The value of Ey is greater than 1, it follows that:
σ = y * √(Ey / 1) > y
According to the distortion-energy criterion, the yield stress in plane strain is greater than the uniaxial yield stress, and is typically taken as 1.15y, where y is the uniaxial yield stress of the material.
Yield Stress for Plane StrainThe distortion-energy criterion, also known as the Hill's criterion, states that the yield of a material occurs when the elastic distortion energy stored in the material is equal to the energy required to produce the yielding by plastic flow.
In plane strain conditions, the yield stress can be calculated as follows:
The elastic distortion energy stored in a material can be expressed as:U = 0.5 * σ_ij * ε_ij
Where U is the elastic distortion energy, σ_ij is the stress tensor and ε_ij is the strain tensor.
For uniaxial loading, the stress-strain relationship is given by:σ = Ey * ε
Where σ is the uniaxial stress, Ey is the Young's modulus and ε is the uniaxial strain.
Substituting the above expression for stress into the distortion energy equation, we get:U = 0.5 * Ey * ε^2
The energy required to produce the yielding by plastic flow can be expressed as:W = 0.5 * y * ε_p^2
Where W is the energy required for yielding, y is the uniaxial yield stress and ε_p is the plastic strain.
Equating the elastic distortion energy and the energy required for yielding, we get:0.5 * Ey * ε^2 = 0.5 * y * ε_p^2
Dividing both sides by 0.5 * ε^2, we get:Ey = y * ε_p^2 / ε^2
Substituting the definition of the uniaxial strain, we get:Ey = y * ε_p^2 / (ε/Ey)^2
Simplifying the above expression, we get:Ey = y * ε_p^2 * Ey^2 / ε^2
Finally, dividing both sides by Ey, we get:1 = y * ε_p^2 / ε^2
Rearranging, we get:ε^2 = y * ε_p^2 / 1
Taking the square root of both sides, we get:ε = √(y * ε_p^2 / 1)
Since ε = σ/Ey, substituting the uniaxial stress-strain relationship, we get:σ/Ey = √(y * ε_p^2 / 1)
Multiplying both sides by Ey, we get:σ = Ey * √(y * ε_p^2 / 1)
Finally, substituting the value of Ey, we get:σ = y * √(Ey / 1)
Since the value of Ey is greater than 1, it follows that:σ = y * √(Ey / 1) > y
Therefore, according to the distortion-energy criterion, the yield stress in plane strain is greater than the uniaxial yield stress, and is typically taken as 1.15y, where y is the uniaxial yield stress of the material.
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study of bluefish locomotion found that their tail motion produces an average thrust of 0.65 N . Suppose a 1.7 kg bluefish that is coasting horizontally at 0.45 m/s suddenly begins tail motion.
Answer:
he fish would travel a horizontal distance of 1.78 meters during the 2 seconds of tail motion
Explanation:
The initial horizontal velocity of the bluefish is 0.45 m/s. When it begins tail motion, it experiences an additional force due to the thrust produced by the tail. The thrust produced by the tail is 0.65 N. We can use Newton's second law to find the acceleration produced by this force:
F = ma
0.65 N = 1.7 kg * a
a = 0.38 m/s^2
This acceleration will cause the velocity of the bluefish to increase over time. The distance the fish travels during this time can be calculated using the kinematic equation:
d = vit + 1/2 at^2
where d is the distance traveled, vi is the initial velocity, a is the acceleration, and t is the time. Since the fish is initially coasting horizontally, its initial vertical velocity is 0 m/s. Therefore, vi = 0.45 m/s. The time interval for which the fish is tail-motoring is not given, so let's assume it is 2 seconds:
d = (0.45 m/s)(2 s) + 1/2 (0.38 m/s^2)(2 s)^2
d = 1.78 meters
Therefore, the fish would travel a horizontal distance of 1.78 meters during the 2 seconds of tail motion.
Suppose a particle is accelerated through space by a 10-N force. Suddenly the particle encounters a second force of 10 N in the opposite direction of the first force. The particle is: a) *brought to a rapid halt b) decelerates gradually to a halt c) continues at the speed it had when it encountered the second force d) theoretically tends to accelerate toward the speed of light e) none of these
The particle cannot accelerate toward the speed of light if no acceleration is applied. The correct answer is e) none of these.
The particle encounters a force of 10 N in the opposite direction of the initial force, creating an unbalanced force. This means that the particle experiences an acceleration of 10 N in the opposite direction, decelerating from its initial velocity.
However, since the acceleration caused by the second force is equal to the acceleration caused by the first force, the particle does not come to a rapid halt, but rather its velocity gradually decreases until it comes to a stop. This means that the correct answer to the question is b) decelerates gradually to a halt.
