When they are moved to a new separation of 8.0 cm, the electric force on each of them will be closest to 0.063 N.
Full question: When two point charges are 2.0 cm apart, each one experiences a 1.0-N electric force due to the other charge. If they are moved to a new separation of 8.0 cm, the electric force on each of them is closest to?
Given:
The point charges are initially at a distance of d = 2 cm.
The initial force experienced by them is F = 1 N.
The electrostatic force experienced by two charges q and Q is defined as,
F = kqQ/d^2
Where
K is the constant and r is the distance between the charges.
The initial force experienced by them will be, F = 1N
Now, the final distance between the charges is changed to 8 cm which is equal to 4d.
So, the new force on the charges will be,
F = kqQ/(4d)^2 = 1/16 = 0.063N.
So, when they are moved to a new separation of 8.0 cm, the electric force on each of them will be closest to 0.063 N.
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what is the speed of light with a frequency of 2.4 x 1013 1/s? give your answer in m/s.
The 299,792,458 m/s is the speed of light with a frequency of 2.4 x 1013 1/s.
What is speed ?
The rate of a directionally changing object's location. The SI unit of speed is created by combining the fundamental units of length and time. Meters per second (m/s) is the unit of speed in the metric system.
What is frequency?
The frequency is expressed in Hertz. A sound wave's frequency is determined by how many vibrations it produces ( f ). Another way to think of frequency is as the quantity of waves that pass a specific spot in a second.
Therefore, 299,792,458 m/s is the speed of light with a frequency of 2.4 x 1013 1/s.
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a particle travels along a straight line with an acceleration of a=(10−0.2s) m/s2 , where s is measured in meters
The required velocity of a particle travelling in a straight line with the given acceleration function at s = 10 m is calculated to be 15.52 m/s.
At, s = 0, the velocity of the particle is v = 9 m/s.
Now, let us find the particle's velocity at s = 10 m,
Consider the acceleration function, a = (10 − 0.2 s)
Since, a = v dv/ds, so the above equation can be written as,
v dv/ds = (10 − 0.2 s)
Integrate the above function using the variable separable approach,
9 to v ∫ v dv = 0 to 10 ∫ (10 − 0.2 s) ds
9 to v (v²/2) = 0 to 10 (10 s - 0.2 s²)
v²/2 - 9²/2 = 10× 10 - (0.2 × 10²)
v = 15.52 m/s
Thus, the velocity as s = 10 m, is 15.52 m/s.
The given question is incomplete. The complete question is 'Determine the velocity of the particle when s = 10 m if v = 9 m/s, at s = 0.'
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A fixed charge (circle) is placed somewhere in empty space. A test charge is placed at point x. If the fixed charge is replaced by one with twice the amount of charge, then the electric force the test charge experiences will:
A. Double B. Quadruple C. Be one quarter as large D. Be halved E. None of the above х
If a test charge is substituted for the fixed charge with one that has twice as much charge, the test charge will experience the following electric forces: Double A.
What exactly does a force in science mean?The definition of "force" is obvious. It is quite fair to use the phrases "push" or "pull" to describe a force at this level. An object simply does not "have in it" or "contain" a power.
What does a force actually signify at its core?When pushed or pulled, a massed object will alter its velocity. A body's resting state can be changed by an outside force.
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-In ordered pair notation, write down the components of vector B⃗ .(Express your answers to the nearest integer.)
-In ordered pair notation, write down the components of vector D⃗ .(Express your answers to the nearest integer.)
-What is true about B⃗ and D⃗ ? Choose from the pulldown list below:
a. They have different components and are not the same vectors.
b. They have the same components but are not the same vectors.
c. They are the same vectors.
According to the question,They have different components and are not the same vectors.
What is the components ?A component is a building block or part of a system that is necessary for the system to function. Components are often interchangeable and can be interlinked with other components to create a complex system. Components can be physical or virtual, and are used in a wide variety of fields, including electronics, engineering, manufacturing, software development, and architecture. Examples of components include individual parts of a car, like the engine, brakes, transmission, and suspension; or components of a computer, such as CPU, RAM, motherboard, and hard drive.
