The ball with a initial velocity of 22 m/s and an angle of 20 degrees above the horizontal covers a distance of 31.6 m, before returning to the ground.
R = u² sin 2θ / g
R = Horizontal range
u = Initial velocity
θ = Angle of projectile made with horizontal
g = Acceleration due to gravity
θ = 20°
u = 22 m / s
g = 9.8 m / s²
R = 22² sin 2 ( 20 ) / 9.8
R = 484 * 0.64 / 9.8
R = 31.6 m
Horizontal range of a projectile is the horizontal distance covered by an object in projectile motion.
R = Horizontal component * Total time
R = u cos θ * 2 u sin θ / g
R = u² ( 2 sin θ cos θ ) / g
R = u² sin 2θ / g
Therefore, the ball will go 31.6 m before returning to the ground
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a change in state involves a change in the______of the particles
Answer: Energy
Explanation: Any change in the states of matter is the result of added or lost energy. For example, when Water is frozen, it loses all of its particle energy, which is why when it's ice, all the particles stick together, but if you boiled the water to make vapor, they fly around like crazy because they have a lot of energy.
A 0.300 kg mass is attached to 26.6N/m spring.It is pulled 0.120 m and released. How much Potential Energy does it have when it is 0.0600 m fro
equilibrium?
Answer:
Explanation:
The elastic potential energy equation is EPE = (1/2) k x2, where k is the spring constant and x the distance from equilibrium. EPE = (0.5)*(26.6 N/m)*(0.0600 m)2 = 0.0479 Joules.
a 2.6 m diameter penstock carries water at a velocity oif 7 m/s to an 80% efficient hydroelectricity generation facility in west virginia that oroduces 12 mw. another 2.275 m diameter penstock carries water at a velocity of 3 m/s to a 74% efficient hydroeelctricity geenration facility in arkansas that produces 9 mw. what is the ratio of the heads of arkansas' reservoir to west virginia's reservoir?
The ratio of the heads of Arkansas reservoir to west virginia's reservoir is 1813: 1120.
Consider the West Virginia reservoir
To calculate the head of the Virginia reservoir, we will use
φ = P / nρgh
where φ is the flow rate, P is the power generated, n is efficiency, ρ is the density of water, g is the acceleration due to gravity, and h is the head.
Given that the flow rate is 7 m/s, the power generated is 12 MW, and 80% is the efficiency.
We know that the density of water is 1000 kg/m³ and acceleration due to gravity is 9.8 m/s²
By using equation 1:
h = P / φnρg
h = 9/3*80/100*1000*9.8
h = 13440
Similarly, the head of the Arkansas reservoir will be
Given that the flow rate is 3 m/s, the power generated is 9 MW, and 74% is the efficiency.
h = P / φnρg
h = 9/3*74/100*1000*9.8
h = 21756
Now, the ratio of the heads of Arkansas reservoir to west virginia's reservoir is:
= heads of Arkansas / head of Virginia
= 21756 / 13440
= 1813 : 1120
Located in a flat delta in southeastern Arkansas Lake Chicot is a natural wonder. The 20-mile former Mississippi Canal is said to be the largest crescent lake in North America and the largest natural lake in Arkansas. The Bull Shoals were named by early French hunters and trappers who used the word boile to describe the area.
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Since gravity is a conservative force, the work done against gravity can be replaced by gravitational potential energy. When an object is thrown vertically upward, its gravitational potential energy true or false?.
A ball's gravitational potential energy will rise as it is launched vertically upward.
An object's gravitational potential energy is the power it has as a result of being in a gravitational field. The gravitational potential energy is most frequently used for an object close to the Earth's surface, when the gravitational acceleration is believed to remain constant at around 9.8 m/s2. Since any point can be chosen as the gravitational potential energy zero (just like any coordinate system zero), the potential energy at a height h above that point is equal to the work that would be needed to lift the item to that height with no net change in kinetic energy. Its weight must be lifted with the same amount of force, so the gravitational potential energy must also be equal. The gravitational potential energy is most frequently used for an object close to the Earth's surface, when the gravitational acceleration is believed to remain constant at around 9.8 m/s2. Multiple factors affect the gravitational potential energy of an object: its mass, the gravitational acceleration it experiences from the earth, and its distance from the ground.
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a 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg , what is the momentum of the tackling dummy after the hit assuming the lineman stops instantly after impact?
A 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg, then the momentum of the tackling dummy would be 322 kg-m/s.
