(a) [tex]-1.5\cdot 10^6 N[/tex]
First of all, we need to calculate the acceleration of the person, by using the following SUVAT equation:
[tex]v^2 -u ^2 = 2ad[/tex]
where
v = 0 is the final velocity
u = 20.0 m/s is the initial velocity
a is the acceleration
d = 1.00 cm = 0.01 m is the displacement of the person
Solving for a,
[tex]a=\frac{v^2-u^2}{2d}=\frac{0-20.0^2}{2(0.01)}=-20000 m/s^2[/tex]
And the average force on the person is given by
[tex]F=ma[/tex]
with m = 75.0 kg being the mass of the person. Substituting,
[tex]F=(75)(-20000)=-1.5\cdot 10^6 N[/tex]
where the negative sign means the force is opposite to the direction of motion of the person.
b) [tex]-1.0\cdot 10^5 N[/tex]
In this case,
v = 0 is the final velocity
u = 20.0 m/s is the initial velocity
a is the acceleration
d = 15.00 cm = 0.15 m is the displacement of the person with the air bag
So the acceleration is
[tex]a=\frac{v^2-u^2}{2d}=\frac{0-20.0^2}{2(0.15)}=-1333 m/s^2[/tex]
So the average force on the person is
[tex]F=ma=(75)(-1333)=-1.0\cdot 10^5 N[/tex]
The average force on the person if he is stopped by a padded dashboard is -1.5 x 10⁶ N.
The average force on the person if he is stopped by an air bag is -10,000 N.
The given parameters;
mass of the person, m = 75 kgvelocity of the person, u = 20 m/sThe deceleration of the car when the padded dashboard compresses an average of 1.00 cm.
s = 0.01 m
[tex]v^2 = u^2 + 2as\\\\0 = 20^2 + (2\times 0.01)a\\\\0 = 400 + 0.02a\\\\0.02a = -400\\\\a = \frac{-400}{0.02} \\\\a = -20,000 \ m/s^2[/tex]
The average force is calculated as;
F = ma
F = 75 x (-20,000)
F = -1.5 x 10⁶ N.
The deceleration of the car when the air bag compresses an average of 15 cm.
s = 0.15 m
[tex]v^2 = u^2 + 2as\\\\0 = u^2 + 2as\\\\-2as = u^2\\\\a = \frac{u^2}{-2s} = \frac{20^2}{-2\times 0.15} = -1,333.33 \ m/s^2[/tex]
The average force is calculated as follows;
F = ma
F = 75 x (-1,333.33)
F = -10,000 N.
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A 65-kg bungee jumper, who is attached to one end of an 85-m long bungee cord that has its other end tied to a bridge, jumps off the bridge and toward the river below. When stretched, the bungee cord acts like a spring and provides a force on the jumper that increases linearly as the cord is stretched. When the bungee cord is stretched to its maximum length, it exerts a 2.2 kN force on the jumper. If the bungee cord is stretched beyond its equilibrium length for a duration of 1.2 seconds, what is the impulse delivered to the bungee jumper
Answer:
The impulse delivered to the bungee jumper is 1.32 kN.s
Explanation:
The situation can be shown graphically as shown in the figure.
Impulse delivered to the bungee jumper = Area under the curve.
The curve represents a triangle and the area of traiangle = (1/2)base×height
The base of the triangle from the graph = 1.2 seconds.
The height of the triangle from the graph = 2.2 kN
Thus,
Impulse = (1/2)×(1.2 seconds)×(2.2 kN) = 1.32 kN.s
A student measures the volume of a gas sample at several different temperatures. The results are tabulated as follows:Temperature of gas (K) Volume of gas (L)298 4.55315 4.81325 4.96335 Formulate a tentative law from the measurements.Check all that apply.
a. The temperature of a gas is directly proportional to its volume.
b. The temperature of a gas is inversely proportional to its volume.
c. The temperature-to-volume ratio of a gas is constant.
d. The temperature-to-volume ratio of a gas isn't constant.