Vector B⃗ has components (2, 3) and vector D⃗ has components (4, -1). Since the components are different, the vectors are not the same.
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an arrow is in mid-flight on its way to a target. at this moment, what force keeps the arrow going forward?
At the moment, there is actually no force that keeps the arrow going forward when it is in mid-flight.
In order to accelerate an object, there must be a net force acting on the object. This is because without any force acting on, an object will be at rest or moving at a constant rate and at one direction.
Acceleration in physics is defined to be the change in velocity over the time elapsed (a = Δv/t). The equation means that an object will be accelerating when it keeps changing velocities.
When the arrow is in mid-flight, it is assumed to be moving at a constant velocity, ignoring the air friction. Therefore, the arrow is not accelerating mid-flight, which means there is no force acting on the arrow at that moment.
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two equally charged particles are held 3.2 ' 10$3 m apart and then released from rest. the initial acceleration of the first particle is observed to be 7.0 m/s2 and that of the second to be 9.0 m/s2 . if the mass of the first particle is 6.3 ' 10$7 kg, what are (a) the mass of the second particle and (b) the magnitude of the charge of each particle?
[tex]a) 4.9X 10^{-7} Kg\\ b) 7.09X10^{-11} C[/tex]
We know that (from Newton’s third law) the magnitude of the force on the second particle due to the first particle [tex]F_{12}[/tex] equals the magnitude of the force on the first particle due to the second particle [tex]F_{21}[/tex] , so:
[tex]F_{12} = F_{21}[/tex]
Given:
The initial acceleration of the first particle, a1 = 7.0 m/s^2
The initial acceleration of the second particle, a2 = 9.0 m/s^2
Mass of the first particle, m1 = 6.3 * 10^(-7) kg
Separation between the two particles, d = 3.2 * 10^(-3) m
Using Coulomb's law, the force between two charges q1 and q2 is given by:
F = k * |q1 * q2| / d^2
Where k is Coulomb's constant.
Coulomb's law is a fundamental law of electrostatics that describes the interaction between charged particles. It states that the force between two point charges is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Since the acceleration of a particle is directly proportional to the net force acting on it, we can write:
m1 * a1 = k * |q1^2| / d^2
m2 * a2 = k * |q2^2| / d^2
Dividing the first equation by the second equation, we get:
m1 * a1 / m2 * a2 = q1^2 / q2^2
(m1 * a1) / (m2 * a2) = (q1^2) / (q2^2)
m2 = m1 * (a1 / a2)
Substituting the known values:
m2 = 6.3 * 10^(-7) kg * (7.0 m/s^2 / 9.0 m/s^2)
m2 = 4.9 * 10^(-7) kg
The mass of the second particle is 4.9 * 10^(-7) kg.
To find the magnitude of the charge of each particle, we can rearrange the first equation:
q1^2 = m1 * a1 * d^2 / k
Substituting the known values:
q1^2 = 6.3 * 10^(-7) kg * 7.0 m/s^2 * (3.2 * 10^(-3) m)^2 / k
q1 = sqrt(6.3 * 10^(-7) kg * 7.0 m/s^2 * (3.2 * 10^(-3) m)^2 / k
=> q1 = q2 = 7.09 × 10^-11 C
Therefore, the correct answers are:
[tex]a) 4.9X 10^{-7} Kg\\ b) 7.09X10^{-11} C[/tex]
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What are three tips to start a healthy dating relationship mentioned in the article? (Site 1)
Faith, respect, and effective communication are the three tips to start a healthy dating relationship mentioned in the article.
What are three recommendations for beginning a happy relationship?
Trust, respect, effective communication, adaptability, a common interest, time apart, different connections (with family and friends), and appreciation. Each partner needs to have confidence in the other. Never should your partner belittle you, test you, or say anything disparaging about you.