What is momentum?It can be defined as the product of the mass and the speed of the particle, it represents the combined effect of mass and the speed of any particle, and the momentum of any particle is expressed in Kg m/s unit.
As given in the problem a 115 kg lineman is working on tackling drills. if he is running at 2.8 m/s and hits a tackling dummy with a mass of 55 kg ,
By using the conservation of the momentum,
Momentum before the collision = momentum after the collision
The momentum of the tackling dummy = m × v
= 2.8 × 115
=322 kg-m/s
Thus, the momentum of the tackling dummy would be 322 kg-m/s.
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a parallel-plate capacitor is formed from two 4.0 cm x 4.0 cm electrodes spaced 2.0 mm apart. the electric field strength inside the capacitor is 1.0 x 106 n/c. what is the charge (in nc) on each electrode?
Equation Q/A = E Electric Field within a parallel plate capacitor
∴ Q = E*Aε
E = 10^6 N/C
A = 4*4 = 16cm^2 = 16 * 10^-4 m^2
ε = 8.852 * 10^-12 F/m
Q = +/- 10^6 * 16 * 10^-4 * 8.852 * 10^-12
= +/- 141.6 * 10^-10 C
= +/- 14.2 nC
You can think of an electric field as a physical field that surrounds all charged particles and pulls on them all.
Before the dielectric breaks down, a parallel plate capacitor can only hold a certain amount of energy. It can be stated as follows: The parallel plate capacitor is a device that uses two parallel plates connected across a battery to create an electric field between them.
A nonmetallic component of a circuit is made in touch with using an electrode, an electrical conductor. Depending on the type of battery, electrodes are a crucial component that can be made of a range of materials.
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The focal point is the point through which parallel incident rays reflecting off the surface of a concave mirror converge. Is this true or false?
When a beam of rays that are parallel to the principal axis is incident on a concave mirror converges at the focal point.
But, if any other set of parallel rays that are not parallel to the principal axis is incident on a concave mirror they will not converge at the focal point. They will converge at a distance of focal length, but not on the focal point.
Thus the given statement is not true.
A frog leaps from flat ground at 6.32 m/s
at a 36.3 angle. What maximum height
does it reach?
(Unit = s)
At hmax, Vy=0
vy=v0y-gt
0=6.32sin(36.3)-9.81t
t=.381 seconds
Δy=v0yt-.5gt^2
Δy=6.32sin(36.3)*.381-.5(9.81)(.381)^2
maximum height=.714 m
an athlete lifts a 350 n set of weights from ground level to a position over her head, a vertical distance of 1.90 m. how much work (in j) does the athlete do? assume the weights are moved at constant speed.
Work is measured in joules or newton-meters
It may be thought of as force * distance
If there were acceleration in this problem, the force would be more than the weight, but because the speed is constant force = weight.
given,
force= 350N
Distance= 2m
work= ?
Work = Force * Distance
= 2m * 350 N
= 700 j or 700 N*M
If you're looking at this from an energy standpoint, you can just consider the final PE as the energy required because there is no KE at the end. so,
PE = m*g*h
and m*g = 350N
h= 2m
PE = 700j or 700 N*M
Hence, the 700N*M work is done by athlete.
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If 2 balls of the same size and different masses roll down a ramp, which ball would be faster; the bigger mass or the smaller mass
Answer:
The bigger mass
Explanation:
This can be explained using F=ma
Let's say the acceleration is same on both balls 10m/s2 however we have different masses.
Pretend small mass ball is 0.5 kg and big mass is 1kg.
10 x 0.5 =5
10 X 1 =10
10 is bigger than 5
1. on the planet arrakis a male ornithoid is flying toward his mate at 25.0 m/s while singing at a frequency of 1200 hz. if the stationary female hears a tone of 1240 hz, what is the speed of sound in the atmosphere of arrakis?
If the stationary female hears a tone of 1240 hertz, then the speed of the sound in the atmosphere of arrakis will be 775 meter per second.
The term "Ducler shift" refers to the apparent change in frequency caused by the source moving closer to the observer or by the relative motion between the source and the object. The formula: true frequency over 1 minus v s over v gives the observed frequency. Let's call this equation 1, shall we? The real frequency in our case is stated as 1200 hertz, but the perceived frequency is reported as 1240 hertz. It is stated that the source's velocity, vs, is 25.0 meters per second. Rearranging equation 1 yields the result that the real frequency over the absorbed is equal to 1 minus b s over v.
