The distance of the pivot point from the center of mass of the object = 0.85 m
Oscillatory motionOscillatory motion is any motion that is repeated at the same time interval and through the same trajectory in its motion.
The simplest oscillatory motion is harmonic motion or simple harmonic motion (SHM).
The simple harmonic motion is a periodic motion that occurs at the same time interval.
We have,
Mass of point = 2.40 kg ⇒ m
Moment of inertia = 1.24 kgm² ⇒ I
Frequency = 0.640 Hz ⇒ f
Acceleration due to gravity = 9.8 m/s² ⇒ g
Now, find the angular velocity first,
ω = 2[tex]\pi[/tex]f
= 2[tex]\pi[/tex] (0.640)
= 4.0192 rad/s
So, the distance of the pivot point from the center of mass of the object is:
ω = [tex]\sqrt{\frac{mgd}{I} }[/tex]
4.0192 = [tex]\sqrt{\frac{(2.40)(9.8)(d)}{1.24} }[/tex]
d = (4.0192)² (1.24) / (2.40)(9.8)
= 20.0309211/23.52
= 0.85 m
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WILL MAKE BRAINLIEST:
A 100 kg object takes one MINUTE to travel 300 m east. It began travelling at 240 m/s and came to a stop (0 m/s) at the end. What was its acceleration?
240
0.8
-4
-2.4
Answer:
To find the acceleration of the object, we can use the formula: acceleration = (final velocity - initial velocity)/time.
Plugging in the given values, we get: acceleration = (0 m/s - 240 m/s)/1 minute.
Since 1 minute is equal to 60 seconds, we can convert the time to seconds to get: acceleration = (0 m/s - 240 m/s)/60 seconds.
Simplifying this equation gives us: acceleration = -4 m/s^2.
Therefore, the acceleration of the object is -4 m/s^2. The correct answer is therefore (-4).
types of eye defects and their corrections
Nearsightedness that makes distant objects appear blurry.
Farsightedness (also called hyperopia) which makes nearby objects appear blurry.
Astigmatism which can make near and far objects appear blurry or distorted.
On a loop the loop a ball of mass m starts from rest a distance 6 R above the table, where R is the radius of the loop. When the ball rolls without friction, at some instant it is right at the top of the loop, a distance of 2 R above the table. At this instant, with what force is it press ing against the track? 1. Zero 2. Because the ball is rolling, it can't exert a force on anything. 3. m g 4. The ball will not be in contact with the track at this point, since it does not have quite enough speed to reach it 5. 3 mg 6. 7m g 7. 2m g 8. 5 m g 9. 6 mg 10. 4 mg
The force with which it pressing against the track is F= r^(−2cr+4er³ ) .
By energy conservation:
[tex]\frac{1}{2}mv_a^2 + mgH = \frac{1}{2}mv_b^2 + mgh[/tex]
[tex]\frac{1}{2}m*0^2 + mg*6R = \frac{1}{2}mv_b^2 + mg*2R[/tex]
[tex]4gR = \frac{1}{2}v_b^2[/tex]
[tex]\sqrt{8gR }=v_b[/tex]
Now by force balance at the top point
[tex]mg + F_N = \frac{mv_b^2}{R}[/tex]
[tex]mg + F_N = \frac{m*8gR}{R}[/tex]
[tex]F_N = \frac{8mgR}{R} - mg[/tex]
[tex]F_N = 7 mg[/tex]
2. [tex]U =cr^2 - er^4[/tex]
Force and potential energy is related by the following equation
[tex]F = - \frac{dU}{dr}[/tex]
[tex]F = - \frac{d}{dr}cr^2 - er^4[/tex]
[tex]F = \hat r (- 2cr + 4er^3)[/tex].
Forces are influences that can change the movement of an object. A force can change the velocity of an object with mass accelerating it. Forces can also be described intuitively by pushing or pulling. A force has both magnitude and direction and is a vector quantity. The word force has a precise meaning.
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Of the first exoplanets found, most were detected by:
A) noting the drop in the star's light as the planet transits its disk.
B) imaging them with the HST in the infrared, where they are easier to stop.
C) noting the Doppler shifts of the star as the planet orbits it from side to side.
D) receiving radio transmissions from them, much like Jupiter emits.
E) detecting the oxygen in their atmospheres spectroscopically.
Of the first exoplanets found, most were detected by: C) noting the Doppler shifts of the star as the planet orbits it from side to side.