What are good relationships?
Healthy relationships involve open communication, honesty, trust, and respect between partners as well as work and compromise from both parties. There is no imbalance of power. Partners are free to make decisions together, respect each other's independence, and take individual actions without worrying about the consequences.
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A box slides down a frictionless ramp inclined at 30 degrees. What is the box’s acceleration? What is the acceleration if the coefficient of friction between the box and ramp is 0.34?
Frictionless ramp: The acceleration of a box sliding down a frictionless ramp inclined at 30 degrees can be determined using the equation for gravitational acceleration:
a = g * sin(θ)
where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), and θ is the angle of the ramp (30 degrees).
a = 9.8 * sin(30) = 4.9 m/s^2
Ramp with friction: If the coefficient of friction between the box and ramp is 0.34, the acceleration can be determined using the equation:
a = g * sin(θ) - μ * g * cos(θ)
where μ is the coefficient of friction.
a = 9.8 * sin(30) - 0.34 * 9.8 * cos(30) = 2.86 m/s^2
So the acceleration of the box sliding down a frictionless ramp inclined at 30 degrees is 4.9 m/s^2, and the acceleration if the coefficient of friction is 0.34 is 2.86 m/s^2.
what tool of l.b. jefferies' trade in rear window saves him from harm once he is discovered by his potentially murderous neighbor? group of answer choices lisa and her quick thinking his dark room chemicals his camera flashbulb the sharp edge of a camera lens
Answer:
The brightness of his flashbulbs temporarily saved him by blinding his would-be assassin.
Convert the following to engineering notation: (a) 0.045 W (b) 2000 pJ (c) 0.1 ns (d) 39,212 as (e) 3 \Omega3Ω (f) 18,000 m (g) 2,500,000,000,000 bits (h) 10^{15} \text { atoms } / \mathrm{cm}^{3}10 15atoms /cm 3
The following data can be converted to the engineering notation as the following. (a) 0.045 W is 45 mW. (b) 2000 pJ is 2nJ. (c) 0.1 ns is 100 pS (d) 39,212 as is 39.212 fs (e) 3 \Omega3Ω is 3Ω (f) 18,000 m is 18 km (g) 2,500,000,000,000 bits is 2.5 terabits (h) 0^{15} \text { atoms } / \mathrm{cm}^{3}10 15atoms /cm 3 is [tex]10^{21} \frac{atoms}{m^{3} }[/tex].
Engineering notation is the representation of expressing the numbers that are too big or too small and are represented in the decimal form times 10 raise to the power. It is similar to the scientific notation but in engineering notation, the powers of ten are always multiples of 3.
Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 100 is used, it is written in scientific notation.
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Compare the normal force exerted on the book by the inclined plane and the weight force exerted on the book by the earth.
Are they equal in magnitude?
1. Yes
2. No
3. Their magnitudes cannot be determined
since the forces are not in the same direction
No, the normal force exerted on the book by the inclined plane and the weight force exerted on the book by the earth are not equal in magnitude.
The normal force acts perpendicularly to the inclined plane, while the weight force is a downward force. Since they are not in the same direction, their magnitudes cannot be determined.
The magnitude of the normal force is determined by the angle of the inclined plane. Since the normal force acts perpendicularly to the inclined plane, it can be calculated by finding the cosine of the angle of the inclined plane multiplied by the weight of the object.
For example, if the inclined plane has an angle of 30°, the normal force would be cos(30°) times the weight of the object. On the other hand, the weight force is determined by the gravitational force, which is a constant and always acts in the downward direction. Thus, the magnitude of the weight force is always equal to the weight of the object.
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Which is carried by waves?
x disturbance
• energy
• matter
• space
The figure shows the electric field lines for two point charges separated by a small distance. Determine the ratio q1/q2.
The figure shows the electric field lines for two point charges separated by a small distance. Determine the ratio is [tex]-\frac{1}{3}[/tex].