As a result, we can be represented as v s over 1 minus f, actual over f absorbed now 1 substituting the values we get 25.0 meter per and over 1 minus 1200 hertz over 1240 hertz. Frequency fur, the rearranging we get 1 minus f real over f absorbed, is equal to v s over v. The sound travels at a speed of 775 meters per second after further calculation.
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describe how two objects can have the same speed but different velocities
Two objects can have the same speed but different velocities. The detailed description is given below.
We can take two escalators to explain the concept. The two escalators are moving up at a speed of 10 m/s. In this case, the two escalators have the same speed and they are moving in the same direction. So, they have the same velocity also.
Now one escalator is moving up at a speed of 10 m/s and the other escalator moving down at a speed of 10 m/s. In this case, both escalators move at 10 m/s, so their speed is the same. But they are not moving in the same direction. Hence their velocity is not the same. One has 10 m/s downwards and the other one has 10 m/s upwards velocity.
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the suspended 2.37 kg mass on the right is moving up, the 1.3 kg mass slides down the ramp, and the suspended 7.8 kg mass on the left is moving down. there is friction between the block and the ramp. the acceleration of gravity is 9.8 m/s 2 . the pulleys are massless and frictionless
In this, two frictionless, smooth inclined surfaces that have the same angle with the horizontal (57.7°) are connected to one another. Blocks are placed on the inclined surfaces.
The left one is white, whereas the right one is black. Then, a frictionless pulley is present here at the edge, and the two blocks are attached to one another using a light string weight made of the white blocks. Assume there are lots of M W. Its weight will therefore be M W G. The black block's weight. M. B. G. Component Here would be that.
This will also be 57.7 degrees if the angle is 57.7. Additionally, this component is M W G, costs 57.7 degrees, and runs horizontally. That is 57.7° M W G Sign. Next, the element perpendicular to this inclination surface for this black block. This part is B G Costs 57.7° and a component along the spring-bound incline of mbG sign 57.7° The blocks are shown to be travelling with an acceleration of A in the direction of the left.
Given to us are MB square markings traveling at 1.5 meters per second. The bulk of this white blog weighs 3.19 kilograms. It is absent. We need to locate it. First, as the white vlog is moving down, use the free body diagram of the white block. Therefore, M W G sign 57.7 degrees force will be more than that tension T for this white block. Thus, using Newton's second rule of motion, the net force will be equal to.
The block's mass times its acceleration equals the block's net force. Using a free body schematic of the ascending black bloc, continue. T will therefore be more for it. Therefore, this equals p – Mbg. indication of 57.7 degrees. Using Newton's second rule of motion, which is equal to M B A, once more This is equation #1, that was equation #1, this is equation #2, this is one, and this is equation #3. hence, adding 1 and 2. It is obvious that the tension will end and that G signed 57.7° will be seen as an exit signal.
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You are designing another dolly-sandbag system for a different actor in the performance. The mass of the dolly and actor combined is 76 kg, and the mass of the sandbag is 18 kg. The coefficient of kinetic friction between the dolly and the stage floor is 0.20. What is the acceleration?
Answer: 0.30 m/s^2
Explanation:
[tex](9.8m/s^{2} )[/tex] · [tex]\frac{(18kg)-0.20(76kg)}{(76kg)+(18kg)}[/tex]
The acceleration of the dolly-sandbag system is 0.29 m/s².
What is force?The definition of force in physics is: The push or pull on a massed object changes its velocity. An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.
A spring balance can be used to calculate the Force. The Newton is the SI unit of force.
Given parameters:
The mass of the dolly and actor combined is: M = 76 kg
the mass of the sandbag is: m = 18 kg.
The coefficient of kinetic friction between the dolly and the stage floor is 0.20.
Let the acceleration is a.
Hence, From Newton's 2nd law of motion, we can write that:
ΣF = (m+M) a
mg - μMg = (m+M) a
a = g (m- μM)/ (m+M)
= 9.8 ( 18 - 0.20×76)/(18+76)
= 0.29 m/s².
Hence, the acceleration of the dolly-sandbag system is 0.29 m/s².
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.A drawing pin is pressed into the notice board. The pointed pin area is 0.25 mm² and the force exerted on the pin is 10 newtons. Compute the pressure.
The pressure exerted is 4 × 10⁷ N/m²
Pressure is the force carried out perpendicular to the surface of an item in step with the unit vicinity over which that force is sent. Gauge pressure is the pressure relative to the ambient strain. numerous units are used for the explicit strain.
