Light bends around the obstacles like the waves and this bend cause the diffraction pattern. single slit shows a diffraction pattern because of the path length difference from waves originating at different parts of the slit.
The double-slit experiment demonstrates that mild and remember can show traits of each classically described wave and debris; moreover, it presents the fundamentally probabilistic nature of quantum.
Mechanical phenomena. young's authentic double-slit experiments have been in fact the primary to illustrate the phenomenon of interference. when he shone mildly via two slender slits and determined the sample created on the display screen, the younger did not locate brilliant regions similar to the slits, however as an alternative noticed vivid and darkish fringes.
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A 2.0 kg piece of metal flying at -1.0 m/s hits a windshield of a 200.0 kg object at 15.00 m/s. They collide and stick together. What is the total momentum before the collision?
The total momentum before the collision is -2.0kgm/s.
What is momentum?
This can be defined as the product of the mass and velocity of an object.
what is the formula for calculation momentum?
momentum Ρ= mass*velocity
=m*v
Given in the equation:
m₁=2.0kg
v₁=-1.0m/s
Calculating the first momentum i.e momentum before collision:
Ρ₁=m₁*v₁
=2.0kg*-1.0m/s
Ρ₁ =-2.0kgm/s
Given in the equation:
m₂=200.0kg
v₂=15.00m/s
Calculating the second momentum:
Ρ₂=m₂*v₂
=200.0kg*15.00m/s
=3,000kgm/S.
Hence the total momentum before the collision will be the first momentum i.e Ρ₁ =-2.0kgm/s
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Answer:
-2.0kgm/s
Explanation:
The other guy said so
a rocket takes off from earth and reaches a speed of 130 m/s in 19.0 s. if the exhaust speed is 1,200 m/s and the mass of fuel burned is 150 kg, what was the initial mass (in kg, including the initial fuel) of the rocket?
The initial mass of the rocket will be 526.2 kg
As we know,
Final speed = 105 m/s
Time = 18.0 s
Exhaust initial speed = 1200 m/s
Mass of burned fuel = 150 kg
We need to calculate the initial mass Which would be 526.2 kg.
What do you mean by Initial and final mass?
The mass of an object at the starting point is known as initial mass while the mass which remains at the last is called Final mass. The Initial Mass Function (IMF) is usually expressed as a power law,
IMF = constant × m −α.
Hence, in the above case we have found the initial mass from the given formula.
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gravity on the moon is 1.6 m/s2. what is the gravitational potential energy of a 1200-kg lander resting on top of a 350-m hill? j
The energy that an object has due to its location in a gravitational field is known as gravitational potential energy. GPE = mgh is the formula for gravitational potential energy. GPE = 1200(1.6)(350) = 672000 J
What is the source of gravitational potential energy?If an object is located at a height that is higher (or lower) than the zero height, it has gravitational potential energy. If an object is situated on an elastic media in a position other than the equilibrium position, it has elastic potential energy.
How is the energy of gravitational potential stored?By utilizing a pump, crane, or engine to raise a mass to a specific height, gravity batteries can store gravitational potential energy. Depending on the mass of the object and also how high it was lifted, the mass now retains a specific gravitational potential energy after being raised.
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an archer shoots a bow horizontally from the same height as the target's bull's-eye, located 25.2 m away. the bow is shot with a speed of 76.9 m/s. how far below the center of the bull's-eye does the arrow hit the target?
The calculated value is a = 16.24°. If the initial speed is the same, launch angles closer to 45° 45° 45° give a longer maximum horizontal distance (range).
These launches have a better balance of the initial velocity components that optimize the horizontal velocity and time in the air. The black dots represent measurements, such as the estimated 3D locations of the object based on the 2D images, while the bullseye represents the true value, such as the true location of the object. Let a be the projectile's angle.
37 sin a° is the vertical component.