The directions that a positive test charge would accelerate if it were placed along the electric field lines are indicated by the lines. Because of this, the lines are pointed in the direction of negatively charged source charges rather than positively charged source charges. Each line must have an arrowhead pointing in the proper direction to convey information about the field's direction. Any number of lines could be present in an electric field line pattern. The number of lines is typically regulated because drawing so many lines tends to make the patterns harder to read. Usually, a few lines around a charge are enough to convey the characteristics of the electric field in the area around the lines.
Field lines emerges from positive charge and go inside negative charge.
[tex]\frac{q_{1} }{q_{2} }[/tex]=[tex]\frac{-6}{18} =-\frac{1}{3}[/tex]
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a 1-megabit computer memory chip contains many 91 ff capacitors. each capacitor has a plate area of 1.22 x 10^-11 m^2. determine the pkate seperation of such a capacitor (assume an empty parallel-plate configuration.
The plate separation of such a capacitor is 1.186 nm or 11.86 Angstroms.
The question is not complete. A similar question is in the attachment. The formula for the capacitance of a parallel plate capacitor
C = ε₀ × A ÷ d
C = capacitance of the capacitor (Farad)C = ε₀ × A ÷ d
C × d = ε₀ × A
91 × 10⁻¹⁵ × d = 8.85 × 10⁻¹² × 1.22 × 10⁻¹¹
91 × 10⁻¹⁵ × d = 10.797 × 10⁻²³
d = 10.797 × 10⁻²³ ÷ 91 × 10⁻¹⁵
d = 0.1186 × 10⁻⁸
d = 1.186 × 10⁻⁹
1 nm (nanometers) = 10⁻⁹ m1 Angstroms = 10⁻¹⁰ md = 1.186 nm
d = 11.86 × 10⁻¹⁰ m
d = 11.86 Angstroms
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a 1000-mw(e) nuclear power plant operates at a thermal efficiency of 33% and at 75% capacity for 1 year. how many kilograms of nuclear fuel are consumed during the year?
The nuclear power plant needs 95.217 kg of nuclear fuel or uranium 235 is used during the whole year to operate.
Here the nuclear power plant produces 1000MW of energy.
So, for one year the total energy that can be produced = 1000× 365× 24 = 8760000 MWh
Since the reactor has a 75% capacity, energy produced = 8760000×75/100 = 6750000 MWh. = 6.75×10⁹ kWh
Converting to joules = 6.75× 10⁹× 3.6× 10⁶ = 2.365×10¹⁶
Thermal efficiency is 33%. So, 2.365×10¹⁶ × 0.33
= 7.80×10¹⁵ J.
To find out the mass, we need to know the number of atoms. So converting the energy to meV.
7.80× 10¹⁵ × 6.242× 10¹² = 4.87 ×10²⁸ meV
From one atom 200 meV is produced.
So, number of atoms = 4.87 ×10²⁸/200 = 2.44×10²⁶ atoms.
No of moles = number of atoms/ Avogadro's number = 2.44×10²⁶/ 6.022 ×10²³ = 405.18 moles.
Mass = Number of moles× molar mass
=405.18 × 235 = 95217.52 g = 95.217 Kg
So the amount of uranium 235 required by the nuclear reactor for an year is 95.217 g.
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which of the three objects experiences the greatest buoyant force?
The highest volume of water is displaced by the lead block and aluminum, which also has the largest volume and the strongest buoyant force.
What kind of force is buoyant, for instance?Here are a few real-world instances of the buoyant force. A ship floating in the ocean, a boat moving down a river, an iceberg floating in the water, a person wearing a life jacket floating in the water, a helium balloon rising in the air, etc. The density has a direct relationship with the buoyant force.
Are heavier things subject to larger buoyant forces?An object feels a buoyant force because the bottom is deeper in the liquid than the top, which results in a stronger upward pressure. As a result, any item submerged in a liquid experiences buoyancy.
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why is a thermometer included in the construction of a calorimeter?
