An object can encounter some resistance when moving through the fluid medium of air.
The drag force is the oppositional force applied by the air to a moving object. The size of the cross section A of the front face of the item, the density of the air, and the square of the object's velocity v all contribute to the drag force.
With motion exclusively in the vertical direction and letting
downward be positive, we have that
dv/dt = g - pv, where g = 32 ft/[tex]s^{2}[/tex], and so
dv/dt + pv = g. The integrating factor is [tex]e^{(pt)}[/tex], so
d/dt([tex]e^{(pt)}[/tex] * v) = g×[tex]e^{(pt)}[/tex] ----->
[tex]e^{(pt)}[/tex] * v = (g/p)*[tex]e^{(pt)}[/tex] + C ----->
v(t) = (g/p) + C×[tex]e^{(pt)}[/tex]
Now v(0) = (g/p) + C = 0, and so C = -g/p, giving us
v(t) = (g/p)×(1 - [tex]e^{(pt)}[/tex]).
Now we are given that lim(t->infinity)(v(t)) = 99 mi/h = 145.2 ft/s,
so since [tex]e^{(pt)}[/tex]-> 0 as t -> infinity we have g/p = 145.2 ft/s ------>
p = 32 ft/s^2 / (145.2 ft/s) = 0.2204 s^-1 .
Next, since we have defined downward as positive, the expression
we have for v(t) will equal dy/dt where y(0) = 0 and y increases as
the paratrooper falls. So
dy/dt = v(t) = (g/p)×(1 - [tex]e^{(pt)}[/tex])), so
y(t) = (g/p)×(t + (1/p)×[tex]e^{(pt)}[/tex]) + K.
Now y(0) = (g/p)×(0 + (1/p)) + K = 0 ----->
K = -(g/p^2) = 32 / 0.2204^2 = -658.76 ft, so
y(t) = (145.2)×(t + (4.5372)×e^(-0.2204×t)) - 658.76.
Next, y(6) = (145.2)×(6 + (4.5372)×e^(-0.2204×6)) - 658.76 = 444.84 feet.
The computed drag coefficient is substantially higher than anticipated.
The free fall distance is the longest distance an individual can travel in a predetermined amount of time. However, the distance covered in the time frame indicated in the news report is significantly greater than the greatest distance that could be covered. Consequently, the news story is exaggerated.
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1.7-3 a polyethylene bar with a diameter d1 5 4.0 in. is placed inside a steel tube with an inner diameter d2 5 4.01 in. (see figure). the polyethylene bar is then compressed by an axial force p. at what value of the force p will the space between the polyethylene bar and the steel tube be closed? for polyethylene, assume e 5 200 ksi and n 5 0.4.
The space between the polyethylene bar and the steel tube will be closed when the applied force P is 476.48 Pounds.
What is Hooke's Law?Hooke's Law is a principle in physics that describes the relationship between the applied force on an object and the resulting deformation of that object. The law states that, within the elastic range of deformation, the magnitude of the deformation (strain) is directly proportional to the magnitude of the applied force (stress).
To determine the force P at which the space between the polyethylene bar and the steel tube is closed, the relationship between the applied force and the resulting deformation of the polyethylene bar needs to be known. Since the polyethylene bar is in the elastic range of deformation, Hooke's Law can be used.
The deformation of the bar is given by:
δ = (Pd1) / (2πE(d1/2) ²)
Where:
δ = deformation (inches)
P = applied force (pounds)
d1 = diameter of the polyethylene bar (inches)
E = modulus of elasticity of the polyethylene (ksi)
The space between the polyethylene bar and the steel tube is closed when the deformation of the bar is equal to the difference in the inner diameters of the two tubes:
δ = d2 - d1
By substituting the given values and solving for P, the force at which the space between the polyethylene bar and the steel tube is closed can be found.