Vertical component: 37 cos °
Time to achieve peak height equals (37 sin a°)/9.8
[2(37 sin a°)/9.8](37cos a°)(horizontal travel) = 75
75*9.8/37*37 = 2sin a° + cos a°
sin 2a° = 0.537
2a° = 32.47°
a = 16.24°
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A cheetah has a mass of 60 kg. It produces a force of 480 n between its feet and the ground. What is its acceleration?.
A cheetah with a mass of 60 kg and a force of 480 N accelerates at a rate of 8 m/s2.
The acceleration of an object is equal to the net force exerted on it divided by its mass, or a = F m, in accordance with Newton's second rule of motion. The force applied divided by the mass of the item yields the acceleration of a moving body. the following:
Mass Force (N) Acceleration (m/s2) (kg)
In response to your inquiry, a cheetah weighs 60 kg and exerts 480 N of force.
Acceleration = 480 x 60
Acceleration equals 8m/s2.
Therefore, the cheetah's acceleration for a mass of 60 kg and a force of 480 N equals 8 m/s2.
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The right answer is "8 m/s²"
Answer explanation:
Acceleration = force / mass
= 480 N / 60 kg
= 8 m/s2
Hope it helps✨✨
how close were your wavelength measurements to the accepted values of wavelengths for the various gases as listed below? what factors do you think might have contributed to any differences, and how might they have affected your measurements?
The accepted values of wavelengths for Hydrogen is a simple atom with a simple spectrum. Besides the three lines we may be able to see in 410 nm.
Gamma rays have incredibly short wavelengths that are only a small percentage of the size of atoms, but other wavelengths can extend as far as the cosmos, despite the fact that the relationship between wave frequency and wavelength is inverse. Although it is not often stated explicitly, electromagnetic radiation wavelengths are frequently represented in terms of the vacuum wavelength, regardless of the medium they pass through.
Electromagnetic radiation's behavior is influenced by its wavelength. Wavelength times frequency equals the speed of light. Energy is obtained by multiplying frequency by the Planck constant. The wave number in centimeters is 1/wavelength. A rough estimate of the wavelength size is shown along with the wavelengths of various regions of the electromagnetic spectrum.
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a stone is dropped from the top of a high cliff with zero initial velocity. in which system is the net momentum zero as the stone falls freely? 1. the stone and the earth 2. none of these 3. the stone itself 4. the stone and the person who drops it
The system with stone and the earth , result to net momentum zero as the stone falls freely.
A stone is thrown down from a high cliff's edge. If the stone and Earth are the only components of the system, then the stone's initial momentum is zero and it does not experience any external forces as it descends. As the stone falls, the system's momentum is zero.
What is linear momentum?
According to the conservation of initial momentum principle, the sum of the initial and final momentums is equal.
m₁u₁ ₊ m₂u₂ = m₁u₁ ₊ m₂u₂
A system made up of a linear system of earth and stone may have zero net momentum.
Therefore, a system of stone and earth can result to a net zero momentum.
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The system with stone and the earth , result to net momentum zero as the stone falls freely.
What is linear momentum?
According to the conservation of initial momentum principle, the sum of the initial and final momentums is equal.
m₁u₁ ₊ m₂u₂ = m₁u₁ ₊ m₂u₂
A stone is thrown down from a high cliff's edge. If the stone and Earth are the only components of the system, then the stone's initial momentum is zero and it does not experience any external forces as it descends. As the stone falls, the system's momentum is zero. A system made up of a linear system of earth and stone may have zero net momentum.
Therefore, a system of stone and earth can result to a net zero momentum.
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What does "jettison" mean? Why are parts of the spacecraft jettisoned?
Answer: 1. throw or drop (something) from an aircraft or ship
2.to ensure mission success just in case the first one fails.
Explanation:
The ladder shown is 3.0 m long and the coefficient of static friction between the floor and ladder is 0.50. There is no friction between the wall and the ladder. What is the minimum angle (in degrees) that the ladder can make with the floor without slipping?