Answer:
Check the first and the third choices:
a. The temperature of a gas is directly proportional to its volumeb. The temperature-to-volume ratio of a gas is constant.
Explanation:
Rewrite the table for better understanding:
Temperature of gas (K) Volume of gas (L)
298 4.55
315 4.81
325 4.96
335 ?
Calculate the ratios temperature to volume with 3 significant figures:
298 / 4.55 = 65.5315 / 4.81 = 65.5325 / 4.96 = 65.5Then, those numbers show a constant temperature-to-volume ratio, which may be expressed in a formula as:
Temperature / Volume = constant, which is a directly proportional variation (the volume increases in a constant proportion to the increase of the temperature).Hence, the correct choices are:
The temperature of a gas is directly proportional to its volume (first statement), andThe emperature-to-volume ratio of a gas is constant (third statement).The data provided by the student supports the formulation of a tentative law that aligns with Charles's law, indicating that the temperature of a gas is directly proportional to its volume, and the temperature-to-volume ratio of a gas is constant when pressure is held constant.
Explanation:The student's measurements of the volume of a gas sample at different temperatures demonstrate a principle in chemistry known as Charles's law. According to this law, the volume of a gas is directly proportional to its temperature when pressure is held constant. Given the data provided, we can infer that as the temperature of the gas increases, so does its volume. This observation can be used to tentatively declare a law based on the student's measurements.
From the answer choices provided:
a. The temperature of a gas is directly proportional to its volume.c. The temperature-to-volume ratio of a gas is constant when measured in kelvins and pressure is constant.These explanations are consistent with the observed data that show the volume of the gas increases with increasing temperature. Thus, choices (a) and (c) are the correct interpretations of the experimental data.
1. What is the average acceleration of a subway train that speeds up from 9.6m/s to 12m/s in .8s on a straight track?
2. An acorn at rest falls from an oak tree. The acorn hits the ground with a velocity of 14.7m/s. How long did it take the acorn to land?
3. What force is necessary to accelerate a 1,250 kg car at a rate of 40m/s^2
4. The mass of a person that weighs 500 N is about...?
PLEASE HELP ME THANK YOU
Explanation:
1. Average acceleration is change in velocity over change in time.
a = Δv / Δt
a = (12 m/s - 9.6 m/s) / 0.8 s
a = 3 m/s²
2. a = Δv / Δt
9.8 m/s² = (14.7 m/s - 0 m/s) / Δt
Δt = 1.5 s
3. Force is mass times acceleration.
F = ma
F = (1250 kg) (40 m/s²)
F = 50,000 N
4. F = ma
500 N = m (9.8 m/s²)
m ≈ 51 kg
The problems are solved by applying physics concepts and formulas: acceleration (`(final velocity - initial velocity)/time`), time (`velocity/acceleration`), force (`mass x acceleration`), and weight (`mass x gravity`), thereby finding the acceleration as 3 m/s², the time as 1.5s, the force as 50,000N, and the person's mass as 51kg.
Explanation:The questions are related to fundamental concepts in Physics; namely acceleration, time, force, and mass.
To find the average acceleration, you use the formula `(final velocity - initial velocity)/time`. Substituting the values, you get `(12m/s - 9.6m/s)/0.8s` which equals 3 m/s².To find the time an acorn takes to land, you use the formula `distance/velocity`. Assuming the acorn falls from rest and no air resistance, the distance is equivalent to velocity multiplied by time. However, because the velocity isn't constant, we must use the formula for velocity in uniformly accelerated motion: velocity = acceleration x time`. In this case, acceleration due to gravity is 9.8m/s², so 14.7m/s = 9.8m/s² x time. Solving that gives time ≈ 1.5s.To find the force to accelerate a car, use the formula force = mass x acceleration. Substituting the values, we get 1250kg x 40m/s², which equals 50000 N.To find a person's mass from weight, use the formula weight = mass x gravity. Given the weight is 500N and assuming gravity is 9.8m/s², rearranging the formula gives mass = weight/gravity which equals approximately 51kg.Learn more about Physics formulas here:https://brainly.com/question/34207444
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An archer shoots an arrow at a 75.0 m distant target; the bull's-eye of the target is at same height as the release height of the arrow. (a) At what angle must the arrow be released to hit the bull's-eye if its initial speed is 35.0 m/s? In this part of the problem, explicitly show how you follow the steps involved in solving projectile motion problems. (b) There is a large tree halfway between the archer and the target with an overhanging horizontal branch 3.50 m above the release height of the arrow. Will the arrow go over or under the branch?