P = (2πE(d1/2)²×(d2-d1)) / d1
P = (2π200(4/2)² × (4.01-4)) / 4 = 476.48 Pounds
Therefore, the space between the polyethylene bar and the steel tube will be closed when the applied force P is 476.48 Pounds.
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how far must the stone fall so that the pulley has 4.30 j of kinetic energy? express your answer numerically in meters to three significant figures.
To calculate the distance first you have to find the angular velocity of the pulley with the formula K.E = 1/2 I ω² using the given value of kinetic energy. Then, also find the potential energy loss of the stone and then the distance.
Since the system here is released from rest, therefore there will be loss in potential energy of the system and gain in its kinetic energy.
Therefore,
Loss in potential energy = gain in (kinetic energy of the pulley + kinetic energy of the stone)
Using the given mass of the pulley disk, find its moment of Inertia.
Inertia (I) = 1/2 mass x radius²
Then, find the angular velocity of the pulley,
K.E = 1/2 I ω²
Finally, find the total kinetic energy of the system by dividing the two fractions of the pulley's kinetic energies .
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a student slowly adds mass to the top of block b. when a total mass m0 has been added to the top of block b, block a begins to accelerate across the tabletop. in a clear, coherent, paragraph-length response, explain in terms of the net force on block a why block a remained at rest even as mass was added to block b, but block a accelerates once a total mass m0 was added to block b.
As a result, the thread holding the two objects together is pushing on them both equally strongly but in different directions.
In this problem, a string connects the two objects, transferring the force of one object to the other. The force is exerted in a different direction while remaining the same magnitude by wrapping the string around a pulley. A string links object A and object B. Gravity will cause object B to fall downward, pulling on one end of the string it is attached to in the process. Newton's law of action-reaction predicts that object B will be pulled upward by this lower end of the string. Object A is attached to the string's other end on the opposite end. Object A is being pulled to the right by this end of the string. Item A is pulled upward by the string, and object B is pulled to the right. The pulley has altered the force's direction of application.
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the acceleration of a particle is defined by the relation 1 , xa k e where k is a constant. knowing that the velocity of the particle is 9v m/s when 3x m and that the particle comes to rest at the origin, determine (a) the value of k, (b) the velocity of the particle when 2x m.
Determine (a) the value of k in light of the fact that the particle has a velocity of +9 m/s at x=-3 m and rests at the origin.
How fast are particles moving?The speed of a particle—real or hypothetical—in a medium because it transmits a pulse is known as the particle velocity. The meter per second (m/s) is the metric unit for particle speed. Most of the time, this pressure wave is longitudinal, such as with noise, but it may also be transverse, similar to the vibration of the a tight string.
Why is a particle at rest important?You could understand the phrase "A particle in repose prefers to stay at rest" to mean that what a particle that isn't moving relative to a certain context aware tends to remain stationary relative to those same things.
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A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 4.0 m/s, skates by with the puck. After 2.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.46 m/s2, determine each of the following.
(a) How long does it take him to catch his opponent? (Assume the player with the puck remains in motion at constant speed.)
1 s
(b) How far has he traveled in that time?
2 m
The time it takes the hockey player to catch his opponent is 8.2s and he has he traveled 130m in that time.
A defenseman's main goal is to keep the team with the puck from scoring into their net. Therefore, the defensemen will frequently step up and stop the puck-bearing team from moving it into their defensive zone when they are skating through the neutral zone. The dump and chase tactic is used in this situation.
a) The given data is:
v = 4 m/s
t = 2.8 s
d=?
Use the formula:
v = d/t....(i)
Put the value of given data in equation (i)
d = v × t
d = 4 m/s × 2.8 s
d = 130 m
Thus, distance will be 8.2 s
Ice hockey skates are typically used for leisure ice skating by themselves, but they can also be used for the sports of ice hockey and ringette. The components of each individual skate are the boot, laces, blade, and blade holder.
b)
d = 8.2 s
t = 2.80 s
Use the formula:
v = d/t....(i)
Put the value of given data in equation (i)
d = v × t
d = 4 m/s × 8.2 s
d = 8.2 s
Thus, distance will be 8.2 s
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6-7 Collisions and Explosions (1-D)
1. A flatcar with mass M, traveling at speed v, collides with and couples to a parked
boxcar. They move off together with a speed of 1/3 v. What is the mass of the boxcar?