Strain is a pressure carried out perpendicular to the surface of an item in keeping with unit location. Mathematically it is P = F/A, in which P is strain, F is force, and A is area. strain is a scalar amount, one that most effectively has value and no directional vector characteristics.
Calculation:-
Given,
area = 0.25 mm2
= 2.5 × 10⁻⁷ m²
Force = 10 N
Pressure = force/area
= 10 / 2.5 × 10⁻⁷
= 4 × 10⁷ N/m²
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A dart shot at a monkey is traveling 10 m/s horizontally, while simultaneously traveling 7 m/s downward. At what angle below the horizontal is the dart traveling? Answer in degrees
The angle below the horizontal the dart shot at 10 m/s horizontally and 7 m/s downward is 55°
In a right angled triangle,
tan θ = Opposite side / Adjacent side
Here the resultant velocity, horizontal and vertical components makes a right angled triangle.
Opposite side = Horizontal component = 10 m / s
Adjacent side = Vertical component = 7 m / s
tan θ = 10 / 7
tan θ = 1.43
θ = [tex]tan^{-1}[/tex] ( 1.43 )
θ = 55°
The formula used to solve the problem is a trigonometric ratio. Trigonometric ratios are applicable only on a right angled triangle. Some of the basic trigonometric ratios are:
sin θ = Opposite side / Hypotenusecos θ = Adjacent side / HypotenuseTherefore, the angle below the horizontal, the dart is traveling is 55°
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A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, what is its instantaneous acceleration?.
A mass on the end of a spring undergoes simple harmonic motion. At the instant when the mass is at its equilibrium position, its instantaneous acceleration is zero
When the restoring force is proportionate to the displacement but acting in the opposite direction, an oscillating mass moves in a manner known as harmonic motion. The sine wave has a constant frequency and amplitude and can be used to describe harmonic motion because it is periodic. The motion of a weight on a spring is an illustration of this.
Simple Harmonic Motion, also known as SHM, is a motion in which the restoring force is inversely correlated with the body's deviation from its mean position. A particle moving in simple harmonic motion experiences acceleration given by the formula a(t) = − 2 x (t). The particle's angular velocity is given in this equation as.
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Jack and Jill carry a bag of bricks to the top of the hill to mend the well. If the bricks weigh 50 N and the hill is
30 m, how much work do they do between them?
Answer:
1500 J
Explanation:
Work = force * distance = 50 N * 30 M = 1500 J
the current in a single-loop circuit with one resistor r is 8.400 a. when an additional resistor of 9.00 ω is inserted in series with the existing resistance, the current drops to 6.384 a. what is r in ohms?
The initial resistance of one resistor r in ohms in series combination is 28.5 Ω.
The resistance depends on the used combination. The resistor combination can be combined in 2 ways which are series combination and parallel. In series combination, the resistance will be added up for each resistor. It can be written as
R = R1 + R2
where R is total resistance, R1 and R2 are the series combination of resistors.
From the question above, the given parameters are
R2 = 9 Ω
I1 = 8.4 A
I2 = 6.384 A
Hence, the current ratio of the initial and final condition is
I1 / I2 = V /R1 / V/(R1 + R2)
8.4 / 6.384 = (R1+R2) / R1
8.4 R1 = 6.384 R1 + 57.456
2.016R1 = 57.456
R1 = 28.5 Ω
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a conductor consists of an infinite number of adjacent wires, each infinitely long and carrying a current i (whose direction is out-ofthe-page), thus forming a conducting plane.
If there are n wires per unit length, magnitude of B measure at A or C is B = Ωo*n*I/2
A key concept in science is the concept of magnitude in physics. The general quantity or distance is referred to as magnitude. When it comes to the elements of movement, we can tie magnitude to an object's size and motion speed.
A particular object's magnitude is determined by its size or quantity. For instance, when it comes to speed, if a car is moving at a quicker rate than a nearby motorcycle, the magnitude of the automobile's speed is greater than the speed of the motorcycle. Although they contain directions as well as magnitude, vector quantities. Vector quantities include things like force, acceleration, speed, velocity, and many others. A vector's absolute value is referred to as its magnitude.
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A ship is at a location of 40° S 77° W. Which type of surface ocean current and tectonic plate boundary are located beneath this ship?
Cool ocean current and a convergent boundary
An ocean current is a continuous flow of water in an oceanic direction; this implies that the water is not the same water, but that it is exchanged within the current at a comparable rate and direction. Temperature and water salinity are only two examples of the elements that influence currents. A continuous, directed flow of ocean water is known as an ocean current, and it is caused by a variety of factors acting on the water, such as wind, the Coriolis effect, breaking waves, cabeling, and variations in temperature and salinity.
