The current flowing through the circuit A is IA = 2ε/(R1 + R2)
b) IB = 2ε/(2R2 + R1) c) P = 0.064
The equivalent resistance of the circuit A in series is calculated as follows;
Re = r1 + r2
The emf of the battery connected to circuit A
emf = e
The current flowing through the circuit A is calculated as follows;
I = V / R
I = e / r1 + r2
Total resitance in circuit A = Req = R1+R1+R2 =2R1 + R2
total emf in circuit A = 2E
I = 2E/Req
I = 2E/(2R1+R2)
given : E = 10 V
R1 = 300 ohm
R2 = 5000 ohm
since connection is in series so current remain same across resistors
I = 2*10/(2*300 + 500)
I = 3.57 x 10^-3 A
power dissipated by R2
P = I^2*R2
P = (3.57 x 10^-3)^2 * 5000
P = 0.064
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the force exerted by the road on each tire of an accelerating car question 4 options: is less than the combined force of all four tires on the road. equals the combined force of all four tires on the road. is more than the combined force of all four tires on the road. noneof the above.
The force exerted by the road on each tire of an accelerating car is less than the combined force of all four tires on the road.
In mechanics, a force is any action that has the potential to change, maintain, or deform a body's motion. The three principles of motion outlined by Isaac Newton in his Principia Mathematica are frequently used to illustrate the idea of force (1687). Newton's first law states that a body at rest or moving uniformly in a straight line will stay in that state until a force is applied to it. According to the second law, a body will accelerate (change in velocity) in the direction of any external force acting on it. The amount of acceleration is directly related to the amount of external force.
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(a) Stone A leaves the player's hand with a velocity of 2.90 m/s.
The mass of stone A is 17 kg.
(i) State the formula linking momentum, mass and velocity.
(ii) Show that the momentum of stone A is approximately 50 kg m/s.
(1)
(2)
Answer:
(a)(i) momentum(kg m/s) = mass x velocity
p=mv
(a)(ii) 17 x 2.90 = 49.3
49.3 is approximately 50 kg m/s
Explanation: mass of stone A is 17 kg and the velocity of stone A is 2.90 m/s. To find momentum is to times mass and velocity.
jupiter has retained almost all of its original atmosphere because of its dramatic, prominent ring system. it is rotating so quickly, with the highest rotation speed of any of the planets. it is so massive and thus has a strong gravitational pull. io's volcanic activity adds material and replenishes the atmosphere.
This means that solid surfaces that must have a constant rotational speed are not visible.
More fundamental is the rotation of the mantle and core. These can be determined by periodic fluctuations in the radio waves emitted by Jupiter and controlled by its magnetic field. The magnetic field (discussed below) originates deep inside the planet and thus shares the internal rotation.
Jupiter was so massive that it was not as hot as the terrestrial planets when it formed, so it retained most of its original atmosphere. Since Jupiter is a ball of gas, it actually experiences differential rotation. Depending on where you are on Earth, the rotation will take a different amount of time.
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a 4.0 kg object moving at 6.0 m/s encounters a 20 n resistive force over a duration of 0.20s. the momentum change (magnitude only) experienced by this object is approximately ns.
The momentum change experienced by the given object is approximately is 4 N/s .
What is Momentum Change ?
The term momentum change is defined the change in the product of an object's mass and velocity.
A force is required for changing momentum of an object. This force applied can increase or decrease momentum and can even change the object's direction .
given that ;
mass of moving object is ⇒ 4 Kg ,
velocity of the moving object is ⇒ 6 m/s ,
the force = 20N .
time for which the force is applied is = 0.20 s .
Now , By Newton's Second Law ,
"the time rate of momentum change is directly proportional to the force applied on the object ".
So , momentum change is = 20 × 0.20
= 4 Ns .
Therefore , the momentum change is 4Ns .
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A circular saw is powered by a motor. When the saw is used to cut wood, the wood exerts a torque of 0.80N on the saw blade. If the blade rotates with a constant angular velocity of 20 rad/s the work done on the blade by the motor in 1.0 minis:
A. 0
B. 480 J
C. 960 J
D. 1400 J
J E. 1800 J
The amount of work performed on the blade by the motor in one minute is 960 J if the blade rotates at a constant angular velocity of 20 rad/s.