(a) [tex]18.4^{\circ}[/tex]
We know that the horizontal distance travelled by the arrow is
d = 75.0 m
We also know that the horizontal range of a projectile is given by
[tex]d=\frac{v^2}{g} sin 2\theta[/tex]
where
v is the speed of the projectile
g = 9.8 m/s^2 is the acceleration of gravity
[tex]\theta[/tex] is the angle of the projectile
Here we have
v = 35.0 m/s
Substituting into the equation and solving for [tex]\theta[/tex], we find
[tex]\theta=\frac{1}{2}sin^{-1} (\frac{dg}{v^2})=\frac{1}{2}sin^{-1} (\frac{(75.0 m)(9.8 m/s^2)}{(35.0 m/s)^2})=18.4^{\circ}[/tex]
(b) 6.2 m
In order to answer this part of the problem, we have to calculate what is the maximum height reached by the projectile in its trajectory.
First of all, we can calculate the vertical component of the velocity, which is given by:
[tex]u_y = u sin \theta = (35.0 m/s) sin 18.4^{\circ} = 11.0 m/s[/tex]
The motion along the vertical direction is a uniformly accelerated motion with constant acceleration
g = -9.8 m/s^2
(negative since it points downward). So we can write
[tex]v_y^2 - u_y^2 = 2gh[/tex]
where
[tex]v_y = 0[/tex] is the vertical velocity at the point of maximum height
h is the maximum height
Solving for h, we find
[tex]h=\frac{v_y^2 - u_y^2}{2g}=\frac{0-(11.0 m/s)^2}{2(-9.8 m/s^2)}=6.2 m[/tex]
Therefore, the arrow will go over the branch (which is located 3.50 m above the ground).
Projectile motion principles can be used to solve this problem. θ can be calculated by substituting the given values into the kinematic equation. To know if the arrow goes over or under the branch, calculate the arrow's height at halfway point and compare with the height of the branch.
Explanation:The subject of this question pertains to projectile motion in physics. In order to solve this, we must apply kinematic equations, specifically the equation for horizontal projectile motion which is θ = arctan[(v² ± √(v⁴ - g*(g*x² + 2*y*v²)) / (g*x)], where v is the initial speed, g is the acceleration due to gravity, x is the horizontal distance, and y is the vertical distance.
First, determine the initial speed in m/s, which is given as 35.0 m/s.Next, set the acceleration due to gravity as g = 9.8 m/s².Then, define the horizontal distance x to the target, which is 75.0 m.Set y = 0, because the release height and target height are the same.Plug these numbers into the equation to find θ, which will need to be calculated twice because of the ± in the equation. You'll get two angles, but only the smaller one is practically possible, because the larger would require the arrow to first rise above the target before falling to it.For part (b), to determine if the arrow will go over or under the branch, calculate the arrow's height at the halfway point using the formula y = x*tan(θ) - [(g*x²) / (2*v²*cos²(θ))]. If this height is greater than 3.5 m, the arrow will go over the branch. Otherwise, it will go under.Learn more about Projectile Motion here:https://brainly.com/question/20627626
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The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10–4 s–1. If the initial concentration of cyclopropane is 1.33 M, what is the concentration of cyclopropane after 644 s?