In order for the particle to theoretically tend to the speed of light, it must experience a constant acceleration in any direction.
Since the two forces are in opposite directions and of equal magnitude, the resultant force is zero, meaning that the particle experiences no acceleration and therefore its speed remains the same.
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1a) Assuming a flat slope for Weber's Law for weight detection what else might be true? (Note: in the real world humans do not have a flat slope for weight detection so the correct answer might be ridiculous in the real world)A. The JND is always 5 poundsB. The JND is always 10% of the starting weightC. The JND is always equal to the starting weightD. Weber's Law would be proven false1b) What might, in the real world, display a flat slope for weight detection?A. A cameraB. An electric scaleC. A humanD. An airplane
In the real world, humans do not have a flat slope for weight detection. However, some devices such as cameras, electric scales, and airplanes may display a flat slope for weight detection.
For instance, when detecting a change in weight with a hand-held device, humans would be less accurate than with a more sophisticated device such as an electric scale. Furthermore, when detecting a change of weight in an environment with multiple stimuli, such as a room filled with noise, humans may not be able to accurately detect the change at all.
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The potential at location A is 452 V. A positively charged particle is released there from rest and arrives at location B with a speed vB. The potential at location C is 791 V, and when re- leased from rest from this spot, the particle arrives at B with twice the speed it previously had, or 2vB. Find the potential at B.
The potential at location B must be 452 V + 339 V = 791 V.
What is potential?Potential is the capacity to become or develop into something, either tangible or intangible. It is an opportunity that, when acted on, can bring about a desired outcome. Potential exists both within individuals and within organizations, and can be realized through purposeful effort, ambition, and hard work.
When a particle is released from rest at location A with a potential of 452 V and arrives at location B with a velocity vB, the work done on the particle in moving it from location A to location B is equal to the difference in potentials between the two locations, or (791 V - 452 V) = 339 V.
This means that the potential at location B must be 452 V + 339 V = 791 V.
When the particle is released from rest from location C with a potential of 791 V and arrives at location B with twice the speed it had previously, or 2vB,
the work done on the particle in moving it from location C to location B is equal to the difference in potentials between the two locations, or (791 V - 791 V) = 0 V.
This means that the potential at location B must be 791 V + 0 V = 791 V, which is the same as the potential at location C.
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Model a 10 μm x 10 μm piece of membrane on a cell as a as a pair of infinite parallel plates separated by a distance d = 5 nm, with a potential difference across the membrane of 70 mV. A. Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates. B. Using the electric field you found in part A, calculate the charge density, σ (charge per unit area), on the plates. (Hint: The E field near to a single plate of charge having a uniform charge density σ, is 2πkCσ where kC = 9 x 109 N-m2/C2.) C. Using the charge density you found in B, calculate the magnitude of the charge on each side of the piece of cell membrane we are modeling and the net charge on the piece of the membrane.
Between the plates, there is a 14 x 10^6 V/m electric field. The plates have a charge density of 2.32 x 10-17 C/m^2 C. The net charge on the membrane piece is 0 C, and the charge on each side of the membrane is 3 x 10-8 C in magnitude.
Part A:
Electric field equation: E = V/dPotential difference: V = 70 mVSeparation between the plates: d = 5 nmConversion of separation to meters: 5 nm = 5 x 10^-9 mCalculation of electric field: E = V/d = 70 mV / (5 x 10^-9 m) = 14,000 V/mPart B:
Equation for electric field near a single plate of charge with uniform charge density: E = 2kCConstant kC: kC = 9 x 10^9 N-m2/C2Electric field from Part A: E = 14,000 V/mCalculation of charge density: E/(2kC) = 14,000 V/m / (2 x 9 x 10^9 N-m2/C2) = 0.0015 C/m2Part C:
Use the equation E = V/d, where E is the electric field, V is the potential difference, and d is the separation between the two plates.The electric field between the plates is 70 mV/5 nm = 14,000 V/m.Use the equation E = 2kCσ, where kC = 9 x 109 N-m2/C2, to calculate the charge density σ.Divide the electric field by 2kC to get the charge density: σ = E/(2kC) = 14,000 V/m / (2 x 9 x 109 N-m2/C2) = 0.0015 C/m2.Multiply the charge density by the membrane area: Q = σ x A = 0.0015 C/m2 x 10 μm x 10 μm = 1.5 x 10-8 C.The net charge on the membrane is equal to twice the charge on one side: 3 x 10-8 C.Read more about Electromagnetism:
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if the spring db has an unstretched length of 2 m, determine the stiffness of the spring to hold the 40-kg crate in the position shown.