A force that generates rotation is known as a torque. demonstrates how well a force can rotate or twist an object.
We are know that,
Torque = F = 0.80N
Angular velocity = ω = 20rad/s
To calculate the value of work done we can use the equation,
work = torque x angular displacement
θ = ωt
θ = 20rad/s x 60s
θ = 1200rad
Then , from the above value we can calculate,
work = 0.80N x 1200rad
W = 960J
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While visiting the Albert Michelson exhibit at Clark University, you notice that a chandelier (which looks remarkably like a simple pendulum) swings back and forth in the breeze once every T = 6.1 seconds.
a) Calculate the frequency of oscillation (in Hertz) of the chandelier.
b) Calculate the angular frequency ω of the chandelier in radians/second.
c) Determine the length L in meters of the chandelier.
d) That evening, while hanging out in J.J. Thompson's House O' Blues, you notice that (coincidentally) there is a chandelier identical in every way to the one at the Michelson exhibit except this one swings back and forth 0.11 seconds slower, so the period is T + 0.11 seconds. Determine the acceleration due to gravity in m/s2 at the club.
The acceleration an object experiences as a result of gravitational force is known as acceleration due to gravity. M/s2 is its SI unit. Its vector nature—which includes both magnitude and direction—makes it a quantity. The unit g stands for gravitational acceleration. At sea level, the standard value of g on earth's surface is 9.8 m/s2.
How do we calculate the gravitational acceleration?
The formula for calculating acceleration due to gravity is given below in its most practical form by these two laws: Where g is the acceleration brought on by gravity, G is the gravitational constant of the universe, M represents mass, and R is distance, g = G*M/R2.
Describe 9.8 m s2?
Lowercase g indicates the gravity acceleration's magnitude, which is 9.8 m/s2. g = 9.8 m/s2. This means that gravity will increase an object's velocity by 9.8 m/s for every second it is in free fall. Following one second, the item is moving at a speed of 9.8 m/s.
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an object with height 0.85 cm is placed a distance 19.75 cm in front of a convex mirror with focal length -6.25 cm,removedde6d0d485ec413711a4e98afe87284678ac0bba70217810ba692cdd66aafdf8cremoved 2m68-57-20-4f-a59d-29897 20% part (a) calculate and enter a value for the magnitude of the distance between the image and the mirror given the values in problem statement. |di||di|
The distance between the image and the mirror is -4.63 cm.
The mirror equation is given by,
1/u + 1/v = 1/f
where, u is the distance to the object = 17.95 cm
v is the distance to the image
f is the focal length = -6.25 cm
Placing the values in the equation, we have
1/17.95 + 1/v = -1/6.25
1/v = -1/6.25 - 1/17.95
1/v = - 0.16 - 0.056
1/v = - 0.216
v = -4.63 cm ( minus sign indicates that the image is behind the mirror and it is virtual)
Thus, the image distance is -4.63 cm.
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a unit load of not less than _volt-amperes per square foot be included for storage spaces in other than dwelling units
A unit load of not less than 1/4 volt-amperes per square foot is included for storage spaces other than dwelling units.
What is unit load?The unit load can be described as the size of an assemblage into which a number of items are combined for ease of storage and handling, for example, a pallet load expresses a unit load that can be moved easily with a pallet jack, or a container load expresses a unit for shipping purposes.
A unit load can pack tightly into a warehouse rack, truck, or intermodal container, yet can be broken apart at a distribution point, generally a distribution center, or wholesaler, for sale to consumers or for use.
A unit load can be defined as the basic storage and transport unit arranged on modular support or in packaging to ensure efficient handling.
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consider a string of length 1.0 meter, fixed at both ends, with mass 100 grams and tension 100 newtons.
Mass is an intrinsic property of a body. It turned into traditionally believed to be related to the quantity of being counted in a physical body until the discovery of the atom and particle physics.