Answer:
.864 M
Explanation:
For first order decomposition,
rate constant k = 1/t x ln a / (a - x )
given , a = 1.33 M , t = 644 s , k = 6.7 x 10⁻⁴ , a - x = ? = b( let )
6.7 x 10 ⁻⁴ = 1/644 x ln 1.33/b
ln 1.33/b = 6.7 x 10⁻⁴ x 644 = .4315
1.33 / b = e⁰ ⁴³¹⁵ = 1.5395
b = 1.33 / 1.5395 = .864 M.
The drag force pushes opposite your motion as you ride a bicycle. If you double your speed, what happens to your force?
Explanation:
The Drag Force equation is:
[tex]F_{D}=\frac{1}{2}C_{D}\rho A_{D}V^{2}[/tex] (1)
Where:
[tex]F_{D}[/tex] is the Drag Force
[tex]C_{D}[/tex] is the Drag coefficient, which depends on the material
[tex]\rho[/tex] is the density of the fluid where the bicycle is moving (air in this case)
[tex]A_{D}[/tex] is the transversal area of the body or object
[tex]V[/tex] the bicycle's velocity
Now, if we assume [tex]C_{D}[/tex], [tex]\rho[/tex] and [tex]A_{D}[/tex] are constant (do not change) we can rewrite (1) as:
[tex]F_{D}=C.V^{2}[/tex] (2)
Where [tex]C[/tex] groups all these coefficients.
So, if we have a new velocity [tex]V_{n}[/tex] , which is the double of the former velocity:
[tex]V_{n}=2V[/tex] (3)
Equation (2) is written as:
[tex]F_{D}=C.(V_{n})^{2}=C.(2V)^{2}[/tex]
[tex]F_{D}=4CV^{2}[/tex] (4)
Comparing (2) and (4) we can conclude the Drag force is four times greater when the speed is doubled.
It is found that a 5.70 m segment of a long string contains three complete waves and has a mass of 180 g. The string is vibrating sinusoidally with a frequency of 55.0 Hz and a peak-to-valley distance of 19.0 cm. (The "peak-to-valley" distance is the vertical distance from the farthest positive position to the farthest negative position). Calculate the wavelenght.
Answer:
1.9 m.
Explanation:
Three complete waves in the length of 5.7 m
The distance traveled by one complete wave is called wavelength.
Thus, the distance traveled by one wave = 5.7 / 3 = 1.9 m
Thus, the wavelength is 1.9 m.
Answer:
wavelength = 3.8 m
Explanation:
As we know that linear mass density is defined as the ratio of mass and length
so here we have
[tex]\mu = \frac{m}{L}[/tex]
[tex]\mu = \frac{0.180}{5.70}[/tex]
now we have
[tex]\mu = 0.0315 kg/m[/tex]
Now it is given that string contains three complete waves
length of one segment on string is half of the wavelength
so here we have
[tex]3\frac{\lambda}{2} = 5.70 m[/tex]
[tex]\lambda = 3.8 m[/tex]
So wavelength of the wave on string is 3.8 m
A rescue plane wants to drop supplies to isolated mountain climbers on a
rocky ridge 235m below?
Part (a)
If the plane is traveling horizontally with a speed of 61.1m/s, how far in
advance of the recipients (horizontal distance) must the goods be dropped?
Part (b)
Suppose, instead, that the plane releases the supplies a horizontal distance
of 425m in advance of the mountain climbers.
What vertical velocity (up or
down) should the supplies be given so that they arrive precisely at the climbers' position?
Answer:
Part (a): The goods must be dropped 422.812 meters advance of the recipients.
Part (b): The supplies must be given with ascendent vertical velocity of V=0.147 m/s to make they arrive precisely at the climbers position.
Explanation:
h= 235m
g= 9.8 m/s²
V= 61.1 m/s
Part a:
fall time of supplies:
[tex]t=\sqrt{\frac{2.h}{g} }[/tex]
t= 6.92 sec
d= V*t
d= 61.1 m/s * 6.92 s
d= 422.812 m
Part b:
d= 425m
d=V*t
t=d/V
t= 6.95 sec
Δt= 6.95 sec - 6.92 sec
Δt=0.03 sec
The supplies must be given ascendent vertical velocity to compensate that difference of time Δt. the half of the difference must be used to the ascendent part and the other half will be used to descendent part of the supplies.