Spring force P on the cable if the spring is compressed 0.025 m when the mechanism is in the position shown is 0.198 kN.
When the mechanism is in the position indicated, the force P on the cable is 0.198 kN if the spring is compressed 0.025 m in 40 kg
When a spring mechanism is adjusted by a length away from its balance length, it exerts a force on items fastened to its end that is continuously coordinated towards its harmonic position. F = - kx. The term "spring steady" refers to the proportional constant k. It is a percentage of the solidity of the spring. The following power is negative (moving towards the left) if x is positive (uprooting to the right), and vice versa. As a result, the spring force often works to restore mass to its harmonious position. The force P on the cable is therefore 0.198 kN. when, the mechanism is in the position shown.
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a subway train starts from rest at a station and accelerates at a rate of 1.60m/s2 1.60 m / s 2 for 14.0 s s . it runs at constant speed for 70.0 s s and slows down at a rate of 3.50m/s2 3.50 m / s 2 until it stops at the next station. Find the total distance covered.
The total distance covered by the subway train is 1796.5 m. The result is obtained by using the equations in uniformly accelerated straight motion.
Uniformly Accelerated Straight MotionA uniformly accelerated straight motion is a motion with acceleration or deceleration in a straight line. The equations apply in horizontal dimension are
v₁ = v₀ + at
v₁² = v₀² + 2ax
x = v₀t + ½ at²
Where
v₀ = initial velocityv₁ = final velocitya = accelerationt = timex = distanceA subway train starts from rest at a station.
It accelerates at a rate of 1.60 m/s² for 14.0 s. It runs at constant speed for 70.0 s.It slows down at a rate of 3.50 m/s² until it stops at the next station.Find the total distance covered!
When it accelerates, the distance is
x₁ = v₀t + ½ a₁t₁²
x₁ = 0 + ½ (1.60)(14.0)²
x₁ = 0 + 0.8(196)
x₁ = 156.8 m
The final speed after 14 s is
v₁ = v₀ + at
v₁ = 0 + (1.6)(14.0)
v₁ = 22.4 m/s
The speed later will be constant for t₂ = 70.0 s.
When it moves with a constant speed (22.4 m/s), the distance is
x₂ = v₁t₂
x₂ = 22.4(70)
x₂ = 1568 m
When it slows down until it stops (v₂ = 0), the distance is
v₂² = v₁² - 2a₂x₃
0 = 22.4² - 2(3.5)x₃
22.4² = 2(3.5)x₃
501.76 = 7x₃
x₃ = 71.68 m
The total distance covered will be
x = x₁ + x₂ + x₃
x = 156.8 m + 1568 m + 71.68 m
x = 1796.48
x = 1796.5 m
Hence, the subway train traveled for a total distance of 1796.5 m.
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The acceleration of an object that has a mass of 0.025 kg and exhibits simple harmonic motion is given by the following equation.????x(????)=(10 m/s2)cos(????????+3????/2)Calculate the object's velocity ????x(????) at time ????=2.0 s, assuming that the velocity of the object is ????x=−3.2 m/s at ????=0 s.
The velocity of the object is (2.0 s) = 0+∫ = −3.2 m/s − 5 m/s = −8.2 m/s
What is velocity?Velocity is a vector quantity that measures the rate of change of an object's position. It is the speed of an object in a given direction and is usually represented by a vector with both magnitude (the speed) and direction. Velocity is the rate at which an object's position changes over time, or the derivative of an object's position with respect to time.
The velocity of the object at time t = 2.0 s can be calculated using the equation for velocity, =0+∫.
We can calculate the velocity at t = 2.0 s by first calculating the integral of the acceleration equation.
∫ = −(10/)sin(+3/2)
Substituting in t = 2.0 s, we get
∫ = −(10/)sin(2+3/2) = −(10/)sin(5/2) = −5 m/s
We then substitute this value into the equation for velocity and substitute in the initial velocity of the object at t = 0 s, 0 = −3.2 m/s, to get:
(2.0 s) = 0+∫ = −3.2 m/s − 5 m/s = −8.2 m/s
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The following circuit diagram is partially incomplete.
A device is added to the electrical circuit to measure the total current in the circuit. Which of the following circuit symbols should be included in the diagram to represent this device?
The device which is used to measure the over all current through the circuit is an ammeter. Option d is the symbol of ammeter.
What is an ammeter ?An ammeter is a device used to measure electric current in amperes, either in direct current (DC) or alternating current (AC). Because only a tiny fraction of the current is sent via the meter mechanism at high levels and the majority is carried by a shunt in parallel with the meter, an ammeter can measure a wide range of current values.