This is a static equilibrium problem. The sum of the torques equals zero, the sum of the forces along x equals zero, and the sum of the forces along y equals zero. Use the point where the ladder contacts the ground as the axis of rotation. At the minimum angle, you're getting the maximum possible value of static
45° s the minimum angle (in degrees) that the ladder can make with the floor without slipping defying friction.
F=μmg
" Moment along the bottom of ladder "
[tex]0.5 Lmg cos \theta=LF_wsin \theta[/tex]
[tex]0.5 Lmg cos \theta=L \mu mg sin \theta[/tex]
[tex]0.5 cos \theta=mu sin \theta[/tex]
[tex]\theta=tan^-1(0.5 )/(\mu)[/tex]
Θ= 45°
Physical friction is all around us. Static friction is the resistance to an object moving along a route. Finally, explain it with a simple example. Consider the common activity we all engage in: walking. While working, we are continuously in contact with the floor. As we advance our feet, motion pushes on the earth as we travel backward.
The fact that friction operates in the opposite direction from relative motion is one important aspect to be aware of in order to decrease friction. This phenomenon might be helpful for slowing down the action until it eventually stops.
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if a proton moves from point 1 to point 2 on an isoline with the same voltage, how much work is done
There is no net work done because of absence in any difference between the potentials.
What is work done to shift a proton?The potential difference between two points in a circuit equals the amount of work done in moving a unit charge from one point to another. If the two points are at the same potential, no NET work is done to move the test charge from one point to another. Some parts of the path may have had positive work done, while other parts of the path may have had negative work done.
Work done = Charge × change in potential
W = q × ΔV
q = 1.6 × 10⁻¹⁹ C
ΔV = 0
W = 1.6 × 10⁻¹⁹ × 0
W = 0
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Which of the following potential problems with question wording have been identified by cognitive psychologists? (Check all that apply.) a) unfamiliar technical terms
b) vague or imprecise terms
c) ungrammatical sentence structure
d) phrasing that overloads working memory
e) embedding the question with misleading information
Option d) phrasing that overloads working memory, potential problems with question-wording have been identified by cognitive psychologists.
Cognitive psychology is the look at mental procedures, along with memory, attention, belief, and language processing, and the way they affect human behavior. Cognitive psychologists expand strategies to assist folks that are experiencing difficulties with one or more of those processes.
Cognitive psychologists normally earn either a Ph. D as a doctor of Philosophy or a Psy. D as a medical doctor of Psychology in cognitive psychology. Similar to psychology coursework, they need education in studies techniques, statistics, neuroscience, and cognitive mastering.
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If a car collides with a moving bus, what type of relationship exists between the force of the car and the force of the bus?.
The correct answer is forces are equal but opposite in direction between car and bus.
What do we mean by Collision?
When two objects collide, forces of equal magnitude and opposite direction are applied to each object. Such pressures frequently result in one thing gaining momentum and gaining speed while the other object slows down (lose momentum).
The force applied to an object to cause an impact—a change in momentum—on it is referred to as the impact force, or momentum. Technically speaking, the Car and the bus would have exerted and felt the same amount of impact force in the event of a collision. Because every action has a corresponding and opposing response, according to Newton's third law.
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The reason that most seti programs choose to listen at microwave radio frequencies is that.
The reason that most SETI programs choose to listen at microwave radio frequencies is that microwaves are the most energy-efficient way to send information.
What is radio frequencies?Radio frequencies are used in transmitters, receivers, computers, televisions, mobile phones and other communication devices. Radio frequencies are also used in carrier current systems such as telephones and control circuits.In 2021 ARPANSA will publish the standard.Standards for limiting exposure to radio frequency fields - 100 kHz to 300 GHz. The ARPANSA RF standard specifies limits for human exposure to RF EMR in the frequency range 100 kHz to 300 GHz.Microwaves have a frequency range of 109 Hz (1 GHz) to 1000 GHz and corresponding wavelengths of 30 to 0.03 cm. Within this spectrum range there are many important communication system applications in both military and civilian settings.To learn more about radio frequencies from the given link :
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an 8.0-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface (see the figure). the bullet remains lodged in the block. the block moves into an ideal massless spring and compresses it by 8.7 cm. the spring constant of the spring is 2400 n/m. the initial velocity of the bullet is closest to
The velocity of the bullet is 1100 m/s.