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A trumpet plays middle C (262 Hz). How fast would it have to be moving to raise the pitch to C sharp (277 Hz)? Use 343 m/s as the speed of sound.
The trumpet would have to be moving at a speed of approximately 345.8 m/s to raise the pitch to C sharp.
What is speed?
In everyday language and kinematics, an object's speed (typically abbreviated as "v") is defined as the size of the change in position that occurs over time or the amount of change that occurs per period of time; it therefore a vector quantity. The instantaneous speed is the upper limit of the average speed as the time interval's duration gets closer to zero; it is calculated by dividing the distance travelled by the time interval's duration. Speed and velocity are distinct concepts.
Speed is measured as distance divided by time.
To raise the pitch of a note by one semitone, the speed of sound must be increased by approximately 6%. In this case, the trumpet would have to be moving at approximately 364 m/s to raise the pitch to C sharp.
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how does Newton's third law describe the force affecting a rocket as it descends to
Answer:
Explanation:
Newton's Third Law states that "every action has an equal and opposite reaction". In a rocket, burning fuel creates a push on the front of the rocket pushing it forward. This creates an equal and opposite push on the exhaust gas backwards.
inner parts of the flattening cloud begin to fall freely inward, raining down on growing object at the center. gravitational potential energy of collapsing gas cloud is converted into heat and radiative energy.
These 2 statements are 2 steps of solar planet formation 1st statement is 3rd step 2nd statement is 4th step.
In the cosmos, there are a lot of planetary systems with solar planets around a host star, similar to our own. Because we refer to things that are connected to our star as "solar," our planetary system is sometimes known as "the solar system," after the Latin word for the Sun, "solis." The Sun, our star, and everything gravitationally connected to it, including the moons, planets, and dwarf planets like Pluto, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, make up our solar system. Thousands of planetary systems orbiting other stars in the Milky Way have been found, in addition to our solar system. The Milky Way galaxy's outer spiral arm is where our solar system is situated. In our solar system, there is only the Sun.
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calculate the magnitude of the force, in newtons, exerted by a 0.115-mg chip of paint that strikes (and sticks to) a spacecraft window at a relative speed of 3.95 × 103 m/s, given the collision lasts 5.95 × 10– 8 s.
Paint chip impacting a spaceship window with a force of 6.67×103 N using a 0.100-mg mass.
Any action that seeks to preserve, modify, or deform a body's motion is considered to be a force in mechanics. Usually, Isaac Newton's three laws of motion from his Principia Mathematica are used to describe the concept of force (1687). A body at rest or moving uniformly in a straight path will stay in that state unless a force is applied to it, according to Newton's first law. According to the second law, any external force that interacts with a body causes it to accelerate (change its velocity) in the force's direction. A vector quantity, force is one that has both magnitude and direction. The rate at which an item changes its velocity is known as the vector quantity known as acceleration. When an object's velocity changes, it is said to be accelerating. On occasion, sports broadcasters will suggest that a person is accelerating if they are travelling quickly. Acceleration, however, has little to do with speed. Even though a person is travelling quickly, they may not be accelerating. A change in an object's speed is referred to as acceleration. An object is not accelerating if it is not changing its velocity.
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Among elements 1 to 18, which element or elements have the smallest effective nuclear charge?.
As we walk across a period from left to right, the effective nuclear charge rises, whereas it falls as we move down the group. The element with the lowest effective nuclear charge will be found on the left side of the periodic table. The periodic table's group 1 includes H, Li, and Na.
Which nuclear charge has a greater impact?A fluorine atom's nucleus has a charge Z of 9, but the valence electrons are mostly screened by the core electrons—four electrons from the 1s and 2s orbitals—and to a lesser extent by the 7 electrons in the 2p orbitals. The cation of sodium thus has the highest effective nuclear charge.
In spite of being in the same period as sodium and phosphorus, chlorine has the most protons in its shell (the most inside the same period), giving it the highest effective nuclear charge.
The amount of shielding electrons may be calculated by deducting the amount of valence electrons from the overall number of electrons in the atom or ion.
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a stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.88 103 m. during this performance the pilot whose weight is 845 n, maintains a constant speed of 2.25 102 m/s.
We calculated that the pilot's apparent weight at the maximum point was 3 70.5 Newton. Additionally, the circular portion's lowest point is equal to 1598.5 Newton.