We know that (momentum after) = (momentum before)
We remember that (Momentum) = (mass) x (speed)
Mass of the flatcar = M
Mass of the boxcar = m
Speed of the flatcar before the collision = v
Speed of the two cars stuck together after the collision = v/3
Total momentum before the collision = M · v
Total momentum after the collision = (M + m) · (v/3)
Momentum is conserved. (Total after) = (total before)
(M + m) · (v/3) = (M · v)
Eliminate parentheses on the left. Mv/3 + mv/3 = Mv
Divide both sides of the equation by v . M/3 + m/3 = M
Multiply both sides of the equation by 3 . M + m = 3M
Subtract M from both sides of the equation. m = 2M
The mass of the boxcar is 2 times the mass of the flatcar.
After release into the synaptic cleft, the neurotransmitter dopamine is actively taken up by the cells via specific dopamine transporters. The drug cocaine interferes with this process and is therefore called a reuptake inhibitor. The inhibition of the transporter at a certain cocaine concentration is qualitatively represented in the following graph. Based on this graph, which of the following describes the effect of cocaine on the kinetics of dopamine reuptake by the transporter?
A) In the presence of cocaine, the maximal rate of transport (Vmax) is unaffected, but the apparent affinity of the transporter for dopamine is reduced.
B) In the presence of cocaine, the maximal rate of transport (Vmax) is reduced, but the apparent affinity of the transporter for dopamine is unaffected.
C) In the presence of cocaine, the maximal rate of transport (Vmax) is enhanced, but the apparent affinity of the transporter for dopamine is unaffected.
D) In the presence of cocaine, both the maximal rate of transport (Vmax) and the apparent affinity of the transporter for dopamine are enhanced.
E) In the presence of cocaine, both the maximal rate of transport (Vmax) and the apparent affinity of the transporter for dopamine are unaffected, but the transporter is nevertheless inhibited.
In the presence of cocaine, maximum transport velocity (Vmax) is unaffected, but the transporter's apparent affinity for dopamine is reduced
Cocaine has psychomotor stimulating effects similar to amphetamines and related compounds. It increases transmitter concentrations at both noradrenergic and dopaminergic synapses and also acts as an anesthetic. Evidence of effects on cellular action potentials suggests that cocaine affects both fast Na+ channels and repolarizing K+, but not Ca2+ channels. Cocaine is not seen to have an affect on Vmax. But it is seen that dopamine transporters decrease its affinity for dopamine in presence of cocaine.
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you need to determine the density of a ceramic statue. if you suspend it from a spring scale, the scale reads 30.4 n . if you then lower the statue into a tub of water, so that it is completely submerged, the scale reads 17.0 n .
In this case, the weight in air is 30.4 N and the weight in water is 17.0 N the density can be found using the formula:
density of object = (weight in air - weight in water) / volume of object
The volume of the statue is required to calculate the density using the formula:
density of object = (weight in air - weight in water) / volume of object
To determine the density of the ceramic statue, you can use the concept of buoyancy. The buoyant force on an object submerged in a fluid is equal to the weight of the fluid that is displaced by the object. This can be calculated using the equation:
density of object = (weight in air - weight in water) / volume of object
In this case, the weight in air is 30.4 N and the weight in water is 17.0 N. To calculate the volume of the object, you will need to measure it or have the information available. Once you have the volume, you can plug it into the above equation and calculate the density of the ceramic statue.
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which of the following diagrams represents the equipotential curves in the region between a positive point charge and a negatively charged metal plate?