A thermometer is included in the construction of a calorimeter to measure the temperature change that occurs during a chemical reaction.
A calorimeter is a device used to measure the heat transfer in a chemical reaction. This measurement is important because it allows scientists to determine the energy change that occurs during a reaction. The energy change can then be used to determine the energy transfer between the system and the surroundings, which is useful in studying thermodynamics.
A thermometer is included in the construction of a calorimeter to measure the temperature change that occurs during a chemical reaction. By measuring the initial and final temperature of the reaction, scientists can determine the energy transfer that has taken place. This is because energy transfer is directly proportional to the change in temperature.
In other words, as energy is transferred from one substance to another, the temperature of the substances will change. By measuring the temperature change, scientists can determine the energy transfer that has taken place. This information is then used to calculate the enthalpy change for the reaction, which is a measure of the energy transfer between the system and the surroundings.
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The radius of the big wheel on a penny-farthing is 0.50 m. Suppose a rider accelerates from rest to a linear speed of 5.0 m/s in 8.5 s. what would the angular acceleration of the big wheel be?
The angular acceleration of the big wheel would be 0.59 rad/s².
The linear speed of a point on the circumference of a wheel can be related to its angular velocity (ω) by the equation v = ωr, where r is the radius of the wheel.
The angular acceleration (α) of the wheel can be found using the equation α = Δω/Δt, where Δω is the change in angular velocity and Δt is the time interval over which the change occurs.
In this scenario, the linear speed of the big wheel is given as 5.0 m/s and its radius is 0.50 m. Therefore, the initial angular velocity of the wheel is ω = v/r = 5.0 m/s / 0.50 m = 10 rad/s. The time interval over which the speed increases is given as 8.5 s.
The final angular velocity can be calculated using the equation ωf = ωi + αt, where ωi is the initial angular velocity and t is the time interval.
Substituting the known values into the equation for angular acceleration, we get α = (ωf - ωi) / t = (10 - 0) / 8.5 s = 1.18 rad/s².
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Blue and white wands are rubbed together and held 1.35 cm apart. If the charge on the white- faced wand is 1.38 x 10-10 C, what is the magnitude of the force each wand ex one? Is the force attractive or repulsive? State your assumptions. (8 pts) erts on the other
We can conclude that the force exerted on each wand is repulsive, as the charges are both of the same sign.
What is mangitude?Magnitude is a measure of the size of a physical quantity usually explain it as a numerical value of the octane used to compare the relative size of different object or phenomena it is typically used to measure the intensity soldiers trained the something magnitude is a concept applicable how many different physical quantities of the light sound and its speed and force.
The magnitude of the force exerted by each wand can be calculated using Coulomb’s Law, which states that the force is equal to the product of the two charges, divided by the square of the distance between them. Since we know the charge on the white-faced wand, we can calculate the force:
F = (1.38 x 10-10 C)2 / (1.35 cm x 10-2 m)2
F = 0.0012 N
The force between the two wands is repulsive, as the charges are both of the same sign.
Assuming that the wands are not charged before they are rubbed together and that the distance between them remains constant, we can conclude that the force exerted on each wand is repulsive, as the charges are both of the same sign.
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a gaseous substance with a molecular weight of 50 is at 200 psia, 300f, and it has a density of 1.5 lbm/ft3. can this gas be treated as an ideal gas?
Yes, this gas can be treated as an ideal gas with a molecular weight of 50 is at 200 psia, 300f, and it has a density of 1.5 lbm/ft3.
This is because the molecular weight of the gas is relatively low, at 50, and the pressure and temperature of the gas are both within the range of the ideal gas law. The ideal gas law states that for a gas at a given temperature and pressure, the product of its pressure and volume is equal to the product of its temperature and molar gas constant. In this case, the pressure, temperature, and molar gas constant are all within the range of the ideal gas law, so the gas can be treated as an ideal gas.
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using the field of view calculated in exercise 1 for the high power lens, what is the approximate diameter of each of the cells in the bacteria coccus form slide in photo 10? show your calculations.