The first exoplanets were found in what way?Instead, the first extraterrestrial planets were found by tracking the star's movement. It's a tiny white lie that kids are taught that planets rotate around the sun. In fact, the entire solar system's mass center revolves around the sun and the planets.
What and when was the first planet discovered?Uranus was the first planet to be found by the use of a telescope; it was identified as a planet in 1781 as a result of observations made using a telescope by Sir William Hershel (UK) and others. On March 13, 1781, Sir William Herschel performed the observations that proved Uranus was not a typical star.
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quantum tunneling is a phenomenon that occurs in quantum mechanics in which particles can pass through barriers that they classically would not be able to overcome. this is because in quantum mechanics, particles do not have a definite position or momentum, but rather exist as a w
When a particle may pass through a potential energy barrier with an energy greater than its kinetic energy, this process is known as tunnelling in quantum mechanics. This remarkable characteristic of tiny particles is crucial in the explanation of a number of scientific processes, including radioactive decay.
How does quantum tunnelling work?An atom or subatomic particle might appear on the other side of a barrier that should be impossible for it to cross due to a phenomena known as quantum tunnelling. It's as though you were out walking when you came across.
Because in this straightforward system, if a particle's energy is below the potential, it will always bounce back, and if it has a higher energy, it will always pass.
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a uniform sphere and a block are placed at rest at the top of a plane with inclination theta above the horizontal the sphere rolls down the plane without slipping and the block slides down the place it is found that tb - 15/7 ts where tb and ts are respectively the time it takes the block and the sphere to reach the bottom of the plane
The time it takes the block and the sphere to reach the bottom of the plane, uniform sphere and a block are placed at rest is 3 second
a=gsinθ1+K2R2
I=25MR2=MK2
K^2/R^2=2/5
θ=g×sin30∘1+25
a=5/7g×12
=57×9.8×12
=3.5m/s2
s=ut+12at2,
15.75=0+12×3.5×t2
t^2=15.75×23.5=9
t=3s
Time is described by physicists as the progression of events through the past, present, and future. A system is essentially timeless if it doesn't change. Time may be viewed as the fourth dimension of reality when describing events that occur in three-dimensional space. Time is something we cannot see, touch, or taste, but we can calculate how much of it has passed. Time is constant everywhere in classical mechanics. The timekeeping mechanisms continue to be accurate. Time is relative, however, as demonstrated by Einstein's special and general theories of relativity. It depends on the viewpoint of the observer. According to the theory of time dilation, intervals between events lengthen as one gets closer to the speed of light (dilates).
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a cylindrical capacitor has an inner conductor of radius 2.6 mmmm and an outer conductor of radius 4.0 mmmm. the two conductors are separated by vacuum, and the entire capacitor is 2.1 mm long.
The capacitance per unit is 1.292 X 10⁻¹⁰.
The radius of inner part of the conductor = r = 2.6 X 10⁻³ m
The radius of outer part of the conductor = R = 4 X 10⁻³ m
Length of the capacitor = l = 2.1 X 10⁻³ m
Capacitance is purely geometrical property. It depends only on length, radius of conductor.
From the formula of cylindrical capacitor,
= C = (2πεl) / ln(R/r)
where ε = 8.85 X 10⁻¹²
But we need capacitance per unit length so,
= C/l = (2πε) / ln(R/r)
= C/l = (2 X 3.14 X 8.85 X 10⁻¹²) / ln ( 4 X 10⁻³ / 2.6 X 10⁻³)
= C/l = 55.58 X 10⁻¹² / 0.43
= C/l = 1.292 X 10⁻¹⁰
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what is climate change?
What Is Climate Change?
Climate change refers to long-term shifts in temperatures and weather patterns. These shifts may be natural, such as through variations in the solar cycle. But since the 1800s, human activities have been the main driver of climate change, primarily due to burning fossil fuels like coal, oil and gas.
Burning fossil fuels generates greenhouse gas emissions that act like a blanket wrapped around the Earth, trapping the sun’s heat and raising temperatures.
Examples of greenhouse gas emissions that are causing climate change include carbon dioxide and methane. These come from using gasoline for driving a car or coal for heating a building, for example. Clearing land and forests can also release carbon dioxide. Landfills for garbage are a major source of methane emissions. Energy, industry, transport, buildings, agriculture and land use are among the main emitters.
The Earth is feeling the heat.
Greenhouse gas concentrations are at their highest levels in 2 million years
And emissions continue to rise. As a result, the Earth is now about 1.1°C warmer than it was in the late 1800s. The last decade (2011-2020) was the warmest on record.