These lines, which are also known as electric field lines, point in the direction that a positive test charge would accelerate if it were placed along the line.
Is there a positive to negative transition in the electric field lines?The direction of an electric field line is always away from a positive charge and in the direction of a negative charge. In actuality, positive and negative charges are where electric fields begin and end.These lines, which are also known as electric field lines, point in the direction that a positive test charge would accelerate if it were placed along the line. As a result, the lines are pointed in the opposite direction of positively charged source charges—that is, toward negatively charged source charges.These lines, which are also known as electric field lines, point in the direction that a positive test charge would accelerate if it were placed along the line.To learn more about electric field refer to:
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Can anyone help me answer this question?
Find the mass of an object whose density is 250 kg / cm^3 and volume is 2000 mm^3.
The Mass of the object is 500kg have a density of 250 kg/cm³.
What is Density?Mass per unit of volume is referred to as density, volumetric mass density, or specific mass. The Latin sign D may also be used, however, the Greek letter rho is more frequently employed to represent density. Mass divided by volume is the mathematical formula for density.
Although this is technically incorrect, density is generally described as a substance's weight divided by its volume. The term "specific weight" is more accurate.
The density and mass concentration of a pure substance is numerically equivalent. Density can affect buoyancy, purity, and packing. Varied materials typically have different densities. At normal temperatures and pressures, osmium and iridium have the highest densities of any known elements.
Volume = 2000mm³ = 2cm³
Density = Mass / Volume
250 = Mass/ 2
mass = 500kg
Hence, the mass will be 500kg.
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approximately 5.4 million hybrid passenger vehicles have been sold in the united states since 1999. approximately 1.4 million plug-in electric passenger vehicles have been sold in the united states since 2010. assume the average energy stored in a hybrid vehicle battery is 1.5 kilowatt-hours (kwh ), and assume the average energy stored in a plug-in electric vehicle battery is 45 kwh .
The total energy stored in these vehicles in gigawatt-hours is 57.4 GWh.
Based on the given information, if 80% of the 5.4 million hybrid vehicles sold in the United States since 1999 are still in service, there are approximately 4.32 million hybrid vehicles currently in use. If the average energy stored in a hybrid vehicle battery is 1.5 kilowatt-hours (kWh), this means that the total energy stored in these vehicles is approximately 6.48 gigawatt-hours (GWh).
Similarly, if 90% of the 1.4 million plug-in electric vehicles sold in the United States since 2010 are still in service, there are approximately 1.26 million plug-in electric vehicles currently in use. If the average energy stored in a plug-in electric vehicle battery is 45 kWh, this means that the total energy stored in these vehicles is approximately 57.4 GWh.
Therefore, the total energy stored in the hybrid and plug-in electric vehicles still in service in the United States is approximately 63.88 GWh. This is a significant amount of energy that can be used for transportation and potentially for other energy needs as well.
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the froude number, fr, is a dimensionless value that describes different flow regimes of open channel flow. if it depends on velocity v , gravitational constant g, and length l, use buckingham pi theorem to show.T/F
False. Buckingham Pi theorem states that if a physical relationship involves a certain number of independent variables, then the relationship can be written as a product of powers of a certain number of dimensionless groups.
What is Buckingham Pi theorem?Buckingham Pi theorem is a mathematical theorem that states that any physical system can be expressed as a combination of an appropriate number of variables, together with the appropriate number of independent dimensionless parameters. The theorem was developed by Edward Buckingham in 1914 and is considered to be the most general form of dimensional analysis.
The Froude number does not depend on the independent variables mentioned (velocity, gravitational constant, and length) so Buckingham Pi theorem is not applicable.
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Which statements about rainbows are true? Choose more than one answer.
The true options about a rainbow are, sunlight slows down as it enters water droplets in the sky. Rainbows are a type of interference pattern. Refracted Sunlight makes the arc in the rainbow.