‘The wavelength of the wave shape on the string is,
1”
31.6 ms
‘95 Hz
If one antinode is formed on the string, then the duration of the string is,
=0.3328 m
2
If two antinodes are formed, then the length of the string is,
“4
allow 7 to be the number of antinodes shaped.
io)
a
_2(1.0m)
© 0.3328 m
Normally, nodes form at both ends of the string. as a result, the range of nodes formed is
Usually extra than one this is the number of nodes fashioned is 6+1=7.
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A very long insulating cylinder of charge of radius2.40 cm carries a uniform linear density of 13.0 nC/m.
If you put one probe of a voltmeter at the surface, how far fromthe surface must the other probe be placed so that the voltmeterreads 200 V?
The distance at which the probe should be placed so that the voltmeter reads 200 V is equal to 0.216 cm.
To find the distance at which the voltmeter reads 200 V, we need to use the equation for the electric potential at a point due to a continuous distribution of charge:
V = k * ∫λ(r')/r' dr'
where V is the electric potential at a distance r from the center of the cylinder, k is the Coulomb constant (8.99 x 10^9 N*m^2/C^2), λ is the linear charge density (13.0 nC/m in this case), and r' is a dummy variable of integration.
To find the electric potential at a distance r from the surface of the cylinder, we can split the integral into two parts: one from the surface of the cylinder (r') to the point where the probe is placed (r), and one from r to the center of the cylinder (which will be a negative value since the charge density is negative):
V = k * [∫λ(r')/r' dr' from r'=r to r'=2.4 cm] + k * [∫λ(r')/r' dr' from r'=2.4 cm to r'=0]
The first term on the right hand side represents the potential at the point where the probe is placed, and the second term represents the potential at the surface of the cylinder. We are given that the potential at the surface is 200 V, so we can set the equation equal to 200 V and solve for r:
200 V = k * [∫λ(r')/r' dr' from r'=r to r'=2.4 cm] + k * [∫λ(r')/r' dr' from r'=2.4 cm to r'=0]
To solve this equation, we need to evaluate the integrals on the right hand side. The first integral is easy to evaluate:
∫λ(r')/r' dr' from r'=r to r'=2.4 cm = λ * ln(2.4 cm/r)
The second integral is a little more tricky, but we can use the fact that the charge density is uniform to simplify it:
∫λ(r')/r' dr' from r'=2.4 cm to r'=0 = λ * ∫1/r' dr' from r'=2.4 cm to r'=0
= λ * [ln(r')] from r'=2.4 cm to r'=0
= λ * [-ln(2.4 cm)]
Substituting these values back into the original equation and solving for r, we find that the distance at which the voltmeter reads 200 V is:
r = 2.4 cm * exp(-200 V / (k * λ))
r = 0.216 cm
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Using the concepts of impulse and momentum, describe how to win a water balloon contest by not breaking the balloon.
Requirements:
o Focus on the catch.
o You must mention how momentum, impulse, force and impact time play a part in the catch.
o You may use diagrams to support your reasoning.
o Remember the equation: ∆p = m∆v = F∆t
Answer:
Below
Explanation:
To win a water balloon contest without breaking the balloon, you must focus on the catch. Momentum, impulse, force, and impact time all play a crucial role in the success of the catch.
The key to catching a water balloon without breaking it is to minimize the impact force on the balloon. The impact force is determined by the momentum of the balloon, the impulse applied to the balloon, and the impact time.
Momentum is the product of an object's mass and velocity. In this case, the water balloon has a certain mass and velocity as it is thrown towards you. The greater the momentum of the balloon, the harder it will be to catch it without breaking it.
Impulse is the product of the force applied to an object and the time over which that force is applied. When catching a water balloon, you must apply an impulse to the balloon in order to stop it. The greater the impulse, the more effectively you will be able to stop the balloon.
The key to catching a water balloon without breaking it is to apply a large impulse to the balloon over a short period of time. This will minimize the impact force on the balloon and prevent it from breaking.
To do this, you must pay careful attention to the movement of the balloon as it is thrown towards you. As the balloon approaches, you must quickly move your hand to intercept it and apply an impulse to stop it. This can be done by cupping your hand and applying a gentle but firm push to the balloon as it hits your hand.