An ammeter is represented by a circle with a capital A inside it in circuit diagrams. Accuracy and working principles of ammeters differ. With accuracy ranging from 0.1 to 2.0 percent, the movement ammeter monitors direct current flowing through a coil hanging between the poles of a magnet.
A moving coil revolving in the field created by a stationary coil is how the electrodynamic ammeter works. Therefore, option d is correct.
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The symbol used in diagram to represent the device is ammeter symbol that is circle with an A in it.
What is electric current?Electric current is defined as the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.
In given circuit,
A device is added to the electrical circuit to measure the total current in the circuit,
Ammeter is the device used to measure the current in a circuit. The ammeter is connected in series with the circuit, so that the current to be measured flows directly through the ammeter.
Ammeter symbol is a circle with an A in it.
Hence, ammeter's symbol will be used in diagram to represent the device.
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Consider the falling of a rock off a cliff into seawater and eventually settling at the bottom of the sea. Rank the energy transfers and transformations involved during this process. Rank the options below potential energy thermal energy kinetic energy
The energy transfers and transformations involved in the falling of a rock off a cliff into seawater occur in the following order: potential energy, kinetic energy, and finally thermal energy.
The energy transfers and transformations involved in the falling of a rock off a cliff into seawater can be ranked as follows:
Potential Energy: At the top of the cliff, the rock has potential energy due to its height relative to the surface of the sea. As the rock falls, this potential energy is converted into kinetic energy.Kinetic Energy: As the rock falls, its potential energy is converted into kinetic energy, which is the energy of motion. The rock's kinetic energy increases as it falls and reaches a maximum just before it hits the surface of the sea.Thermal Energy: When the rock hits the surface of the sea, it transfers some of its kinetic energy into thermal energy, which is the energy associated with the movement of particles in a substance. This transfer of energy results in a small amount of heating of the seawater. The rock will continue to transfer energy into thermal energy as it sinks to the bottom of the sea, but this transfer will become less and less significant as the rock loses kinetic energy and slows down.In summary, the energy transfers and transformations involved in the falling of a rock off a cliff into seawater occur in the following order: potential energy, kinetic energy, and finally thermal energy.
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a dog lifts a 1.5 kg bone straight up through a distance of 0.2 m. How much work was done by the dog?
Answer:
see below
Explanation:
we have ,
mass = 1.5kg height = 0.2 mWe know,
Work = mgh
Work = 1.5kg * 10m/s² * 0.2m
Work= 3J
and we are done!
1 point
A man jumps from an airplane and his speed of descent is given by V=50(1-e0.21) meters per second, where t is the
time in seconds. Find the time taken for his speed to reach 40 m/s.
Type your answer.....
The time taken for the man's speed to reach 40 m/s is 8.15 seconds.
What do you mean by speed?
Speed is the rate at which something moves or operates. It is usually measured in units such as miles per hour (mph) or kilometers per hour (kph). Speed is often used to describe the rate of change in a physical quantity, such as the speed of light. It can also be used to describe the rate of change in a process or activity, such as the speed at which a computer can process data.
So,
V = 50(1-e^-0.21t)
40 = 50(1-e^-0.21t)
e^-0.21t = (50-40)/50
-0.21t = ln((50-40)/50)
t = ln((50-40)/50)/-0.21
t ≈ 8.15 seconds
Therefore, the time taken is 8.15 seconds.
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The enthalpy of vaporization of Substance X is 21.0 kj/mol and its normal boiling point is 19. C Calculate the vapor pressure of X at -98. C Round your answer to 2 significant digits.
The vapor pressure of Substance X at -98. C is 1.01 atm, rounded to 2 significant digits.
What is vapor pressure?Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase. It is an indication of a liquid's evaporation rate. It is directly related to the vapor's temperature, and increases with increasing temperature.
ln (P2/P1) = (ΔHvap/R) * ((1/T1) – (1/T2))
where:
P2 = vapor pressure of the substance at temperature T2
P1 = vapor pressure of the substance at temperature T1
ΔHvap = enthalpy of vaporization of the substance
R = ideal gas constant
T1 = normal boiling point of the substance
T2 = temperature at which the vapor pressure is being calculated
In this case, we are trying to calculate the vapor pressure of Substance X at -98. C.