Are rainbows caused by refraction or diffraction?The result of light striking water droplets is a multicolored arc. A rainbow is a meteorological phenomenon that appears in the sky as a spectrum of light due to light reflection, refraction, and dispersion in water droplets. It appears as a circular arc with various colors. The part of the sky right across from the Sun is where rainbows brought on by sunlight always occur.
When light encounters a water droplet, it is bent at the air-water interface and penetrates the droplet, where it is divided into seven hues. The light then reflects inside the droplet before being refracted out into the atmosphere once more, creating a rainbow appearance.
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two securities that have different risks and returns?a. standard deviationb. coefficient of variation
For the two securities that have distinct risks and returns, the appropriate measure is the A: standard deviation.
A standard deviation (symbol σ) is a measure of how disseminated the data is in relation to the mean. A low standard deviation indicates that data are clustered around the mean; while a high standard deviation shows that data are more spread out.
Standard deviation is used to measure and compare the two securities that have distinct risks and returns. So option A: standard deviation is the correct answer.
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determine the work required to deflect a linear spring with a spring constant of 70 kn/m by 20 cm from its rest position. (5points)
The work required to deflect a linear spring by 20 cm from its rest position with a spring constant of 70 kn/m is 1.4 KJ.
What is spring constant?spring constants (physics) A spring property defined as the ratio of the force acting on the spring to the displacement induced by it. Hooke's Law states that as a spring is extended, the force exerted is proportional to the increase in length from the equilibrium length. F represents the force, while x represents the change in spring length. The spring constant is the proportional constant k. It is a measure of the stiffness of the spring. When a spring is stretched or compressed by an amount x from its equilibrium length, it produces a force F = -kx in the direction of its equilibrium position.
Here,
spring constant=70 KN/m
d=0.2 m
W=kx²/2
=70*10^3(0.2²)/2
=1.4 KJ
The work required to deflect a linear spring with a spring constant of 70 kn/m by 20 cm from its rest position is 1.4 KJ.
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1. How much force is required to
accelerate a 795 kg car by 15 m/s2?
Answer: 11925 N
Explanation: It's a very simple question.
According to Newton's 2nd law,
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
F=ma
where m = mass of an object
a= acceleration
F = 795*15
=11925 N
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Homework and les...
A charged particle, labeled A, is located at the midpoint between
two other charged particles, labeled B and C, as shown. Particles
B and C are fixed in place (they cannot move). The sign of the
charges on all three particles is the same. When particle A is
released, it starts drifting toward C. What can be determined
from this behavior?
A
The charge on A is larger than the charge on B.
The charge on A is
larger than the charge on C.
The charge on B is larger than the charge on C.
The charge on C is larger than the charge on B.
The charge on B is larger than the charge on A.
B
the variation of pressure with density in a thick gas layer is given by , where c and n are constants. noting that the pressure change across a differential fluid layer of thickness dz in the vertical z-direction is given as , obtain a relation for pressure as a function of elevation z. take the pressure and density at z
This is a relation for pressure as a function of elevation z.
What is pressure?Pressure is a measure of the force that is applied over a given area. It is expressed in units such as pounds per square inch, atmospheres, or pascals.
Let the pressure at z be denoted by P(z) and the density at z be denoted by ρ(z).
From the given relation, we have
$$\frac{dP}{d\rho}= c\rho^n$$
The given relation for pressure change across a differential fluid layer of thickness dz in the vertical z-direction is given as
$$dP = -g \rho dz$$
where g is the acceleration due to gravity.
Substituting for $dP/d\rho$ in terms of $\rho$ from the first expression and integrating both sides with respect to $z$, we get:
$$P(z) - P(0) = -g \int_0^z \rho^{n+1} dz + C $$
where C is a constant of integration. Since $P(0)$ denotes the pressure at z=0, it can be written as:
$$P(z) = -g \int_0^z \rho^{n+1} dz + P(0) $$
This is a relation for pressure as a function of elevation z.