By applying the right amount of impulse over a short period of time, you can effectively stop the balloon and prevent it from breaking. This will allow you to win the water balloon contest without breaking the balloon.
In summary, to win a water balloon contest without breaking the balloon, you must focus on the catch. Pay attention to the movement of the balloon and apply an impulse to stop it over a short period of time. This will minimize the impact force on the balloon and prevent it from breaking.
A charged particle moves in a circular path in a uniform magnetic field.
Which of the following would increase the period of the particle's motion?
Check all that apply.
Increasing its charge
Increasing its mass
Increasing the field strength
Increasing its speed
A charged particle moves in a circular path in uniform magnetic field, then following would increase the period of the particle's motion: Increasing its charge and Increasing the field strength.
What would increase the period of the motion of particle?For charged particle moving in circular path in uniform magnetic field, centripetal force is provided by magnetic force,
q v B = mv²/r
Here, q is charge, v is velocity and B is magnetic field
m is mass, r is radius of the orbit
The period of the motion is given as :
T= 2πr/v
Substituting value of T in previous equation.
Now, q v B= m Tv³/2π
Hence, T= 2πq B/mv²
Here, we can clearly see that the period is: directly proportional to the charge and the magnetic field but inversely proportional to mass and square of the speed.
Therefore, increasing its charge and the field strength will increase the period of the particle's motion.
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discovery of mineral perchlorate on mars by the phoenix lander was significant because group of answer choices
The lander discovered falling snow and soil chemistry that has important implications for life. The largest finding of perchlorate, a substance on Earth that may be poisonous to certain organisms while providing nourishment for others.
What is the real name of Earth?Contrary to popular belief, Earth is not known by a recognized international name. "A common misinterpretation of the civilization's scientific name is "Terra." Earth is the planet's commonly used name in English, especially in science.
What are the specifics of Earth?Soil, air, liquid, and life are the components of Earth. There are flat areas, valleys, and mountains on the earth. The air is made up of many gases, mostly nitrogen and oxygen. Rain, snow, ice, rivers, lakes, seas, and streams are all forms of water.
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turn on the supply of fig 13.4 and measure the voltage vab. then calculate the current il using the measured value of the 47 resistor
At the junction of two resistors, a voltage (V1) proportional to the measured voltage will be shown. The Arduino's analogue pin can then be attached to this junction.
This formula can be used to determine the voltage. Vm = (R2/(R1+R2)) * V1 The Arduino then measures the voltage V1. A voltage divider circuit that consists of two resistors linked in series as shown can be used to solve this problem. The voltage to be measured (Vm) is linked to one end of this series connection, and the ground is attached to the other end.
Vab can be determined visually to be 14 volts. First, use your eyes. Write down the following values for the voltages and currents specified by Ohm's law using just your eyes: Your biggest error, in my opinion, was failing to realise that the ground (shown in green) is connected to both the 6 volt supply and the 5 ohm resistor.
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-The Kepler Conjecture: this quantity is maximized for HCP and FCC crystals
-Reciprocal: specific volume
-It is the ratio between kinematic and dynamic velocity
-Melting point line has a negative slope when this is greater for liquids than for solids
According to the Kepler Conjecture, this amount is maximal for crystals of HCP and FCC. This is the reciprocal of a certain volume, and it represents density as the ratio of kinematic to dynamic velocity.
The Kepler conjecture is a mathematical theory involving sphere packing in three-dimensional Euclidean space, and it is named after the 17th-century mathematician and astronomer Johannes Kepler. A planet's orbits around the sun are accurately described by Kepler's third law in terms of their period and distance. According to Kepler's Laws of Planetary Motion, planets move in elliptical orbits with the Sun as their point of focus, cover the same amount of space in the same amount of time regardless of where they are in their orbit, and have orbital periods that are proportional to their distance from the Sun.
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Antoine burns some charcoal, and a very small diamond (!), and makes the ____________ that the only product of both reactions is a heavy gas (carbon dioxide).
Antoine burns some charcoal, and a very small diamond, and makes the observation that the only product of both reactions is a heavy gas (carbon dioxide).