Many people think climate change mainly means warmer temperatures. But temperature rise is only the beginning of the story. Because the Earth is a system, where everything is connected, changes in one area can influence changes in all others.
The consequences of climate change now include, among others, intense droughts, water scarcity, severe fires, rising sea levels, flooding, melting polar ice, catastrophic storms and declining biodiversity.
The Earth is asking for help.
People are experiencing climate change in diverse ways
Climate change can affect our health, ability to grow food, housing, safety and work. Some of us are already more vulnerable to climate impacts, such as people living in small island nations and other developing countries. Conditions like sea-level rise and saltwater intrusion have advanced to the point where whole communities have had to relocate, and protracted droughts are putting people at risk of famine. In the future, the number of “climate refugees” is expected to rise.
Every increase in global warming matters
In a series of UN reports, thousands of scientists and government reviewers agreed that limiting global temperature rise to no more than 1.5°C would help us avoid the worst climate impacts and maintain a livable climate. Yet policies currently in place point to a 2.8°C temperature rise by the end of the century.
The emissions that cause climate change come from every part of the world and affect everyone, but some countries produce much more than others. The 100 least-emitting countries generate 3 per cent of total emissions. The 10 countries with the largest emissions contribute 68 per cent. Everyone must take climate action, but people and countries creating more of the problem have a greater responsibility to act first.
Photocomposition: an image of the world globe looking worried to a thermometer with raising temperatures
We face a huge challenge but already know many solutions
Many climate change solutions can deliver economic benefits while improving our lives and protecting the environment. We also have global frameworks and agreements to guide progress, such as the Sustainable Development Goals, the UN Framework Convention on Climate Change and the Paris Agreement. Three broad categories of action are: cutting emissions, adapting to climate impacts and financing required adjustments.
Switching energy systems from fossil fuels to renewables like solar or wind will reduce the emissions driving climate change. But we have to start right now. While a growing coalition of countries is committing to net zero emissions by 2050, about half of emissions cuts must be in place by 2030 to keep warming below 1.5°C. Fossil fuel production must decline by roughly 6 per cent per year between 2020 and 2030.
Growing coalition
Adapting to climate consequences protects people, homes, businesses, livelihoods, infrastructure and natural ecosystems. It covers current impacts and those likely in the future. Adaptation will be required everywhere, but must be prioritized now for the most vulnerable people with the fewest resources to cope with climate hazards. The rate of return can be high. Early warning systems for disasters, for instance, save lives and property, and can deliver benefits up to 10 times the initial cost.
We can pay the bill now, or pay dearly in the future
Climate action requires significant financial investments by governments and businesses. But climate inaction is vastly more expensive. One critical step is for industrialized countries to fulfil their commitment to provide $100 billion a year to developing countries so they can adapt and move towards greener economies.
Climate finance
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a painter (of mass 81 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 22 kg directly over one of the bars (see figure). you can assume the plank is massless, and is long enough to reach to the other building.
a. If the bars are separated by a distance 1.2 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall?
0.325 m far from the bar on the the right can the painter walk before the plank starts to fall.
Calculation :
balancing the moment of forces about right bar
22kg * g* L = 81* g * L
d = (22/81)*L
d = (22/81)*1.2
d = 0.325 m
The word "force" has a precise meaning. At this level it is appropriate to describe the force as pushing or pulling. A force does not contain or "have within" an object. A force is applied from one object to another. The concept of force is not limited to living things and inanimate things
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a rectangular coil of n turns and of length a and width b is rotated at frequency f in a uniform magnetic field , as indicated in fig. 30-40. the coil is connected to co-rotating cylinders, against which metal brushes slide to make contact. (a) show that the emf induced in the coil is given (as a function of time t) by 2pfnabb sin(2pft) 0 sin(2pft).
ε = 2πfNabB sin2πft = εsin2πft this is the proved equation for the emf induced in the coil as a function of time t.
What does an EMF mean?Electromagnetic radiation-induced electric and magnetic forces. Researchers are examining whether the electromagnetic fields (EMFs) produced by electrical equipment, wireless and cellular cellphones, and power lines might result in cancer or other negative health effects. likewise known as electromagnetic field.