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If a laborer weighing 895N and carrying bricks weighing 575N to scaffold up a ladder 3.1 m above the ground how much work has he done? If he climbed the ladder in 12.0 seconds what was his power output?show your work
If he climbed the ladder in 12.0 seconds, the laborer's power output is 394.875 watts.
What is work?Work is the product of force and distance and is measured in Joules (J). In physics, work is the energy transferred to or from object via application of force along a displacement.
As, work = force x distance x cos(theta)
So, the work done by the laborer would be:
work = (895 N + 575 N) x 3.1 m x 1 = 4738.5 J
As, power = work / time
where time is measured in seconds.
power = 4738.5 J / 12.0 s = 394.875 W
So, the laborer's power output is 394.875 watts.
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An inclined track is secured to a table. The height of the highest point of the above the tabletop is h1. The height from the tabletop to the floor is h2. A block of as M is released from rest and slides down the track such that all the frictional forces are considered negligible. The block leaves the track horizontally and strikes the ground at a distance D. Which of the following statements is correct about the scenario? Select two answers.
answer choices
the total mechanical energy of the system containing only the block increases from the moment of release to the moment it hits the ground.
the total mechanical energy of the system containing only the black remains constant
the total mechanical energy of the block-earth system remains constant
the total mechanical energy of the block-earth system increases from the moment of release to the moment it hits the ground.
The total mechanical energy of the block-earth system remains constant, and the total mechanical energy of the system containing only the block increases from the moment of release to the moment it hits the ground.
What is mechanical energy?Mechanical energy is energy associated with the motion and position of an object. It is the sum of both the kinetic energy, which is energy associated with the object's motion, and the potential energy, which is energy associated with the object's position. Mechanical energy is present in a variety of forms, including kinetic energy, potential energy, heat, and elastic energy. Mechanical energy is converted into other forms of energy, such as thermal energy, electrical energy, and chemical energy. Mechanical energy can be used to do work, such as turning a crank to lift a heavy object, and can be harnessed to power machines and devices. Mechanical energy is an important concept in physics and engineering, as it can be used to analyze the motion and behavior of objects, and to develop solutions to problems.
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what two quantities could be graphed to yield a straight line whose slope could be used to calculate a numerical value for the mass of the cart?
Railway tracks or the freeway quantities could be graphed to yield a straight line whose slope could be used to calculate a numerical value for the mass of the cart.
What is Slope ?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. According to linguists, the Middle English adverb aslope, which meaning "at an angle," is where the term slope is said to have originated. You can use the word's noun form to describe things that are sloped or at an angle, such as a steep hill or a ramp.
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A sea If the determine 103,000 N Im² divor. density 35M 10301 H=10M total ko no ros belos Surface of the Sea be Sea water is 1.03g/cm²³3 and g=10Nig take atmospheric Pressure to be 103000.calculate total pressure
A sea or an ocean's water is known as seawater or salt water. Oceans around the world have an average salinity of 3.5% (35 g/L, 35 ppt, 600 mM).
What is the density of the sea?Fresh water has a density of 1 g/cm3 at 4 oC (see section 5.1), but adding salts and other dissolved substances raises the density of surface seawater to between 1.02 and 1.03 g/cm3. Seawater's density can be raised by lowering its temperature, raising its salinity, or raising the pressure.Oceans are frequently referred to as "seas" by people. Geographers define a sea as an area of the water that is entirely or partially contained by land.Density can be defined as a substance's weight in relation to its volume. A gramme per millilitre is about how dense water is, however this might vary depending on temperature or the things that are dissolved in it.To learn more about seawater refer to:
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i.
An ant crawl around a circular track of are length 22cm. At an instant it makes an
angular displacement 45°, then the radius of that circular track iS
The correct answer is 2.77m.
a teacher finds an old lightbulb in a supply room. the teacher asks a student to design a procedure to determine if the lightbulb is ohmic or nonohmic. the student plans to connect the light bulb to batteries of different emfemf and measure the potential difference across and the current through the lightbulb. which of the following is the best way to analyze the data to determine if the lightbulb is ohmic or nonohmic?
