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]f a stone is thrown vertically upward from the surface of the moon with a velocity of 10 m/s, its height (in meters) after seconds is . (a) what is the velocity of the stone after 7 seconds? (b) what is the velocity of the stone after it has risen 25 m?
a) The velocity of stone after 7 seconds is 1.62 m/sec.
b) The velocity of the stone after it has risen 25 m is -[tex]\sqrt{17}[/tex]
a) h(t) = 10t - 0.83[tex]t^{2}[/tex]
velocity = [tex]\frac{dh}{dt}[/tex](t) = 10 - 2*0.83*t
[tex]\frac{dh}{dt}[/tex] (7) = 10 - 2*0.83*7
= 1.62 m/sec
The stone after 7 seconds is 1.62 m/sec
b) h(t) = 25
10t - 0.83[tex]t^{2}[/tex] = 25
t = 50/83 (10 + [tex]\sqrt{17}[/tex])
[tex]\frac{dh}{dt}[/tex] = 10 - 2*0.83*(50/83)(10 + [tex]\sqrt{17}[/tex])
= 10 - (10 + [tex]\sqrt{17}[/tex])
= - [tex]\sqrt{17}[/tex] m/sec.
The stone after it has risen 25 m is - [tex]\sqrt{17}[/tex] m/sec.
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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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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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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.
OPEN ENDED QUESTION
The skater eventually comes to a stop.
What has happened to all of the skater's
original potential energy?( this is on the Ed puzzle skate park please help I’m about to cry
Answer:
The maximum amount of kinetic energy the skateboarder can have is entirely dependent on the amount of potential energy of the system.
Explanation:
As the skateboarder moves, her potential energy is converted to kinetic energy (KE), or the energy of motion as her position changes along the track and the velocity changes.
Answer:
Explanation:
Kinetic energy turned into internal energy.
Potential energy has not changed.
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
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
Forces with magnitudes of v = 135 newtons and u = 280 newtons act on a hook (see figure). The angle between the two forces is 45°. Find the direction and magnitude of the resultant of these forces. (Hint: Write the vector representing each force in component form, then add the vectors. Round your answers to two decimal places.)
To find the resultant force we will first find the component force of the forces given, to do this, we need to remember that any vector can be express in component form by:
[tex]\begin{gathered} \vec{v}= \\ \text{ where } \\ v\text{ is the magnitude } \\ \theta\text{ is the angle of the vector with respect to the positive x-axis.} \end{gathered}[/tex]For force u we notice that its magnitude is 280 N and its angle is zero, then we have:
[tex]\begin{gathered} \vec{u}=<280\cos0,280\sin0> \\ \vec{u}=<280,0> \end{gathered}[/tex]For force v we know that its magnitude is 135 N and its angle is 45°, then we have:
[tex]\begin{gathered} \vec{v}=<135\cos45,135\sin45> \\ \vec{v}=<95.46,95.46> \end{gathered}[/tex]Now that we have both vectors in component form we add them to get the resultant in component form:
[tex]\begin{gathered} \vec{F}=\vec{u}+\vec{v} \\ \vec{F}=<280,0>+<95.46,95.46> \\ \vec{F}=<375.46,95.46> \end{gathered}[/tex]Once we have the resultant force in component form we can find its magnitude and direction if we remember that they are given by:
[tex]\begin{gathered} F=\sqrt{F_x+F_y} \\ \theta=\tan^{-1}(\frac{F_y}{F_x}) \end{gathered}[/tex]Plugging the values we found for the components we have:
[tex]\begin{gathered} F=\sqrt{375.46^2+95.46^2} \\ F=387.41 \end{gathered}[/tex]and
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{95.46}{375.46}) \\ \theta=14.27 \end{gathered}[/tex]Therefore, the magnitude of the resultant force is 387.41 N and the direction is 14.27°
What is your total displacement if you walk 30m East and 50m North?
The total displacement would be 110m.
The total distance is 50 m + 30 m + 30 m = 110 m. The displacement is the shortest route from the starting point. It is solved using vectors.
What is Displacement?
Displacement is a vector quantity which depends on the direction of motion but distance is a scalar quantity which just sums up all the given quantity values. The displacement is simply the difference between the locations of the two markers and is unrelated to the route used to get there. It is a vector quantity that has a direction and magnitude.