How to prove that emf induced in the coil as a function of time t ?Since, the coil of conducting wire is placed in a magnetic field,
number of turns = N
frequency = f
area = A
now, angular velocity of coil, ω = 2πf
in time t coil is rotated by θ angle, θ = ωt
Magnetic field through coil, φ = ΦB. dA = ΦB.dAcosθ
dA = area of N turns = NA
φ = NABcosθ
After putting value of θ, φ = NABcosωt
ε = dφ/dt
ε = d/dt×NABcosωt
= -NAB [-ωsinωt]
= NABωsinωt
ε = NAB2πft
area of rectangular coil, A = a×b
ε = Nab2πfsin2πft
sin2πft = 1, emf will be maximum
εmax = ε' = NabB2πf
ε = ε'sin2πft
ε = 2πfNabB sin2πft = εsin2πft
Hence proved that the emf induced in the coil is given as a function of time t.
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At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirror's radius of curvature is0.560m.
(a) Locate the image of a patient10.6m from the mirror. (Use the correct sign conventions.)
cm (from the mirror)
(b) Indicate whether the image is upright or inverted.
upright
inverted
(c) Determine the magnification of the image.
At an intersection of hospital hallways, a convex spherical mirror is mounted high on a wall to help people avoid collisions. The magnitude of the mirror's radius of curvature is0.560m. The image of a patient Located at -0.2877m. The image is an upright and a virtual image. The magnification of the image is 0.0271.
The image location can be calculate as follows:
The values of the image distance and focal length for a convex mirror are negative. using the mirror formula
1 = 1/u + 1/v
f u v
where,
f is the focal length = Radius of curvature/2 = 0.560/2 = 0.28m
u is the object distance = 10.6m
v is the position of the image
1 = 1 + 1
f u v
1 = 1 + 1
0.28 10.6m v
3.57 = 0.094 - 1/v
3.57 - 0.094 = -1/v
3.476 = -1/v
v = -1/3.476
v = -0.2877m
B) The fact that the image distance is negative indicates that the image is virtual and upright. Every upright image has a negative image distance.
C) Magnification: image/object distance
Magnification = 0.2877/10.6
Magnification= 0.0271.
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Two objects rest on a uniform surface. A person pushes both with equal force. If the first object starts to move faster than the second, what can be said about their masses?
Question 10 options:
The mass of the first object is less than that of the second object.
No inference can be made because mass and force are not related to each other.
The mass of the first object is equal to the mass of the second object.
The mass of the first object is greater than that of the second object
Answer: The mass of the first object is less than that of the second object.
Explanation:
ΣF = ma
a = ΣF/m
Thus, given two objects acted on by the same ΣF, a is inversely proportional to m. If a is larger, m must be smaller and vice-versa.
In an experiment, a student measured the volume of a substance while the mass was changed. The student measured up to five kilograms. The graph of the data is plotted below.
A volume versus mass graph is shown with mass on the vertical axes from 1 to 10 kilograms and volume on the horizontal axis from 1 to 5 milliliters. A line from the origin through all points and beyond.
Which of the following is an error the student made in creating an accurate graph?
The axes and graph are based only on measured values.
The axes are labeled with the incorrect variables.
The plotted points do not show all data collected.
The title has the incorrect order for the variables.
The graph is incorrect because; the title has the incorrect order for the variables. Option D
What is a graph?We know that a graph is made up of two parts. It has two axes and these are what we call the parts of the graph. It is common that we would have the independent variable on the x axis and then we have the dependent variable on the y axis.
With this said, we would now have to look at the graph that has been attached so that we can be able to see what the error in the graph that has been plotted as shown is and how the error that is in the graph can be able to be correct as the student is trying to pass information by the use of a graph system.
The title of the graph can be seen to show that the volume rather than the mass is plotted on the y axis.
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10. A 40 Kg crate (rubber chickens, perhaps?) is pulled across the ice with a rope. A force of 100 N is applied at an angle of 30 degrees with the horizontal to a rope attached to the crate, as shown above. Neglecting friction, calculate the acceleration of the crate. Calculate the upward force the ice exerts on the crate as it is pulled. (2.17m/s/s, 342N)
The acceleration of the crate is 1.82m/s2 and the upward force the ice exerts on the crate as it is pulled is 339.5N
How do you calculate the acceleration and the upward force?The force Fx causing the acceleration is the horizontal component of the pull force F=90 Non the mass m=kg for the angle θ=36∘ to the horizontal.