We can plug in the known values into the equation to calculate the vapor pressure of Substance X at -98. C:
ln (P2/P1) = (21.0 kj/mol/8.314 J/mol-K) * ((1/19) – (1/273))
ln (P2/P1) = 0.0087
P2 = exp (0.0087) * P1
P2 = 1.009 * P1
P2 = 1.009 * 1.00 atm (atm is the vapor pressure of Substance X at 19. C, its normal boiling point)
P2 = 1.009 atm
Therefore, the vapor pressure of Substance X at -98. C is 1.01 atm, rounded to 2 significant digits.
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the ampacity adjustment factors of 310.15(b)(3)(a) shall not apply to conductors installed in surface metal raceways where the __________.
conductors are not subjected to additional heat due to the raceway installation.that the raceway provides increased cooling and/or ventilation.
What is the ventilation ?Ventilation is the process of providing fresh air to an enclosed space and removing stale air from the same space. It is an important factor in maintaining the quality of air in an environment, both in terms of temperature, humidity, and gaseous pollution. Ventilation is accomplished by either mechanically or naturally moving air from an area of high pressure, where it is typically warmer, to an area of lower pressure, where it is typically cooler. Mechanical ventilation is typically used in closed buildings or spaces, such as homes, offices, and industrial buildings, while natural ventilation relies on the natural flow of air through open windows, doors, and other openings.
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an athlete swings a ball, connected to the end of a chain, in a horizontal circle. the athlete is able to rotate the ball at the rate of 7.28 rev/s when the length of the chain is 0.600 m. when he increases the length to 0.900 m, he is able to rotate the ball only 6.39 rev/s. (a) What is the centripetal acceleration of the ball at 7.72 rev/s? (answer in m/s^2)
(b) What is the centripetal acceleration at 6.39 rev/s?
(a) The centripetal acceleration of the ball at 7.72 rev/s is 30.2m/s²
(b) The centripetal acceleration at 6.39 rev/s is 33.9m/s².
What is a radius?
It is possible to define a circle as the locus of a point travelling on a plane while maintaining a constant distance from a fixed point. The radius of a circle is the distance from any point on the circle to its centre.Using the definition of speed and noting that the ball travels in a circular path,
v= d/Δt
= 2πR/T
where R is the radius of the circle and T is the period, that is, the time interval required for the ball to go around once. For the periods given in the problem,
8.00rev/s→T= 1/8.00rev/s =0.125s
6.00rev/s→T= 1/6.00rev/s =0.167s
Therefore, the speeds in the two cases are: 8.00rev/s→v= 2π(0.600m)/ 0.125s
=30.2m/s²
6.00rev/s→v= 2π(0.900m)/0.167s
=33.9m/s²
Therefore, 6.00rev/s gives the greater speed of the ball.
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A centrifuge rotor rotating at 9000 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.73 m⋅N
Part A: If the mass of the rotor is 3.72 kg and it can be approximated as a solid cylinder of radius 0.0760 m, through how many revolutions will the rotor turn before coming to rest?
Express your answer to three significant figures.
Part B: How long will it take?
Express your answer to three significant figures and include the appropriate units.
Answer:
Look below
Explanation:
Part A:
The initial angular velocity of the rotor can be found using the formula:
ω = v/r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the cylinder. Since the rotor is rotating at 9000 rpm, we can convert this to radians per second:
ωi = (9000 rpm) x (2π/60 s) = 942.48 rad/s
The final angular velocity is zero. The frictional torque acting on the rotor is given by:
τ = Iα
where τ is the torque, I is the moment of inertia, and α is the angular acceleration. The moment of inertia for a solid cylinder is:
I = (1/2)mr^2
Substituting in the given values and solving for α, we get:
α = τ/I = (1.73 m⋅N) / [(1/2)(3.72 kg)(0.0760 m)^2] = 371.7 rad/s^2
The final angular velocity is zero, so we can use the formula:
ωf^2 = ωi^2 + 2αθ
where θ is the angle of rotation. Solving for θ, we get:
θ = (ωf^2 - ωi^2) / (2α) = (0 - (942.48 rad/s)^2) / (2 x 371.7 rad/s^2) = 6.76 revolutions
Therefore, the rotor will turn approximately 6.76 revolutions before coming to rest.
Part B:
The time it takes for the rotor to come to rest can be found using the formula:
ωf = ωi + αt
where ωf is the final angular velocity, ωi is the initial angular velocity, and α is the angular acceleration. Solving for t, we get:
t = (ωf - ωi) / α = (0 - 942.48 rad/s) / 371.7 rad/s^2 = 2.535 s
Therefore, it will take approximately 2.535 seconds for the rotor to come to rest.
Oil molecules are non polar. How will a stream of oil react near a positively charged comb?