The descriptions of scientists engaging in activities that are part of the scientific method.
When Antoine burns charcoal and a small amount of diamond, then in that case, each Carbon atom will form a tetrahedral bond with the other four carbon atoms which are present in a Diamond.
Due to the formation of the tetrahedral bond the structure becomes more and more compact and rigid.
Hence, the missing word is given below.
Antoine burns some charcoal, and a very small diamond (l) and makes the observation that the only product of both reactions is a heavy gas.
Missing word:- Observation
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the wind speed is 200 km/h air density is 1.3 kg/m^3 estimate the force of the wind on an adult standing facing the wind
The force of the wind on an adult standing facing the wind will be 518.4 Newtons if the wind speed is 200 km/h and the air density is 1.3 kg/m³.
To calculate the force of the wind on an adult standing facing the wind, you can employ the following formula:
Force (in Newtons) = 0.00256 × wind speed(in km/h)² × surface area(in m²) × air density(in kg/m³)
According to the given question, wind speed is 200 km/h, the air density is 1.3 kg/m³, and we'll assume the adult has a surface area of 1.8 m². Putting these values in the formula we get:
Force = 0.00256 × 200² × 1.8 × 1.3
= 0.00256 × 40000 × 1.8 × 1.3
= 256 × 1.8 × 1.3
= 518.4 Newtons
So, the force of the wind on an adult standing facing the wind will be 518.4 Newtons if the wind speed is 200 Km/h and the air density is 1.3 kg/m³.
This is a rough estimate, as the actual force of the wind on an adult will rely on varied aspects such as the shape of their body, the angle at which they are encountering the wind, and the kind of clothing they are wearing.
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Describe the trends in the U.S. energy demands and the amount of this energy generated from nuclear power since 1970. Include in your answer any relationships that may exist between them. Consider data provided above and possibly extra research. As you make your claim ALWAYS use evidence to support your response.
The overall energy consumption in the United States has nearly tripled since 1970, and electricity consumption has grown even faster.
How is the energy consumption?The U.S. economy is heavily dependent on energy for everything from manufacturing and transportation to agriculture and housing. Power sources and uses are constantly changing.
A total of 98 quadrillion BTUs of energy were consumed in the United States in 2010, according to estimates. This is a little less than its peak in 2007, but nearly three times higher than its level in 1950 (34.6 quadrillion BTUs).
The average American uses 2.5 gallons of oil, 8.86 pounds of coal, and 246 cubic feet of natural gas per day. Each person in a household uses 12 kilowatt-hours (kWh) of electricity per day. The overall U.S. energy consumption dropped 3.1% from peak levels in 2019 in 2021.
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the speed of light is the fastest anything in the universe can go if it is traveling through space.________ can break that speed limit.
The speed of light is the fastest anything in the universe can go if it is traveling through space. Much faster than light can break that speed limit.
How quickly must you go in order to surpass the speed of light?We can never go faster than light. Or, to be more precise, in a vacuum, we can never travel at the speed of light. In other words, the 299,792,458 m/s upper limit of the universe's speed is the speed at which all other particles must move in order to exist.
What is the light's 3x10 8 speed?In a vacuum, light travels at a speed of 3 108 m/s. About 8 minutes pass before sunlight reaches Earth.
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when discussing gravitational force, do we look at the distance between the edges of objects, or the distance between their centers
The distance between two masses is measured between their edges, from their centers, or from one mass's edge to its center.
What do mean by gravitational?This moon's gravitational pull causes water tides to fluctuate over time. strong movement or propensity towards something or someone, whether inherent or external: The reasons why they are drawn to destructive behavior have been the subject of extensive inquiry.
What is gravitational and example?This term force of gravity refers to the force that the earth exerts on a body. Such examples include the downward motion of water in a river, its downward motion of a ball thrown into the air, and also the downward motion of the fruits and leaves that fall from a tree towards the ground.
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Place the events involved in generation of an action potential in the correct order of occurrence from left to right : Hyperpolarization K+ channels close; Na+ channels close K+ channels open; Threshold stimulus Na channels open; Na influx Depolarization; K+ efflux Repolarization
4, 2, 1, 5, 3 ;Threshold stimulus, Na+ channels open, Na+ influx, depolarization, Na+ channels close, K+ channels open, K+ efflux, repolarization,. Hyperpolarization, K+ channels close.