The approximate diameter of each cell in the Bacteria Coccus Form slide in Photo 10 is 0.33 micrometers.
The formula to calculate the diameter of an object in the field of view is:
diameter = field of view (FOV) / magnification
First, we need to convert the FOV from millimeters to micrometers:
0.2mm = 200µm
Now, we can use the formula to calculate the diameter:
diameter = 200µm / 600 = 0.33µm
So, the approximate diameter of each cell in the Bacteria Coccus Form slide in Photo 10 is 0.33 micrometers.
Field of View (FOV) is the extent of the observable world that is seen at any given moment. It refers to the extent of the observable environment that is seen by an observer's eye or a camera lens. In the context of visual representation, FOV is often expressed as an angle, which defines the breadth of the visible area. A larger FOV allows more of the environment to be seen at once, while a smaller FOV provides a narrower, more focused view.
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9.15 electron microscopes can obtain images with several hundred-fold higher resolution than
Electron microscopes can obtain images with several hundredfold higher resolution than optical microscopes because of the short wavelength obtainable from a beam of electrons.
Electron microscopes differ from light microscopes in that they generate an image of a specimen using an electron beam rather than a light beam. Because electrons have a much shorter wavelength than visible light, electron microscopes can produce higher-resolution images than traditional light microscopes.
Thus, the resolution of an electron microscope for imaging cellular structure or proteins is theoretically limitless. Because of the objective lens system in electron microscopes, the resolution is practically limited to 0.1 nm.
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Sasha lifts a couch from the ground floor of her house to the attic. If
the couch has a mass of 120 kg and is lifted 8.2 m, then what is the
energy gained by the couch?
J
Use g-9.81 m/s2 and do not include units in your answer.
Work done or energy used to lift the mass is the product of the force applied on it and the displacement. The energy used for a force of 1176 N here is 9643.2 J.
What is work done ?Work done is a vector quantity measuring how effectively the force make a displacement. Thus, it is the product of force and displacement. Work done by body is equal to the energy used by it.
Here the force that has to be applied to lift the mass is equal to its weight
F = mg
m = 120 kg
g = 9.8 m/s²
then F = 120 × 9.8 m/s² = 1176 N.
Displacement of the couch = 8.2 m.
then work done = F. ds
W = 8.2 m ×1176 N = 9643 J.
Therefore, the energy gained by the coach is equal to the work done by the person that is 9643 J.
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Why is kinetic energy not conserved in inelastic collisions? What if, theoretically, there was an inelastic collision that did not generate any heat?
Kinetic energy is not conserved in inelastic collisions because part of the energy is converted into internal energy. If there was an inelastic collision that did not generate any heat, it would still result in a decrease in total kinetic energy, as the internal energy would remain constant.
In an inelastic collision, kinetic energy is not conserved due to the conversion of some of the energy into internal energy. This is the case even if the collision does not produce any heat.
The total kinetic energy still decreases, as the internal energy remains constant. Therefore, in an inelastic collision, part of the kinetic energy is transformed into internal energy, resulting in a decrease in the total kinetic energy of the system.
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What simple machine you would use to do the following job. You want to build a jump for your bike. Your dad said you can use the pile of dirt out behind the garage for it.
We can use a log and arock or something hard to make a pivot and place on it the log to build a jump.
BUILD HIGHER JUMPThere are several exercises that can be done to increase the height of the jump.
The exercise to train the jump is by jumping jack. Jumping jacks is a type of exercise plyometric that can help you jump higher by building lower body strength. This exercise can also increase the heart rate.
Jumping jacks are useful for improving performance in activities that require you to move quickly in different directions.
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A 0.230-kg baseball is thrown with a speed of 41 m/s.What is the ball's momentum?
The momentum of the 0.230-kg baseball thrown with a speed of 41 m/s is 9.53 kg m/s. This means that if the ball were to collide with an object with equal and opposite momentum, the combined momentum of the two objects would be zero.