Fx = F cos36 ∘
=90cos36∘
≈72.81N
According to Newton's second Law, the acceleration a due to the net force Fx=72.81N equals the force divided by the mass m of the crate, i.e.
a = F / m
=72.81 / 40kg
≈1.82m/s2
The upward force mentioned in the question is the normal reaction
N of the ice. It is equal to the weight of the crate mg minus the vertical component Fy of the pull force F i.e.
N = mg − Fy
= mg − F sin36∘
= 40kg*9.81m/s2 − 90sin36∘N
≈339.5N
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A copper wire loop is constructed so that its radius r can change. It is held near a solenoid that has a constant current through it.
a. Suppose that the radius of the loop were increasing. Use Lenz's law to explain why there would be an induced current through the wire. Indicate the direction of current.
b. Check your answer regarding the direction of the induced current by considering the magnetic force that is exerted on the charge in the wire of the loop.
c. Find the direction of the magnetic moment of the loop and the direction of force exerted on the loop by the solenoid.
The top page will receive the current in the loop, and the bottom page will receive it out of the loop.
(a) Because B is constant and there is a constant magnetic Feld, we may recast the change in flux as shown above. Since A is positive, the loop will have a negative emf, which corresponds to an induced magnetic moment on the page that points to the left. The loop's current will flow into and out of the page in opposite directions. V=-Δφ/ Δt = -B·ΔA/ Δt
(b) Individual electrons in the wire loop can be imagined travelling radially outward as the loop's radius grows. We'll take into account one at the top of the loop (which is moving up the page). The Lorentz force Law is F=q(v)=qvB(yx)=-qvB.
(c) Circular orbits will emerge from constant forces pointing into the center of the loop (around the wire). We can tell we have positive current there since the force is pointing into the middle of the loop (into the page).
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The diagram shows 2.0-kilgram cart traveling at a constant speed in a horizontal circle of radius 3.0 meters. The magnitude of the centripetal force of the cart is 24 newtons Use this information t0 answer the following question(s). 2.0-kg Cart A What is the speed of the cart shown in the diagram? 3.0 m
The linear speed of the cart is determined as 6 m/s.
What is the speed of the cart?
The speed of the cart is calculated by applying the formula for centripetal acceleration as shown below;
Mathematically, the formula for centripetal acceleration is given as;
a = v² / r
where;
v is the speed of the cartr is the radius of the carta is the centripetal acceleration of the cartv² = ar
v = √ ( ar )
F = ma
a = F / m
a = 24 N / 2 kg
a = 12 m/s²
Substitute the given parameters and solve for the speed of the cart as shown below;
v = √ ( ar )
v = √ ( 12 x 3 )
v = 6 m/s
Thus, the speed of the cart is a function of centripetal acceleration and the radius of the circular path.
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What device to observe the relationship between volume and number of moles at constant pressure and temperature?
J- shaped tube is a device used to observe the relationship between volume and number of moles at constant pressure and temperature.
This is based on Boyle's law: A gas law known as Boyle's law asserts that a gas's pressure is inversely proportional to its volume when it is held at a fixed temperature and of a given mass.
To put it another way, as long as the temperature and volume of the gas remain constant, the pressure and volume of the gas are inversely proportional to one another. The Anglo-Irish chemist Robert Boyle proposed Boyle's law in the year 1662.
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What is the largest atom of period 4
The largest atom of period 4 is Potassium (K).
What are the elements of period 4?
One of the chemical elements in the fourth row (or period) of the periodic table of the elements is known as element of period 4. The periodic table is organized into rows to show recurrent (periodic) tendencies in the chemical behavior of the elements as their atomic number rises.
One element is present in each of the eighteen groups, making up the fourth period's 18 elements, which start with potassium and end with krypton. d-block, which includes transition metals, makes its first appearance in the table.
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Step 1 of 2:
If we ignore air resistance, a falling body will fall 16t^2 feet in t seconds. What is the average velocity between t=8 and t=8.4? Round your answer to two decimal places if necessary.
____ft/second
Step 2 of 2
If we ignore air resistance, a falling body will fall 16t^2 feet in t seconds. Estimate its instantaneous velocity at t=8 using difference quotients with h=0.1, 0.01, and 0.001. If necessary, round the difference quotients to no less than six decimal places and round your final answer to the nearest integer.
_____ ft/second
The average velocity of the body is 12.8ft/s and the speed of the body when t is 8 seconds is 256 ft/s.
We are ignoring the air resistance and the body is falling whose side is changing with the time as,
x(t) = 16t²
Where,
x is in feet,
t is in seconds.