When the bullet lodges into the block, as there is no net external force, the momentum of the system will be conserved. After that when the block + bullet system compresses the spring, the energy of the system remains conserved. The kinetic energy is conserved into the potential energy of the spring.
Velocity is the directional speed of an object in movement as an illustration of its price of the trade-in position as found from a particular frame of reference and as measured through a specific standard of time.
Calculation:-
Mass of block, M = 4 Kg
Mass of bullet, m = 8 g = 0.008 Kg
Compression in spring, x = 8.7cm = 0.087 m
Let's first solve the energy conservation,
K.E. = P.E.
(1/2)(M+m)V2 = (1/2)kx2
V2 = 2400*(0.087)2/(4+0.008)
V2 = 4.53
V = 2.13 m/s
Now, conserving the momentum,
mv = (M+m)*V
v = (4+0.008)*2.13/0.008
The velocity of the bullet, v = 1066.6 m/s
Rounding to the velocity as 1100 m/s
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A ball is pushed downhill with an initial velocity of 3. 0 m/s. The ball rolls down a hill with a constant acceleration of 1. 6 m/s2. The ball reaches the bottom of the hill in 6. 0 s. What is the ball's velocity at the bottom of the hill?.
The ball's velocity at the bottom of the hill is 12.6 m/s. The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity.
Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed. Additionally, it is inversely proportional to transit duration and proportionate to displacement. Its measurement is in meters per second (m/s). The velocity formula is shown below: V = s/t.
Where V is the end velocity, u the beginning velocity, a the acceleration, and t the duration,
We obtain the response by substituting the data. 12.6 m/s.
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A student builds an electromagnet using a battery, an iron nail. And some insulated wire. The wire is wrapped around the nail 50 times and then connected to the battery. What changes could the student make to increase the strength of the electromagnet?.
To enhance the strength of the electromagnet, the student must enlarge the nail, wrap additional wire around the nail, increase the voltage of the battery, and enlarge the nail.
How does an electromagnet work?An electromagnet's mechanics are not extremely sophisticated. Wrapping a piece of conductive wire, usually copper, around a metal object accomplishes the task.
Until electricity is applied, this looks to be nothing more than a jumbled collection of parts, much like Frankenstein's monster.
An electromagnet, on the other hand, does not need to be activated by a storm. A current is introduced and flows through the wire, which can be supplied by a battery or another power source.
Therefore, to enhance the strength of the electromagnet, the student must enlarge the nail, wrap additional wire around the nail, increase the voltage of the battery, and enlarge the nail.
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What is the mass of an object if it takes a net force of 1,022 N to accelerate at a rate of 24 m/s2?
find A, Fn, and Fg
42.58 kg is the mass of an object if it takes a net force of 1,022 N to accelerate at a rate of 24 m/s2
F=ma
F= force= 1,022 N
m= mass=?
a=acceleration=24 m/s2
F=ma
a=F/m
a= 1,022 N/24 m/s2
a=42.58 kg
In physics, mass is used to express inertia, a property common to all matter. In essence, it is the resistance of a mass of matter to changing its course or speed in response to the application of a force.
The more mass a body has, the less of a change an applied force makes. Using Planck's constant, the kilogram, the ISU's unit of mass, is equivalent to 6.62607015 1034 joule seconds (SI). One kilogram is multiplied by one square meter per second to yield one joule.
Since the second and the meter have already been defined in terms of other physical constants, the kilogram is determined by precise measurements of Planck's constant.
