 38.8 m
Vx = 19.5 cos 45 = 13.8 m/s horizontal speed
t = R / Vx = 38.8 / 13.8 = 2.81 sec
v = (55 - 38.8) / 2.81 = 5.76 m/s (about 12.9 mph)