The gated sodium ion channels on the neuron's membrane quickly open during the depolarization phase, letting sodium ions (Na+) from the outside flood inside the cell. The nerve's intrinsic charge shifts from -70 mV to -55 mV as the sodium ions enter the cell fast. Depolarization is when an internal change in a cell results in a shift in the distribution of electric charges, leaving the cell with a less negative charge than the surrounding area. Depolarization is essential for several cell processes, cell-cell communication, and general organism physiology. A rise in membrane potential is referred to as depolarization. In other words, as sodium ions enter the intracellular fluid due to the opening of voltage-gated sodium cations, the membrane potential increases.
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The electric potential, which is a scalar field, may be represented graphically by equipotential curves. The lines of electric field may be obtained from those equipotentials.
Several points have been indicated with black dots on the diagram below. Consider the direction of the electric field at each of those points, and drag the best-choice arrow label, or the E=0, if appropriate, to the corresponding bucket.
While the region with the lowest electric potential (20 V) will have the highest electric field, the region with the highest electric potential (80 V and 70 V) will also have the highest electric field.
Equipotential curves: what are they?Relationship between electric potential and electric field
E = V/d
where;
V is electric potential (V)
E is electric field (V/m)
d is the distance (m)
A two-dimensional curve where a function's value is constant. Isarithm, isopleth, and contour line are other names that are equivalent.
A location with a high electric potential (80 V or 70 V) will have a high electric field, whereas a region with a low electric potential (20 V) will have a low electric field since electric field and electric potential are directly proportional.
Describe the electric field.The field that surrounds electrically charged particles and pulls on all other charged particles in the field is known as the electric field.
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what average net force is required to accelerate an 8kg bicycle to a speed of 6.2m/s in 5s?
The average net force required to accelerate an 8kg bicycle to a speed of 6.2m/s in 5s is 9.92 Newton.
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.
Given that: mass of the bicycle: m = 8 kg.
Final speed : v = 6.2 m/s.
Time interval: t = 5 s.
Hence, average net force applied on it = change in momentum/time interval
= 8 kg × 6.2 m/s/5 s
= 9.92 Newton.
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the student designs an experiment to study the period of oscillation for an object on a spring. the student measures the mass of a sphere as m
A spring's spring constant is quadrupled by the oscillation period of an item on it.
Oscillation is defined as what?The pendulum's periodic to-and-fro motion is referred to as the Simple pendulum's oscillatory motion. One oscillation of a pendulum is defined as the motion of a bob as it moves from one end to the other and returns to the starting point.
How do motion and oscillation vary from one another?When an item goes back and forth frequently, this is referred to as an oscillatory motion. Periodic motion, on the other hand, describes a motion in which an item repeats a route after a set amount of time. However, not all periodic movements are oscillatory; only oscillatory motions are all periodic.
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A 60-kg person riding a bike puts all her weight on each pedal when climbing a hill. The pedals rotate in a circle of radius 16 cm. Part A What is the maximum torque she exerts? Express your answer to two significant figures. VO AEO ...] ? T= m.N
The maximum torque is 94.08 Nm and the rider can increase this by putting the leg on the edge of the paddle.
Torque is defined as the force that causes the rotation of an object on an axis. It is measured in Nm.
Mass of the person = m = 60 Kg
Radius of the circle = r = 16 cm = 0.16 m
Force = F = mg
Torque = t =
= t = F X r X sinθ
= t = mg X r X sinθ
= t = 60 X 9.8 X 0.16
= t = 94.08 Nm
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___ is experimental coefficient of kinetic friction the slope of the line of best fit between kinetic frction and normal force
Answer is Force, The kinetic fiction force, also known as sliding friction, only affects moving objects (thus the term "kinetic"). Pushing a box across floorboards is an example of this force opposing sliding motion.