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What is the acceleration of a vehicle that
changes its velocity from 300 km/h to a dead
stop in 20 s ?
Answer in units of m/s
2
What is one idea why a relatively dense protogalactic cloud more likely to produce an elliptical galaxy than a spiral galaxy?.
The higher gas density forms stars more efficiently, so all the gas is converted into stars before a disk can form.
What is density ?Density is a measure of how much "stuff" is in a given space. For example, a block of the heavy element lead (Pb) is denser than the softer, lighter element gold (Au). Styrofoam blocks are less dense than bricks. Defined as mass per unit volume. Object density is one of the most important and easily measured physical properties. Density is commonly used to identify pure substances and to characterize and estimate the composition of various types of mixtures.The density of an object or substance can be calculated from the formula: Density in kilograms per cubic meter equals mass in kilograms divided by volume in cubic meters (p = m/v).To learn more about density from the given link :
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The velocity selector in in a mass spectrometer consists of a uniform magnetic field oriented at 90 degrees to a uniform electric field so that a charge particle entering the region perpendicular to both fields will experience an electric force and a magnetic force that are oppositely directed.
If the uniform magnetic field has a magnitude of 12.1 mT, then calculate the magnitude of the electric field that will cause a proton entering the velocity selector at 43.4 km/s to be undeflected. Give your answer in units of kV/m.
The magnitude of the electric field that will cause a proton to enter the velocity selector and to be undeflected is 0.525 kV/m.
When a proton enters a region with a uniform electric and magnetic field, the magnetic force and the electric force will affect the motion of the protons. The electric field is perpendicular to the velocity of a proton. The magnetic field is perpendicular to both the velocity of the proton and the electric field and has an opposite direction to the electric force. When the proton is undeflected it means the forces balance.
F electric = F magnetic
qE = qvB
E = vB
[tex]v = \frac{E}{B}[/tex]
v = velocity of the proton (m/s)E = the magnitude of the electric field (V/m)B = the magnitude of magnetic field (T)Parameter
B = 12.1 mT = 12.1 x 10-3 T = 1.21 x 10-2 Tv = 43.4 km/sConvert velocity to m/s
[tex]v = 43.4 \times \frac{1 \: km}{1 \: s} = 43.4 \times \frac{1,000 \: m}{1 \: s}[/tex]
v = 43.4 x 103 m/s
v = 4.34 x 104 m/s
Calculate the magnitude of the electric field
E = B x v
E = 1.21 x 10-2 x 4.34 x 104
E = 525.14 V/m
[tex]E = \frac{525.14}{1,000}[/tex]
E = 0.525 kV/m
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Which option is correct and explain why in detail?
The statement about the movement of the object that is true is that the object is at rest at position Y. Option D
What is the maximum height?Let us recall that the projectile is a kind of motion that involves making an object to move along a parabolic path. This parabolic path is a curved path. A typical example of the projectile motion is the is the image that have been shown in the question.
We can see that the path of the object as it s moving is curved through the points X, Y and Z. One thing that is worthy of note from the diagram s that the lowest point of the object is at point Z and the highest point of the object is at point Y.
Why we need the facts that are mentioned above in mind is that the projectile would have zero velocity at the highest point but would have the highest velocity at the lowest point of its motion.
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Ali and kris are driving to a city that is 120 miles from their house. They have already traveled 20 miles, and they are driving at a constant rate of 50 mi/h. Write a function that models their distance from home as a function of time. What is a reasonable domain for this situation?.
The remaining distance that would result from multiplying the speed by the time t will be added to the 20 miles that make up the total distance. The domain's response would be 0 t 2.
By distance, what do you mean?The distance or amount of between two objects, points, etc. The condition or fact of being far from another in space; distance. a straight line in space It would take too long to walk seven miles in one hour. A wide body of water encircled the ship.
What are length and distance?A segment's or a room's dimensions are examples of things that can be measured in terms of length. Distance is the separation between two things, like two cities and two points.