Lo
Electric toothbrushes can be effective in removing dental plaque. One model consists of a head 1.10 cm in diameter that rotates back and forth through a 70.0 degrees angle 7600 times per minute. The rim of the head contains a thin row of bristles.Part A: What is the average angular speed in each direction of the rotating head, in rad/s?Part B: What is the average linear speed in each direction of the bristles against the teeth? (to two sig. figures)Part C: Using your own observations, what is the approximate speed of the bristles against your teeth when you brush by hand with an ordinary toothbrush? (Estimate that the toothbrush turns back and forth through 45 degrees five times per second) (in cm/s, two sig. figures).
The average angular speed in each direction of the rotating head is 9.42 rad/s.
The average linear speed in each direction of the bristles against the teeth is 5.09 cm/s.
The approximate speed of the bristles against the teeth when brushing by hand with an ordinary toothbrush is 1.26 cm/s.
Part A: The formula ω = Δθ/Δt can be used to determine the rotating head's average angular speed in each direction.
Where Δθ denotes the angular displacement, Δt denotes the rotational time, and ω denotes the angular speed.
In this instance,
Δt = 1/(7600/2) s/rotation, and Δθ= 70.0 degrees = 70.0 x (π/180) radians.
Thus, ω = (70.0 x (π/180)) / (1/(7600/2)) = 9.42 rad/s is the average angular speed in each direction.
Part B: The following equation can be used to determine the average linear speed of the bristles against the teeth:
v = rω
where r is the head's radius (0.55 cm), v is the linear speed, and ω is the angular speed.
The average linear speed is therefore v = 0.55 x 9.42 = 5.09 cm/s in each direction (rounded to two significant figures)
Part C: Although it is challenging to measure precisely, it is possible to estimate the speed of the bristles against the teeth when brushing by hand with a regular toothbrush. The average linear speed can be estimated using the formula v = rΔθ/Δt if we suppose that the bristles rotate through an average displacement of 45 degrees five times each second.
Where Δθ = 45 degrees, Δt = 1/5 s, and r = the radius of the bristles (estimated as 0.2 cm).
So, the average linear speed is approximately:
v = 0.2 x (45 x (π/180)) / (1/5) = 1.26 cm/s (rounded to two significant figures).
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Help meee!
Please for my physics Home work
a 240 g air-track glider is attached to a spring. the glider is pushed in 10.4 cm and released. a student with a stopwatch finds that 8.00 oscillations take 12.0 s .
The spring constant of the spring is 5.1N/m.
The formula for calculating the period of oscillation is expressed as:
[tex]T = 2\pi \sqrt{\dfrac{m}{k}}[/tex]
,where m is the mass of the spring and k is the spring constant.
Making the spring constant "k" the subject of the formula will give;
[tex]k = 4\pi^2\dfrac{m}{T^2}[/tex]
Get the period of oscillation "T"
[tex]T = \dfrac{1}{f}[/tex]
frequency "f" is the number of oscillations completed in one second.
If a student with a stopwatch finds that 8 oscillations take 12.0 s, the number of oscillations in one sec will be 12/8 = 1.5 oscillations.
Period T = 1/1.5 = 0.67 seconds
Get the required spring constant,
[tex]k = 4\pi^2\dfrac{0.240}{(0.67)^2}\\k = 21.06[/tex]
Hence the spring constant of the spring is 21.06 N/m.
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A 0.8-kg apple falls from a tree branch that is 2.5 m above the ground. How fast is it moving when it hits the ground, in m / s ? (Round your answer to one decimal place if necessary.)
The required, apple is moving at a velocity of 7 m/s when it hits the ground.
What is the equation of motion?The equation of motion is a mathematical expression that describes the relationship between the position, velocity, and acceleration of an object. It can be used to predict the motion of an object
The velocity of the apple just before it hits the ground can be calculated using the equation of motion for freely falling objects, which is:
v = √2gs
where v is the final velocity, g is the acceleration due to gravity (9.8 m/s²),
v = √2gs
Substitute the values in the above equation,
v = √[2 × 9.8 × 2.5]
v = 7 m/s
So the apple is moving at a velocity of 7 m/s when it hits the ground.
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find the center of mass of a right-circular cone with a base radius r, height h, and a non- uniform mass density varies as the square of the distance from apex (tip of the cone).
The center of mass of a right-circular cone with a base radius r, height h, and a non-uniform mass density varies as the square of the distance from apex (tip of the cone) is:
ρ(x, y, z) = k * (√(x^2 + y^2 + z^2))^2
where k is a constant of proportionality.