This sort of friction has a particular coefficient of friction (such as rolling friction). The materials used to create the contacting surfaces are particular to this coefficient. The coefficient will be higher on a rougher surface. This is the equation that will assist you in determining the coefficient of kinetic friction: The force holding the items together, or the force perpendicular to the surfaces in contact, is known as the normal force.
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suppose a cylindrical solenoid of radius r and turns per length n has a clockwise current that decreases according to the function i
Due to the unit current being passed through the first coil, mutual inductance is FLUX induced in the second coil.
Let me represent the larger coil's current. the magnetic field (B) there in
B = μ₀n i where n is the number of turns per unit length.
B = μ₀ (N / L) i
Magnetic flux associated with small coil placed near its axis
Flux(Ф)= B X πR² X N
Flux(Ф) =μ₀ (N / L) i X πR² X N
Flux(Ф)== μ₀ (N² / L) i X πR²
Flux(Ф) induced by unit current
M = μ₀ (N² / L) X πR²
The questions is incomplete I answered it in general way.
A solenoid has length L, radius R, and number of turns N. A second smaller solenoid of length L, radius R and number of turns N is placed at the center of the first solenoid, such that their axes coincide. What is the mutual inductance of the pair of solenoids
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in the overhead view of fig. 15-48, a long uniform rod of mass 0.600 kg is free to rotate in a horizontal plane about a vertical axis through its center. a spring with force constant k
The period of the small oscillations that result when the rod is rotated slightly and released is 0.0653s.
Harmonic motion, where the damping force is proportional to the velocity, which is a realistic damping force for a body moving through a fluid is called damped harmonic motion.
If τ=−Cθ, where τ is the torque, θ is the angle of rotation, and C is a constant of proportionality, then the angular frequency of oscillation is ω= sqrtC/I and the period is T=2π/ω=2π sqrtI/C.
where, I is the rotational inertia of the rod. The plan is to find the torque as a function of θ and identify the constant C in terms of identies given in question.
Now using T=2π sqrtI/C, we get
T= 2π sqrtm/3K
putting given quantities,
T= 0.0653s.
The question is incomplete, the complete question is
In the overhead view of above figure, a long uniform rod of mass 0.600kg is free to rotate in a horizontal plane about a vertical axis through its center. A spring with force constant k=1850N/m is connected horizontally between one end of the rod and a fixed wall. When the rod is in equilibrium, it is parallel to the wall. What is the period of the small oscillations that result when the rod is rotated slightly and released?
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A bowling ball of mass 7.22 kg and radius 10.2 cm rolls without slipping down a lane at 3.20 m/s . Calculate its total kinetic energy.
The total kinetic energy of the bowling ball is 51.75 Joules.
The mass of the bowling ball is 7.22 Kg and the radius of the ball is 10.2cm.
The radius in meter is 0.102 m.
The ball is rolling without slipping with a speed of 3.20m/s.
The total kinetic energy of the bowling ball is given by,
KE = 1/2Mv²(1+k²/r²)
where,
M is the mass of the ball,
v is the speed of the ball on the lane,
k is the radius of gyration,
r is the radius of the ball.
Putting values,
KE = 0.5 x 7.22 x 3.2 x3.2 x 1.4
KE = 51.75 Joules.
The total kinetic energy of the ball is 51.75 Joules.
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a) calculate i) the gain (vout/vin) of the op-amp (without c1), and ii) the gain (vout/vin) of the op-amp with c1 paralleled with r2. include your calculation in the report.
The negative sine is because current flows from input to output, but as in current flows from output to input is - 10 V/V.
Calculation:-
1. V in - 0 / 10 = - 10v/V
Therefore Vout / V in = - 10 V/V
2. V in - 0 / 10 = - 10v/V + 0 - V out / 20 sn
therefore V out / V in = - 1/ 0.1 + 200 ns.
Note that for practical signal scaling, an inverting amplifier can have a gain of less than 1, while a non-inverting amplifier must have a gain of at least 1. you'll need to power the op-amp with V+ and V- to have enough range to comfortably accommodate the expected signal output.
The formula for the output voltage Vout also shows that the circuit is linear for the fixed gain of the amplifier since Vout = Vin x gain. This property is very useful for converting small sensor signals into larger voltages.
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