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A solar eclipse happens when…
A. the Moon’s shadow crosses Earth’s surface.
B. the Earth’s shadow crosses the Sun’s surface.
C. the Earth’s shadow crosses the Moon’s surface.
D. the Sun’s shadow crosses the Moon’s surface.
Answer:
A. the Moon's shadow crosses Earth's surface.
Explanation:
When the Moon orbits Earth, the Moon moves between the Sun and Earth. When this happens, the Moon blocks the light of the Sun from reaching Earth. This causes an eclipse of the Sun or a solar eclipse. During a solar eclipse, the Moon casts a shadow onto Earth.
Answer:
a) Moon’s shadow crosses Earth’s surface.
Explanation:
A solar eclipse happens when the Moon’s shadow crosses Earth’s surface. Hence, the option (a) is correct answer.
Assume that the light emitted by a hot filament or hot metal bar is made to pass through a low density gas, and the emergent light is then analyzed in a spectrometer; what kind of spectrum is seen in this case?.
we will see absorption line spectrum in this case.
We see Absorption lines usually as dark lines, or lines of reduced intensity, on a continuous spectrum. In this example when the light emitted by a hot filament or hot metal bar is made to pass through a low density gas, and the emergent light is then analyzed in a spectrometer, then we can see the absorption spectrum.
Dark line comes When electrons go from one energy level to another, the difference in those energy level is a specific value, and not a range of values. they will absorb the photons if they are transitioning upwards towards a higher energy, corresponding to the wavelength of light which has the specific amount of energy they need to ascend.
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A certain microwave ha a wavelength of. 032m. Calculate the frequency of the microwave
The frequency of microwave is 9.4 ×10⁹ Hz when it has wavelength of 0.032m.
What is wavelength?The distance between two identical points (adjacent crests) in adjacent cycles of a waveform signal as it moves through space or along a wire is known as its wavelength. In wireless systems, this length is commonly specified in meters (m), centimeters (cm), or millimetres (mm).
The relationship between wavelength and frequency is inverse, as shown by the equation.
c=λ⋅v
where,
λ - the wavelength of the wave
v - the frequency of the wave
c - the speed of light in a vacuum, approximately equal to 3⋅10⁸ms⁻¹
This demonstrates that low frequency waves have long wavelengths while high frequency waves have small wavelengths.
Since the wave's wavelength is relatively long, a high frequency is to be anticipated. Fill in your values in the aforementioned equation to find v.
c = λv
∴ v = c/λ
v = 3.10⁸ms⁻¹/ 0.032m
v = 9.4 ×10⁹ s⁻¹
v = 9.4 ×10⁹ Hz
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a 45.0-kg woman stands up in a 60.0-kg canoe 5.0 m long. she walks from a point 1.00 m from one end to a point 1.00 m from the other end. if you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process?
Answer:
Measure the CM from the left end of the canoe
M x = (45 * 1 + 2.5 * 60) M = 105
x = (45 + 150) / 105 = 1.86 m from left end
After she walks 3 m the CM is from the left end
M y = (45 * 4 + 60 * 2.5)
y = (45 * 4 + 60 * 2.5) / 105 = 3.14 m
The left end of the canoe has moved 1.28 m to left
(The CM cannot move without an external force)
Check:
She increases the CM by 45 (3 - 1.28) = 77.4
Canoe movement decreases the CM by 60 * 1.28 = 76.8
1.28 is close
Do you think that the seeds of gymnosperms would likely be dispersed by animals?
Seeds of gymnosperms likely are not dispersed by animals because they are not enclosed in a fruit as occurs with angiosperm seeds.
What are gymnosperms and angiosperms?
Gymnosperms and angiosperms are different taxonomic groups of seed plants, which have certain particular features such as the presence of fruits angiosperms, it being an adaptive advantage for the dispersion of seeds through animals.
Therefore, with this data, we can see that gymnosperms and angiosperms are different groups of seed plants and angiosperms are evolutionary are more adapted to disperse their seed through animals due to the presence of fruits.