The velocity of the body can by found as,
v(t) = 32t
Now, the average velocity between t = 8 seconds to t = 8.4 seconds is,
v(t) = 32(8.4 - 8)
v(t) = 32 x 0.4
v(t) = 12.8 ft/s.
Now, the velocity at the instance, when t= 8 seconds.
v(t) = 32t
Putting t = 8 seconds,
v(t) = 32(8)
v(8) = 256ft/s.
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idggfjnfnghnmjrgm jrmjrtmjmjmjmrghj jkm jh hjmjfm ftd f f
Answer:
I agree as this is a very moving piece of information
FILL IN THE BLANK If we add fresh water and salt water to raw iron in the first two test tubes, respectively, then we will observe: ________and if we omit oxygen or water from the iron in the 3rd and 4th test tubes, respectively, then we will observe: _________
Raw iron will rust more quickly in salt water when we add it to the first two test tubes, which will be filled with fresh and salt water, respectively.
The iron in the third and fourth test tubes will rust more quickly if oxygen or water are removed from them, respectively. Iron is susceptible to rusting, a form of corrosion. When iron is exposed to oxygen and water, rusting happens because hydrated iron(III) oxide is created. This means that any action we take to keep iron away from oxygen or water will delay the rusting process. When iron is exposed to salts or a low pH, the rusting process is also sped up. There is no water in a tube with simply air, but the nail is exposed to the air. Since air contains some water vapour, water will eventually find its way inside the tube. In tap water, there is always a little amount of dissolved oxygen gas. This indicates that the tube already contains water and oxygen.
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A cannon is to fire up to 500 m horizontally. What should be the angle of projection, if the shells are fired with a velocity of 100 m/s? (g=10 m/s^2 )
The 15 ° is the the angle of projection, if the shells are fired with a velocity of 100 m/s.
What is angle of projection ?
Angle of projection: The angle created between the projection's direction and the horizontal line drawn there.
What is velocity ?
The velocity of the body or object determines its direction of motion. Speed is frequently a scalar number. In its most basic form, velocity is a vector quantity. It gauges how rapidly a distance changes. It is the pace at which displacement is altering.
Given V=100ms and Range R=500m and g=10m/s²
Let the angle of projection is θ with the horizontal.
Horizontal velocity Vh =Vcosθ=100cosθ
Vertical velocity Vv =Vsinθ=100sinθ
∴ Time of flight = 2Vv/g = 2×100sinθ/g
⇒ Range =Vh ×Time of flight
⇒ 100cosθ×2×100sinθ/g =500 ⇒sin2θ=1/2
⇒2θ=30° ⇒θ=15 °
Therefore, 15 ° is the the angle of projection, if the shells are fired with a velocity of 100 m/s.
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A particle P of mass 0.5 kg rests on a rough plane inclined at angle α to the horizontal, where
sin α = 0.28. A force of magnitude 0.6 N, acting upwards on P at angle α from a line of greatest slope
of the plane, is just sufficient to prevent P sliding down the plane (see diagram). Find
(i) the normal component of the contact force on P, [2]
(ii) the frictional component of the contact force on P, [3]
(iii) the coefficient of friction between P and the plane.
Answer: To solve this problem, we can use the equations of static equilibrium to determine the forces acting on the particle P. In equilibrium, the sum of the forces and the sum of the moments must be zero.
Explanation:
(i) The normal component of the contact force on P is 0.58 N.
(ii) The frictional component of the contact force on P is 0.11 N.
(iii) The coefficient of friction between P and the plane is 0.19.
The forces operating on the particle P can be ascertained using the equations for static equilibrium. The total of the moments and the forces must be zero in an equilibrium state.
The contact force on P has a normal component of 0.58 N.
The 0.11 N frictional component of the contact force on P.
P and the plane experience 0.19 coefficient of friction.
What is meant by frictional component?Friction between two surfaces causes kinetic energy to be converted into thermal energy when they move in relation to one another (that is, it converts work to heat). The utilization of friction produced by rubbing pieces of wood together to start a fire serves as an example of how this attribute can have dramatic effects.
When a viscous fluid is agitated, for instance, kinetic energy is transformed into thermal energy. Wear, which can result in component damage or performance degradation
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during a solar eclipse, the moon, earth, and sun all lie on the same line, with the moon between the earth and the sun.