Find Center of Mass ConeTo find the center of mass of a right-circular cone with a base radius "r" and height "h", and a non-uniform mass density that varies as the square of the distance from the apex, we need to use the following formula:
Let "m" be the total mass of the cone, then the center of mass can be found using the following formulas for the x, y, and z-coordinates:
x-coordinate:
x_cm = (1/m) * ∫∫∫_V x * ρ(x, y, z) * dV
y-coordinate:
y_cm = (1/m) * ∫∫∫_V y * ρ(x, y, z) * dV
z-coordinate:
z_cm = (1/m) * ∫∫∫_V z * ρ(x, y, z) * dV
where V is the volume of the cone, ρ(x, y, z) is the mass density function, and the integration is performed over the entire volume of the cone.
Since the mass density varies as the square of the distance from the apex, we have:
ρ(x, y, z) = k * (√(x^2 + y^2 + z^2))^2
where k is a constant of proportionality.
Substituting this into the above equations, we can find the center of mass of the cone.
The final result will depend on the specific values of r, h, and k, and the integration may be challenging to perform analytically. But numerical integration methods can be used to approximate the center of mass with good accuracy.
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determine the magnitude and location of the resultant of the distributed load. (you must provide an answer before moving to the next part.)
The magnitude of the resultant would be 40 N, the location of the resultant is 0 m.
What is resultant?Resultant is a term used to refer to the combined effect of two or more forces acting on an object. It is the vector sum of the individual forces acting on the object, and can be determined by adding the individual vectors of the forces together.
The magnitude of the resultant of the distributed load can be calculated by summing the forces at each point and then resolving them into components. The location of the resultant can then be determined by calculating the moment of the distributed load.
For example, if the load is distributed over a distance of 4 m and has a magnitude of 10 N/m,
the magnitude of the resultant would be 40 N.
This can be calculated by summing the forces at the start and end points (40 N = 10 N + 10 N + 10 N + 10 N).
The location of the resultant can then be determined by calculating the moment of the distributed load.
This is done by finding the sum of the moments at each point and then dividing by the total force (location = moment / force).
In this case, the moment at each point is 0 Nm, so the location of the resultant is 0 m.
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Complete Question is attached Below:
Help meee!
Please for my physics Home work
A ball is in motion. At some point in its motion, its instantaneous acceleration vector is perpendicular to its velocity vector. At this point in its motion, which statement is true?
The ball changes direction without changing its speed
At that point in its motion, the ball changes direction without changing its speed, is the a true statement.
What is instantaneous acceleration?Instantaneous acceleration refers to the rate of change of an object's velocity at a specific point in time. It measures the change in an object's velocity over an infinitesimal amount of time and is the derivative of velocity with respect to time.
This statement is true because when the acceleration vector is perpendicular to the velocity vector, it means the ball is changing direction without changing its speed. The direction of the acceleration vector determines the change in direction, and the magnitude of the acceleration vector determines the rate of change in speed. If the acceleration vector is perpendicular to the velocity vector, it means that the direction is changing, but the speed is not changing.
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You are designing a diving bell to withstand the pressure of seawater at a depth of 25.0 m.
a. What is the gauge pressure at this depth? (You can ignore changes in the density of the water
with depth) (2 marks)
b.
At this depth, what is the net force due to the water outside and the air inside the bell on a
circular glass window 30.0 cm in diameter if the pressure inside the diving bell equals the
pressure at the surface of the water? (You can ignore the small variation of pressure over
the surface of the window.) (3 marks)
Psw 1.03x10³ kgm³
Psw
=
-3
1.03 x 10³kgm ³
p=pgh
F = PA
a. The gauge pressure at this depth is 250 kPa.
b. The net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter is 7.5 kN.
What do you mean by pressure?
Pressure is a measure of the force applied over a given area and is usually expressed in units such as pascals (Pa) or pounds per square inch (psi). It is a fundamental physical quantity found in all areas of physics, including fluid dynamics, thermodynamics, and mechanics.
a. The pressure at a certain depth in a body of water is given by the equation P = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water. In this case, the gauge pressure at a depth of 150 m is equal to 250 kPa.
b. The net force on the glass window can be calculated by using the formula F = Pπr2, where P is the pressure, π is the mathematical constant, and r is the radius of the window. In this case, the net force on the window is 7.5 kN, which can be calculated as 7.5kN = 250kPa × (0.15m)2 × 3.14.
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A long, straight wire carries a current of 8.00A. At one point, a proton, 7.00mm from the wire travels at 4.00×
[tex] {10}^{8} [/tex]
ms parallel to the same direction as the current Find the magnetic force that is acting on the proton because of the magnetic field produced by the wire.