To calculate the vertical velocity:
Vo= g * Δt/2
Vo= 9.8 m/s² * (0.03 sec/2)
Vo= 0.147 m/sec
Part (a) The horizontal distance in advance the goods should be dropped is approximately 422.812 meters
Part (b) The velocity to be given to the supplies is approximately 0.394 m/s up
The reason the above values are correct is as follows:
The known parameters are;
The vertical distance of the climbers below the airplane, h = 235 m
The horizontal velocity of the airplane, v = 61.1 m/s
Acceleration due to gravity, g ≈ 9.81 m/s²
Part (a) Required:
The distance in advance of the recipients the goods must be dropped
Solution:
The time, t, it will take the goods to drop is given by the following formula for free fall;
[tex]t =\mathbf{ \sqrt \dfrac{2 \times h }{g }}[/tex]
[tex]t =\ \sqrt {\dfrac{2 \times 235 }{9.81 } } \mathbf{\approx 6.92}[/tex]
The time it will take the goods to drop, t ≈ 6.92 seconds
The distance in advance the goods should be dropped, d, is given as follows;
Distance , d = Velocity, v × Time, t
∴ d = Velocity of the airplane, v × The time it will take the goods to drop, t
Which gives;
d ≈ 61.1 m/s × 6.92 s = 422.812 meters
The horizontal distance in advance the goods should be dropped, d ≈ 422.812 meters
Part (b) Given:
The horizontal distance in advance the airplane releases the supplies, d = 425 meters
Required:
The vertical velocity (up or down) to be given the to supplies so they arrive at the climbers position
Solution:
The time the supplies spend in the air, t, is given as follows;
t = d/v
Where;
v = The horizontal velocity of the airplane = 61.1 m/s
∴ t = 425 m/(61.1 m/s) = 6.95581015 s ≈ 6.96 s
The vertical distance of travel, s, is given by the following kinematic equation of motion
s = u·t + (1/2)·g·t²
Where;
u = The vertical velocity downwards
s = The distance = 235 meters (below)
g = +9.81 m/s² (downward motion)
Plugging in the values gives;
235 = u·6.96 + (1/2)×9.81×6.96² = 6.96·u + (1/2)×9.81×6.96 = 237.606048
u·6.96 = 237.606048- 240.345 = -2.738952
u = -2.738952/6.96 ≈ -0.394
The velocity to be given to the supplies, u ≈ -0.394 m/s down ≈ 0.394 m/s up (wards)
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Different units can be used to measure the same physical quantity, differing only by some multiplicative factor. The cgs unit for magnetic field, the gauss, is equal to ________ tesla.
Answer: the creect answer is 10^-4
Explanation:
CGS stands for Cetimetre-Gram-Metre system and Gaussian units constitute a metric system of physical units.
One gauss (G) is equivalent to 1x10^-4 tesla (T) and is used as a unit for measuring magnetic field strength.
Explanation:The cgs unit for magnetic field strength is the gauss (G), which is a smaller unit compared to the SI unit of tesla (T). When converting from gauss to tesla, the relation is that 1 gauss is equal to ×10-4 tesla. For reference, the Earth's magnetic field at its surface is about 0.5 G, or 5 × 10-5 T.
The work done by an engine equals one-fourth the energy it absorbs from a reservoir. True or False
True IF the engine is 25% efficient. False otherwise.
A skydiver has reached terminal velocity—she now falls at a constant speed, so her acceleration is zero. Is there a net force on her? If so, what is the direction?
Answer:
No, the net force on the skydiver is zero
Explanation:
According to Newton's Second Law, the net force on an object is equal to the product between the mass of the object and its acceleration:
[tex]F=ma[/tex]
where
F is the net force
m is the mass of the object
a is the acceleration
In this problem, the acceleration of the skydiver is zero:
a = 0
This implies that also the net force on the skydiver is zero, according to the previous equation:
F = 0
So, the net force on the skydiver is zero. This occurs because the air resistance, which points upward, exactly balances the force of gravity on the skydiver, acting downwards.