Hence, the total displacement if you walk 30m East and 50m North would be 110m.
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Answer:
58.31 meters northeast
Explanation:
The displacement can be modeled into the vector equation of [tex]\displaystyle{\vec s = 30\hat x + 50\hat y}[/tex]. We can find the magnitude of displacement by applying Pythagoras Theorem. Suppose we have a two-dimensional vector equation [tex]\displaystyle{\vec v = a\hat x + b\hat y}[/tex] then the magnitude of vector is [tex]\displaystyle{|\vec v\, | = \sqrt{a^2+b^2}}[/tex].
Therefore, the magnitude of displacement is:
[tex]\displaystyle{|\vec s\, | = \sqrt{30^2+50^2}}\\\\\displaystyle{=\sqrt{900+2500}}\\\\\displaystyle{=\sqrt{3400}}\\\\\displaystyle{\approx 58.31 \ \sf m}[/tex]
Since 30 meters east and 50 meters north form northeast direction then the displacement is 58.31 meters northeast.
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 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
If the same elevator accelerates downwards
with an acceleration of 1.2 m/s
2
, what is the
upward force exerted by the elevator floor on
the passenger?
The upward force exerted by the elevator floor on the passenger is 7.6 times mass of the passenger.
What is force?A force in physics is an effect that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Given in question elevator accelerates downwards with an acceleration of 1.2 m/s². There is acceleration due to gravity working downward which is 9.8 m/s².
So, net acceleration due to gravity is given as 9.8 - 1.2 = 7.6 m/s²
The upward force exerted by the elevator floor on the passenger is mass times acceleration, 7.6 times mass of passenger.
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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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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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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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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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What is the weight of a boy with a mass of 50 kg on Earth?
Use g= 9.81 m/s² and do not include units in your answer.
Answer:
490.5
Explanation:
Force = Mass × Acceleration
Since, Weight is a force and 'g' is the acceleration due to the earth's gravity,
Weight = Mass × g
Weight = 50 kg × 9.81 m/s² = 490.5 kg-m/s² or 490.5 N
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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suppose a 62-turn coil lies in the plane of the page in a uniform magnetic field that is directed into the page. the coil originally has an area of 0.25 m2. it is stretched to have no area in 0.100 s. what is the magnitude of the induced emf (in volts) if the uniform magnetic field has a strength of 1.50 t?
The magnitude of electromotive force is 232.5 volts.
We need to know about the electromotive force of induction to solve this problem. The emf induction appears when there is any change in magnetic flux. The magnitude of emf can be determined by
ε = N dΦ / dt
where N is coil turns, ε is electromotive force, dΦ is change in magnetic flux and dt is time interval.
From the question above, the parameters given are
N = 62
A/t = 0.25 m² / 0.1 s
t = 0.1 s
B = 1.5 T
By substituting the given parameters, we can calculate electromotive force
ε = N . dΦ / dt
ε = 62 . B . A / t
ε = 62 . 1.5 . 0.25 / 0.1
ε = 232.5 volts
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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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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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during keon's golf drive, the angular velocity of his club is zero at the top of the backswing and 33 rad/s at the bottom of the downswing just before ball impact. the downswing lasts 0.29 s, and the distance from the club head to the axis of rotation is 1.88 m at the bottom of the downswing. what is the average tangential acceleration of the club during the downswing (in m/s2)?
The average tangential acceleration of the club during the downswing is 113.79 rad/s².
Centripetal acceleration is due to the change within the direction of tangential speed, whereas tangential acceleration is due to any trade inside the value of the tangential speed.
The tangential acceleration is while the rotational velocity adjustments, that is 0 for uniform circular motion. while vector speed adjustments path however not important. for this reason Tangential acceleration =zero. Angular acceleration is the trade in angular velocity divided by using time, whilst tangential acceleration is the change in linear speed divided through time.
given,
∆ ω = 33 rad/s
∆t = 0.29 sec
α = (change in ω)/(change in t)
α = 33 rad/s / 0.29 s = 113.79 rad/s²
tangential acceleration = r α = 1.88*113.79 = 213.93 m/s2
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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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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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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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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
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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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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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