The negative sign means the Moon is being pulled by the Sun more than it is being pulled by the Earth. Net force on Moon is -2.237×10^26 N
F = G * (M1 * M2) / R^2
G = 6.67×10^-11 m^3/(kg*s)
M = Mass of object
R = Distance between objects
F = force
Force between Moon and Earth
G * (7.35×10^22 kg * 5.97×10^24 kg) / (3.84×10^5 km)^2 = 1.98×10^26 N
Force between Moon and Sun
G * (7.35×10^22 kg * 1.99×10^30 kg) / (1.50×10^8 km - 3.84×10^5 km)^2 = 4.36×10^26 N
Net force on Moon
1.98×10^26 N - 4.36×10^26 N = -2.237×10^26 N
The negative sign means the Moon is being pulled by the Sun more than it is being pulled by the Earth.
Only the Moon orbits Earth naturally. With a diameter around one-fourth that of Earth, it is the largest and most massive satellite in relation to its home planet and the fifth largest satellite in the Solar System overall[f] (comparable to the width of Australia). [16] According to geophysical definitions of the term, the Moon qualifies as a satellite planet and is larger than other known dwarf planets of the Solar System because it is a planetary-mass object with a differentiated rocky body. [17] It has no major magnetic field, atmosphere, or hydrosphere. The only satellite in the Solar System known to have a higher surface gravity and density is Jupiter's moon Io, which has a gravity and density around one-sixth that of Earth (0.1654 g).
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he impulse exerted on the bowling pin equals the negative of the of the ___ projectile during collision.
Acceleration
Its velocity would change during a very short time interval
Its direction would change
Change in momentum
The projectile's impulse is equal to the bowling pin's impulse in the negative, which in turn is equal to the projectile's change in momentum in the negative.
Impulse is commonly denoted by the letter J and is equivalent to the change in momentum ( p Delta p p). According to the impulse-momentum theorem, an object will experience an impulse that is equal to the change in its momentum. An object's impulse during a collision is always equal to the change in momentum. If a collision does not cause the system to lose any net kinetic energy, it is referred to as elastic. In elastic collisions, momentum and kinetic energy are both conserved.
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Simple harmonic motion for a block of mass.
the problem gives x(t)= A cos( (k/m)^(1/2) * t) A block of mass m is attached to a spring whose spring constant is k. The other end of the spring is fixed so that when the spring is unstretched, the mass is located at x=0. Assume that the +x direction is to the right.
we obtain v0 =−xm ωsinϕ=3.06m/s.
What is harmonic motion?
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.
What is mass?
The amount of matter in a particle or object is represented by its mass, which is denoted by the symbol m. In the International System (SI), the kilogram serves as the default unit of mass (kg).
ω= mK = 2.00kg/10100Nm
=7.07rad/s.
Energy methods provide one method of solution. Here, we use trigonometric techniques based on Eq. x=x m cos(ωt+ϕ) and Eq. v=−ωx
msin(ωt+ϕ).
(a) Dividing Eq. v=−ωxm
sin(ωt+ϕ) by Eq.x=xmcos(ωt+ϕ), we obtain
xv=−ωtan(ωt+ϕ)
So that the phase (ωt+ϕ) is found from ωt+ϕ=tan−1( ωx−v )=tan −1( (7.07rad/s)(0.129m)
−3.415m/s).
With the calculator in radians mode, this gives the phase equal to –1.31rad. Plugging this back into Eq.x=xmcos(ωt+ϕ), leads to 0.129m=xmcos(−1.31) ⇒xm=0.500m.
(b) Since ωt+ϕ=–1.31rad at t=1.00s, we can use the above value of ω to solve for the phase constant ϕ. We obtain ϕ=–8.38rad (though this, as well as the previous result, can have 2π or 4π (and so on) added to it without changing the physics of the situation). With this value of ϕ, we find x0=xmcosϕ=−0.251m.
(c) And we obtain v0 =−xm ωsinϕ=3.06m/s.
Therefore, we obtain v0 =−xm ωsinϕ=3.06m/s.
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to create the amount of energy that was discovered to be coming out of active galaxies you need an object with a lot of gravity: a .
In a black hole, the pull of gravity is so great that not even the most powerful electromagnetic waves can make their way out. According to general relativity, a black hole can arise if a massive object is so compact that it warps spacetime.
The event horizon is the threshold beyond which it is impossible to travel. According to general relativity, there are no locally observable features despite the fact that crossing them might drastically change the course of an object's life. A black hole is very similar to a perfect black body in that it does not reflect any light.