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A 20 m long, uniform bridge of weight 100 kN is supported at each end by pillars, as shown. The pillars exert forces T₁ and T2 on the ends of the bridge. What are the values of T₁ and T2 when a van of weight 24 kN is on the bridge, 5 m from the left-hand pillar?
Answer
T1=68 kN
Explanation:
A 20 m long, uniform bridge of weight 100 kN is supported at each end by pillars, as shown. The pillars exert forces T₁ and T2 on the ends of the bridge. What are the values of T₁ and T2 when a van of weight 24 kN is on the bridge, 5 m from the left-hand pillar is T1=68 kN
What are the types of force ?Force can be defined as pushing or pulling of any object resulting from the object’s interaction or movement, without force the objects can not be moved, can be stopped or change the direction.
Force is a quantitative interaction between two physical bodies, means an object and its environment, there are different types of forces in nature.
If an object in its moving state will be either static or motion, the position of the object will only be changed if it is pushed or pulled and The external push or pull upon the object called as Force.
The contact force types are the force that occurs when we apply some effort on an object such as Spring Force, Applied Force, Air Resistance Force, Normal Force, Tension Force, Frictional Force
Non-Contact forces are another type of forces occur from a distance such as Electromagnetic Force, Gravitational Force, Nuclear Force
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what is the angular acceleration of the pencil when it makes an angle of 10.0 degrees with the vertical? express your answer numerically in radians per second squared to three significant figures. view available hint(s)
The angular acceleration of the pencil when it makes an angle of 10.0 degrees with the vertical is 2.553 rad/s² of every meter length of the pencil.
If the pencil is in the position 10.0 degrees with the vertical, the weight of the pencil in the middle of the pencil will go down. Look at the triangle, x is the distance to calculate the torque.
[tex]\frac{x}{\frac{1}{2} L} = sin \: 10^o[/tex]Newton's second law of rotation
∑τ = Iα
wx = Iα
[tex]w \frac{1}{2} L \: sin \: 10^o = \frac{1}{3} m L^2 \alpha[/tex]
[tex]mg \frac{1}{2} \: sin \: 10^o = \frac{1}{3} mL \alpha[/tex]
[tex]g \frac{1}{2} \: sin \: 10^o = \frac{1}{3} L \alpha[/tex]
[tex]\alpha = \frac{g \frac{1}{2} \: sin \: 10^o}{\frac{1}{3} L}[/tex]
[tex]\alpha = \frac{3 g \: sin \: 10^o}{2L}[/tex]
[tex]\alpha = \frac{3 \times 9.8 \times 0.1736}{2L}[/tex]
[tex]\alpha = \frac{2.553}{L}[/tex]
Because the length of pencil unknown
α = 2.553 rad/s² of every meter length of the pencil.
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How high would a skater need to start on a previous incline to make it up and around a loop that is 6.1meters high?
The skater need to start 7.525 meter high.
Let,
The skater need to start on a previous incline at height = h.
Mass of the skater = m
Given, height of the loop = 6.1 meter.
Radius of the loop; r = 6.1/2 meter = 3.05 meter.
Let to make it up and around a loop that is 6.1meters high, the man required minimum velocity v on the highest point of the loop.
So, centripetal force at highest point = weight of the man
⇒ mv²/r = mg
⇒ v = √(gr)
Then, potential energy of the skater at height h is = mgh.
And, minimum energy of the skater at the highest point of the loop is = potential energy + minimum kinetic energy.
= mg(2r) + 1/2 mv²
= 2mgr + 1/2 mgr
= 5/2 mgr
According to conservation of energy,
potential energy of the skater at height h = minimum energy of the skater at the highest point of the loop
⇒ mgh = 5/2 mgr
⇒ h = 5/2 r =( 5/2 )× 3.05 meter = 7.525 meter.
Hence, required height is 7.525 meter.
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