The correct answer is B) Graphing the potential difference across the lightbulb as a function of the current through the lightbulb to see if there is a linear relationship.
An ohmic material is one that has a linear relationship between the current flowing through it and the potential difference across it. The resistance of an ohmic material does not change with the current flowing through it.
Therefore, the best way to analyse the data to determine if the lightbulb is ohmic or nonohmic is to graph the potential difference across the lightbulb as a function of the current through the lightbulb. If the graph is a straight line, it indicates that the lightbulb is ohmic. If the graph is not a straight line, it indicates that the lightbulb is nonohmic.
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Complete Question:
A teacher finds an old lightbulb in a supply room. The teacher asks a student to design a procedure to determine if the lightbulb is ohmic or nonohmic. The student plans to connect the light bulb to batteries of different emf and measure the potential difference across and the current through the lightbulb. Which of the following is the best way to analyse the data to determine if the lightbulb is ohmic or nonohmic?
A) Calculating the resistance for each pair of potential difference and current measurements, and then averaging all of the resistance values.
B) Graphing the potential difference across the lightbulb as a function of current through the lightbulb to see if there is a linear relationship.
C) Graphing the power of the lightbulb as a function of the potential difference across the lightbulb to see if there is a linear relationship.
D) Averaging all of the values of the potential difference and averaging all the values of the current and then calculating an overall value for resistance based on averages
If a laborer weighing 895N and carrying bricks weighing 575N to scaffold up a ladder 3.1 m above the ground how much work has he done?
Answer:
Explanation:
W=Fd
While painting the top of an antenna 206 m in height, a worker accidentally lets a 1.30-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?
While painting the top of an antenna 206 m in height, a worker accidentally lets a 1.30-L water bottle fall from his lunchbox, the increase in temperature of the water is approximately 0.48 degrees Celsius.
To find the increase in temperature of the water bottle.
To calculate the change in mechanical energy of the water bottle, we can use the following formula:
Δ[tex]E_{mech[/tex] = m × g × h
where m is the mass of the water bottle, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height of the antenna (206 m).
Δ[tex]E_{mech[/tex] = 1.30 kg × 9.81 m/s² × 206 m
Δ[tex]E_{mech[/tex] ≈ 2605.646 J
Since the worker accidentally drops the bottle, we know that the change in mechanical energy is negative (lost energy).
Now, to find the increase in temperature (ΔT) of the water, we can use the formula:
Δ[tex]E_{int[/tex] = m × c × ΔT
where Δ[tex]E_{int[/tex] is the change in internal energy (heat), m is the mass of the water bottle, c is the specific heat capacity of water (approximately 4186 J/(kg°C)), and ΔT is the increase in temperature we want to find.
Since the quantity of heat (Q) is equal to the magnitude of the change in mechanical energy (|Δ[tex]E_{mech[/tex]|):
|Δ[tex]E_{mech[/tex]| = m × c × ΔT
ΔT = |Δ[tex]E_{mech[/tex]| ÷ (m × c)
ΔT ≈ 2605.646 J ÷ (1.30 kg × 4186 J/(kg°C))
ΔT ≈ 0.48°C
Thus, the increase in temperature of the water bottle is approximately 0.48°C.
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A vertical force of 80 lb acts on the crankshaft
I need to see all work for these not just the steps!
Part A Determine the horizontal equilibrium force P that must be applied to the handle. The bearings are properly aligned and exert only force reactions on the shaft.
Part B Determine the x, y, z components of force at the smooth journal bearing A.