Answer:
Explanation:
jajs poza
If a particle is projected with speed 30m/s at an angle tan ¹2, find the greatest height and the corresponding horizontal distance. Find also the time of flight.
Answer:
The greatest height will be as follows:
h = (v²sin2θ)/2g
h = [(30m/s)² (2)] / (2 × 9.8 m/s²)
h = 225m
The corresponding horizontal distance will be as follows:
d = (v² sinθcosθ)/g
d = [(30m/s)² (2 × 1)] / 9.8 m/s²
d = 306m
The time of flight will be as follows:
t = (2v sinθ) / g
t = (2 × 30m/s × 2) / 9.8 m/s²
t = 12.24s
The given problem is a projectile motion problem in Physics. It can be solved using the formulas of kinematics considering the initial velocity of the particle and the angle of projection. Substituting the given values in their respective formulas will determine the time of flight, maximum height, and horizontal distance.
Explanation:The subject matter of this question is based on the physics principle of projectile motion. To solve this problem, we can use some basic formulas of kinematics regarding time of flight, maximum height, and horizontal distance. The angle of projection here is given as \\tan^{-1}2\\ which equals approximately 63.4 degrees.
Firstly, the time of flight (T) can be found using the formula: T = 2u*sin(theta)/g, where 'u' is the initial velocity, 'theta' is the angle of projection, and 'g' is the acceleration due to gravity (approx. 9.81 m/s\^2 ).
Secondly, the greatest height (H) can be found using the formula: H = u^2*sin^2(theta)/2g.
Last but not least, the horizontal distance or the range (R) can be found using the formula: R = u^2*sin(2*theta)/g.
By substituting the given values in these formulas, we will be able to find the time of flight, the greatest height, and the horizontal distance.
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in which of the following types of circuits can the total power of the circuit be determined by adding the power dissipation of all the parts of the circuit?
In an equal circuit, all parts are associated across one another, subsequent in precisely two arrangements of electrically normal places.
The complete power in a series circuit is equivalent to the amount of power disseminated by the individual resistors.
The complete power disseminated will be equivalent to the amount of the power dispersed by every individual obstruction. Contingent upon the qualities that are known, blends of the power equation, also as Ohm's regulation, can be utilized to work out power disseminated (or some other obscure worth).
An equal circuit disseminates more power than a series circuit. For similar arrangements of resistors, the complete obstruction of the equal circuit is consistently lower than the all-out opposition in a series circuit.
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A small frictionless 4.40 kg cart is released from rest at the top of a hill (assume the hill is perfectly straight and flat, like a ramp). A student is interested in how the motion of the frictionless cart on the hill differs from the motion of a solid cylinder when they are released from rest. The length of the hill from starting point to ending point is 366 m and the point of release for the cart is 53 m above the ending point.
a.) Determine the acceleration of the cart.
b.) Determine the time it takes the cart to travel from the starting point to the ending point.
Now, the solid cylinder with the same mass as the cart and a radius of 0.024 m is released from rest at the top of the hill. Assume there is more than enough friction so that the cylinder rolls without slipping.
c.) Determine the acceleration of the cylinder.
d.) Determine the time it takes the cylinder to travel from the top of the ramp to the bottom.
The acceleration of the cart is 43.12 m/s².
Time it takes the cart to travel from the starting point to the ending point is 3.8 sec.
Acceleration of the cylinder is a = g - (v²)/R.
Time it takes the cylinder to travel from the top of the ramp to the bottom is d = v_0t + 1/2at².
How to calculate acceleration and time?a.) The acceleration of the cart can be calculated using the formula g = 9.8 m/s², where g is the acceleration due to gravity. a = F/m = m × g = 4.40 kg × 9.8 m/s² = 43.12 m/s²
b.) The time it takes the cart to travel from the starting point to the ending point can be calculated using the kinematic equation:
d = v_0t + 1/2at²,
where d is the distance traveled, v_0 is the initial velocity (which is 0 for this case), a is the acceleration (determined in part a), and t is the time.
366 m - 53 m = 313 m
313 = 0t + 1/2(43.12)t² = 1/2(43.12)t²
313 = 21.56t², t² = 313 / 21.56
t² = 14.52, t = √14.52 = 3.8 sec.
c.) The acceleration of the cylinder can be calculated using the formula a = g - (v²)/R, where v is the linear velocity of the cylinder's center of mass and R is the radius of the cylinder.
d.) The time it takes the cylinder to travel from the top of the ramp to the bottom can be calculated using the kinematic equation:
d = v_0t + 1/2at²,
where d is the distance traveled, v_0 is the initial velocity (which is 0 for this case), a is the acceleration (determined in part c), and t is the time.
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