What's more, the same spectrum as a black body with a temperature inversely proportional to its mass is predicted by quantum field theory in curved spacetime for the radiation that event horizons generate. Stellar black holes have temperatures on the order of billionths of a Kelvin, making direct observations nearly impossible.
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a bottle has a mass of 36.00 gg when empty and 95.94 gg when filled with water. when filled with another fluid, the mass is 89.22 g. Determine the specific gravity of the other fluid.
The specific gravity of the other fluid in the bottle with a mass of 53.22 g is determined to be 0.8879.
The ratio of a material's density to a predetermined reference substance is the substance's specific gravity. If anything has a specific gravity, it will either float or sink. When tested against water, the specific gravity of a solid or liquid is compared; if it is less than one, it will float, and if it is greater than one, it will sink. Then, the specific gravity of a material is given by, [tex]RD = \frac{\rho_{\text{substance}}}{\rho_{\text{reference}}}[/tex].
The mass of water in the bottle is 95.94 g - 36.00 g = 59.94 g. And the mass of another fluid in the bottle is 89.22 g - 36.00 g = 53.22 g. Then,
[tex]\begin{aligned}\text{specific gravity of other fluid}&=\frac{\rho_{\text{fluid}}}{\rho_{\text{water}}}\\&=\frac{\frac{m_f}{V}}{\frac{m_w}{V}}\\&=\frac{m_f}{m_w}\\&=\frac{53.22}{59.94}\\&=0.8879\end{aligned}[/tex]
The answer is 0.8879.
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Two events occur 100 m apart with an intervening time interval of 0.60 µs. The speed of a reference frame in which they occur at the same coordinate is:
1.1c
0.56c
0.25c
1.8c
Clocks at rest in a reference frame where the two events occur are used to calculate the proper time between the events.
A. take place simultaneously B. take place at the same coordinates C. are separated by the maximum distance a light signal can travel in the given amount of time.
E On the x axis of reference frame S, there are two simultaneous events, one at x = a and the other at x = +a. An observer going in the direction of positive x says.
They are seen in reference frame S, which is travelling at a positive x-motional speed of 0.95c. The clocks of S are zeroed when the sources of the two frames coincide at time t = 0.
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The resistivity of a semiconductor can be modified by adding different amounts of impurities. A rod of semiconducting material of length L and cross- sectional area A lies along the z-axis between I= 0 and 1= L. The material obeys Ohm's law, and its resistivity varies along the rod according to p(2)=poexp(-x/L). The end of the rod at r=0 is at a potential Vo greater than the end at x=L
And p(2)=poexp(-x/L) describes how its resistivity changes along a rod. The rod's end at r=0 has a potential Vo that is higher than the end at x=L.Ohm's law is followed by the substance,
Solution p(x)=p₀ exp(-x/L)
(a) we know that R=PL/A
dR=ρ(x)dx/A=p₀ e[tex]^{-x/L}[/tex] dx/A
R=p₀/A[tex]\int\limits^L_0 e^{-x/L} \, dx[/tex]
R=(p₀L/A)(1-e⁻¹)
(b)I=V₀/R=V₀A/p₀L(1-e⁻¹)
(c)ρ=E/J
E=ρJ
E(x)=Ip₀e[tex]^{-x/L}[/tex]/A=V₀Ap₀ e[tex]^{-x/L}[/tex]/p₀L(1-e⁻¹)A
Hence E(x)=V₀ e[tex]^{-x/L}[/tex]/L(1-e⁻¹)
(d)R(x)=∫dR=p₀/A[tex]\int\limits^x_r e^{-x/L} \, dx[/tex]
R(x)=Lp₀/A(1-e[tex]^{-x/L}[/tex])
starting from left end of rod ,there is potential drop IR(x) at distance x
∴V(x)=V₀-IR(x)
V(x)=V₀( e[tex]^{-x/L}[/tex] -e⁻¹)/(1-e⁻¹)
The current through a conductor between two places is directly proportional to the voltage across the two points, according to Ohm's law. The typical mathematical equation that captures this relationship is reached by including the resistance as the constant of proportionality.
where I denotes the current flowing through the conductor, V is the voltage applied across the conductor, and R denotes the conductor's resistance. The R in this relationship is constant and independent of the current, according to Ohm's law. Although the previous equation cannot be referred to as Ohm's law if the resistance is not constant, it can still be used to define static/DC resistance. The conductivity of the great majority of electrically conductive materials is accurately described by Ohm's law, an empirical relation.
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