Part C Determine the x, y, z components of force at the thrust bearing B.
x-component: 0 lb (there is no force acting in the x-direction)
y-component: 0 lb (there is no force acting in the y-direction)
z-component: 80 lb (this is the vertical force acting on the crankshaft)
Part C:x-component: -80 lb (this is the horizontal force P that must be applied to the handle in the opposite direction to achieve equilibrium)
y-component: 0 lb (there is no force acting in the y-direction)
z-component: 0 lb (there is no force acting in the z-direction)
CrankShaft Force ComponentsPart A:
To determine the horizontal equilibrium force P that must be applied to the handle, we need to consider the forces acting on the crankshaft. The only force acting on the crankshaft is the vertical force of 80 lb, which means that a horizontal force P must be applied to the handle in the opposite direction in order to achieve equilibrium. Therefore, P = -80 lb (the negative sign indicates that the force is in the opposite direction).
Part B:
The x, y, and z components of force at the smooth journal bearing A are as follows:
x-component: 0 lb (there is no force acting in the x-direction)
y-component: 0 lb (there is no force acting in the y-direction)
z-component: 80 lb (this is the vertical force acting on the crankshaft)
Part C:
The x, y, and z components of force at the thrust bearing B are as follows:
x-component: -80 lb (this is the horizontal force P that must be applied to the handle in the opposite direction to achieve equilibrium)
y-component: 0 lb (there is no force acting in the y-direction)
z-component: 0 lb (there is no force acting in the z-direction)
Note: The above is based on the assumption that the bearings are properly aligned and exert only force reactions on the shaft.
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figure q21.7 shows some of the electric field lines due to three point charges arranged along the vertical axis. all three charges have the same magni- tude. (a) what are the signs of the three charges? explain your reasoning. (b) at what point(s) is the magnitude of the elec- tric field the smallest? explain your rea- soning. explain how the fields produced by each individual point charge combine to give a small net field at this point or points.
The charges q1 and q3 are positive while charge q2 is negative.
The fundamental quantity in electrostatics is electric charge. There are two kinds of charge, positive and negative. Charges of the same sign repel each other; charges of opposite sign attract. Charge is conserved; the total charge in an isolated system is constant.Electric field is a vector quantity, is the force per unit charge exerted on a test charge at any point. The electric field produced by a point charge is directed radially away from or toward the charge.Field lines provide a graphical representation of electric fields. At any point on afield line, the tangent to the line is in the direction of E and at that point. The number of lines per unit area (perpendicular to their direction) is proportional to the magnitude of E and at the point.Electric field lines go away from charge q1 and q3, therefore these charges are positive.
Field line come towards the charge q 2, therefore this charge is negative.
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a black mamba snake has a length of 2.60 m and a top speed of 4.50 m/s. suppose a mongoose and a black mamba find themselves nose to nose. in an effort to escape, the snake accelerates past the mongoose at 8.37 m/s2 from rest.
The snake takes 0.53 seconds to reach its top speed.
Speed is defined as: The rate of change of the object's position in any direction. Speed is measured as the ratio of distance traveled and time traveled. In physics, an equation of motion is an equation that describes the behavior of a physical system related to motion as a function of time..
We know the snake's initial speed (zero) and its final speed (4.50 m/s). Also, its acceleration is 8.37 m/s2
The relevant equation is:
v = v0 + at
4.50 = 0 + 8.37t
0.53 s = t
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A helium balloon has a volume of 2.00 L at 101 kPa. As the balloon rises the pressure drops to 97.0 kPa. What is the new volume?
Answer:
The volume of a gas is inversely proportional to the pressure at constant temperature, according to Boyle's law. Mathematically, it can be expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
As the temperature is constant, we can use the following formula to calculate the new volume of the balloon:
V1 / P1 = V2 / P2
where V1 = 2.00 L, P1 = 101 kPa, P2 = 97.0 kPa.
V2 = (V1 * P2) / P1
V2 = (2.00 L * 97.0 kPa) / 101 kPa = 1.9608 L
So, the new volume of the helium balloon is 1.9608 L.