Momentum is a measure of an object's motion and is calculated by multiplying its mass and velocity. In physics, it is an important concept as it is conserved in many cases and helps to predict how objects will interact with each other.
The momentum of an object can be calculated using the formula: p = mv, where p is momentum, m is the mass of the object, and v is its velocity. In this case, the mass of the baseball is 0.230 kg, and its velocity is 41 m/s. Therefore, the momentum of the baseball can be calculated as follows:
p = mv = 0.230 kg * 41 m/s = 9.53 kg m/s.
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According to newton's third law of motion, when one object exerts a force on a second object, what are the forces?.
When object A exerts a force on object B, object B must exert an equal and opposite force on object A. This law essentially expresses a certain symmetry.
Forces always occur in pairs, and one body cannot exert a force on another without experiencing the force itself. Newton's third law of motion states that whenever a first object exerts a force on her second object, the first object experiences a force equal but opposite to the force it is exerting . Newton's third law of motion states that whenever the first object exerts a force on his second object, the first object experiences a force equal but opposite to the force it is exerting .
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deciding that a process that fills bottles with soda is functioning properly by checking the weights for a sample of bottles is an example of inferential statistics.. T/F
True. Checking the weights of a sample of bottles to decide if a process that fills bottles with soda is functioning properly is an example of inferential statistics.
Inferential statistics is a branch of statistics that involves using a sample of data to make inferences or conclusions about a larger population. In this case, the sample of bottles is used to make inferences about the entire process of filling bottles with soda, with the goal of determining if the process is functioning properly. This type of statistical analysis is used to make informed decisions and predictions about a population based on limited information, making it an important tool in many industries and fields.
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Numerical problem ? A load of 680N is lifted from A to C by 500N force on an inclined plane as shown in the diagram study the. diagram and calculate.? input work
The work done is 6000J
What is Work Done?The product of a force's component acting in the displacement's direction and its magnitude is known as the work done by the force. Formula.
The following formula can be used to determine work by multiplying force and distance in the direction of the force. Unit: W = F d.
Given
Load: 680 Effort: 500 Ed: 12 Meters Ld: 8 metersOutput work formula
L*Ld = 680*8 = 5440
Hence the output is 5440J
Input work
We know
the input work formula is
E*Ed
500*12= 6000J
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william tell must split the apple atop his son's head from a distance of 27 m. when william aims directly at the apple, the arrow is horizontal. at what angle must he aim it to hit the apple if the arrow travels at a speed of 35 m/s?
The angle at which William Tell must aim the arrow is approximately 32.2 degrees.
To find the angle at which William Tell must aim the arrow to hit the apple, you need to use the equation of motion for a projectile under constant gravitational acceleration.
Let's call the angle at which William aims the arrow "θ". Then, the horizontal velocity of the arrow (vx) can be found using vx = 35 m/s x cos(θ). The vertical velocity of the arrow (vy) can be found using vy = 35 m/s x sin(θ).
Using the kinematic equation for vertical motion under constant acceleration, we can find the time it takes for the arrow to reach the height of the apple:
vy = v0 + a x t
0 = 35 m/s x sin(θ) - 9.8 m/s² x t
t = (35 m/s x sin(θ)) / 9.8 m/s²
Next, use the horizontal velocity of the arrow and the time found above to find the horizontal distance it travels:
x = vx x t
x = 35 m/s x cos(θ) x (35 m/s x sin(θ)) / 9.8 m/s²
Finally, set x equal to the distance to the apple (27 m) and solve for θ using trigonometry:
27 m = 35 m/s x cos(θ) x (35 m/s x sin(θ)) / 9.8 m/s²
cos(θ) = sqrt(9.8 m/s² x 27 m / (35 m/s)²)
θ = arc cos(sqrt(9.8 m/s² x 27 m / (35 m/s)²))
The angle at which William Tell must aim the arrow is approximately 32.2 degrees.
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