A stunt pilot performing a loop during an airshow has been described to us. the vertical circle's loop. During his performance, he gives us the radius of the circle as 3.08 into 10 to the power three m.
We are provided the weight of the pilot, which is 614. For one second, Newton maintains a speed of 2.2 into tend to the bar at a distance of 2 m. We need to know the pilot's apparent weight in newtons while he is at the highest point of the loop. Now, the formula for the pilot's mass can be expressed as being equal to the pilot's weight divided by the acceleration caused by gravity. adding the values together results in 614. too unexplored by exploration.
You get the mass of the pilot, which is 62.65 kgs Hill, when you add gravity. The apparent weight of the pilot will be equal to the normal force generated by the airplane seat. At this point, we may use the formula M to determine the apparent weight off the pilot at the highest point in the circular journey. N in this case stands for the pilot's apparent weight. We find the apparent weight of Mars to be 62.65 kgs multiplied by velocity, which is 2.2 and 2 10 to the part two m for a second, by adding the pilot's speed and the circular portion's radius, r. entire square.
The normal force of the seat on the pilot will be zero since the apparent weight of the pilot at his or her highest point throughout the circle in the case of weightlessness is Newton. With the numbers we have divided by Mars being She took 165 and shoes as replacements, we get the speed of the pilot at weightlessness state equal to 173.7 meters per second. As a result, its speed at this point will be equal to root of wait, multiplied by Baridis divided by mass.
Now your parent wait of the pilot at the lowest point can we given us Baron, well being equal to and we square r plus right, substituting the values, we have 62.65 Kgs to point to entertain the part to the whole square divided by yes, 614. Newton solving which we get the apparent weight of the pilot, the lowest point equal to 1598 0.5. Newton which is the apparent weight of the pilot at the lowest point of the circular what therefore Therefore we determined the apparent weight of the pilot at the highest point being equal to 3 70.5 Newton. And at the lowest point of the circular part being equal to 1598.5 Newton.
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Convection, conduction, or radiation??
Answer: Conduction
Explanation: Radiation is the receiving of heat via waves from the air, Convection is the transfer via liquids. Conduction is the transfer of heat between two solids.
Five ramps lead from the ground to the second floor of a workshop, as sketched below. All five ramps have the same height; ramps B, C, D and E have the same length; ramp A is longer than the other four. You need to push a heavy cart up to the second floor and you may choose any one of the five ramps. Assuming no frictional forces on the cart, which ramp would require you to do the least work?
1. Same work for ramps B, C, D or E; more work for ramp A.
2. Same work for the straight ramps A and B; less work for ramps C, D, and E.
3. Ramp D.
4. Ramp E.
5. Ramp B.
6. Ramp A.
7. Ramp C.
8. Same work for all five ramps.
9. Unable to determine without knowing the exact profiles of ramps C, D or E.
By assuming no frictional forces on the cart, Same work for all five ramps would require you to do the least work.
What exactly is a frictional force?The force produced by two surfaces coming into contact and sliding against one another is referred to as frictional force. The following variables impact the frictional force, Surface roughness and the amount of force pressing them together have the biggest an impact on these forces.
What is work-energy theory and how is it supported?According to the work energy theorem, the net change in a body's energy is equal to the work that is done on it. K.E. or P.E. Proof: Consider a mass'm' object travelling at a 'u' starting velocity. Allow a body to vary its velocity to v in response to a constant force, F.
Let h be the height of the ramps. Since there is no friction, we can use the
work-energy theorem.
Wtot = Wperson + Wgravity = ∆K
Hence for all the ramps,
Wperson = −Wgravity + ∆K = mgh + ∆K
In particular, if ∆K = 0 (the cart starts from rest and ends at rest),
Wperson = mgh, for all the ramps.
So, the Same work for all five ramps.
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Exercise write the peice wise
function {h(x) x
r(x) a<=x
K(x) x>=b} in terms
Of one function
A piecewise-defined function in mathematics is one that is composed of several smaller functions, each of which has a certain interval of the domain it applies to. Instead of being a property of the function itself, piecewise definition is a means to express the function.
In terms of r(x),
r(x) <= x when x >= b
A function that is defined by many sub-functions, each of which applies to a specific interval of the main function's domain, is referred to as a piecewise-defined function in mathematics (also known as a piecewise function or a hybrid function) (a sub-domain).
When an input value passes specific "boundaries," a rule or relationship changes. In these cases, we employ piecewise functions to explain the situation.
For instance, it happens frequently in business that the price per piece of a particular item gets decreased after the quantity bought exceeds a certain threshold.
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