A soft drink (mostly water) flows in a pipe at a beverage plant with a mass flow rate that would fill 220 0.355 - L cans per minute. At point 2 in the pipe, the gauge pressure is 152kPa and the cross-sectional area is 8.00cm2. At point 1, 1.35m above point 2, the cross-sectional area is 2.00cm2.
a) Find the mass flow rate.
b) Find the volume flow rate.
c) Find the flow speeds at points 1 and 2.
d) Find the guage pressure at point 1.
Answer:
a) 1.301 kg/s
b) 0.001301 m³/s
c) V₁ = 6.505 m/s, V₂ = 1.626 m/s
d) 118.93 kPa
Explanation:
Given:
The number of cans = 220
The volume of can, V = 0.355 L = 0.355 × 10⁻³ m³
time = 1 minute = 60 seconds
gauge pressure at point 2, P₂ = 152 kPa
b) Thus, the volume flow rate, Q = Volume/ time
Q = (220 × 0.355 × 10⁻³)/60 = 0.001301 m³/s
a) mass flow rate = Volume flow rate × density
since it is mostly water, thus density of the drink = 1000 kg/m³
thus,
mass flow rate = 0.001301 m³/s × 1000 kg/m³ = 1.301 kg/s
c) Given:
Cross section at point 1 = 2.0 cm² = 2 × 10 ⁻⁴ m²
Cross section at point 2 = 8.0 cm² = 8 × 10 ⁻⁴ m²
also,
Q = Area × Velocity
thus, for point 1
0.001301 m³/s = 2 × 10 ⁻⁴ m² × velocity at point 1 (V₁)
or
V₁ = 6.505 m/s
for point 2
0.001301 m³/s = 8 × 10 ⁻⁴ m² × velocity at point 1 (V₂)
or
V₂ = 1.626 m/s
d) Applying the Bernoulli's theorem between the points 1 and 2 we have
[tex]P_1+\rho gV_1 + \frac{\rho V_1^2}{2}=P_2+\rho gV_2 + \frac{\rho V_2^2}{2}[/tex]
or
[tex]P_1=P_2+\rho\timesg(y_2-y_1)+\frac{\rho}{2}(V_2^2-V_1^2))[/tex]
on substituting the values in the above equation, we get
[tex]P_1=152+1000\times 9.8(1.35)+\frac{1000}{2}(1.626^2-6.505^2))[/tex]
it is given that point 1 is above point 2 thus, y₂ -y₁ is negative
or
[tex]P_1=118.93\ kPa[/tex]
thus, gauge pressure at point 1 is 118.93 kPa
A diffraction grating with 750 slits per mm is illuminated by light which gives a first-order diffraction angle of 34.0°. What is the wavelength of the light?
Explanation:
The diffraction angles [tex]\theta_{n}[/tex] when we have a slit divided into [tex]n[/tex] parts are obtained by the following equation:
[tex]dsin\theta_{n}=n\lambda[/tex] (1)
Where:
[tex]d[/tex] is the width of the slit
[tex]\lambda[/tex] is the wavelength of the light
[tex]n[/tex] is an integer different from zero
Now, the first-order diffraction angle is given when [tex]n=1[/tex], hence equation (1) becomes:
[tex]dsin\theta_{1}=\lambda[/tex] (2)
We know:
[tex]\theta_{1}=34\°[/tex]
In addition we are told the diffraction grating has 750 slits per mm, this means:
[tex]d=\frac{1mm}{750}[/tex]
Solving (2) with the known values we will find [tex]\lambda[/tex]:
[tex]\lambda=(\frac{1mm}{750})sin(34\°)[/tex] (3)
[tex]\lambda=0.00074559mm[/tex] (4)
Knowing [tex]1mm=10^{6}nm[/tex]:
[tex]\lambda=745.59nm[/tex] >>>This is the wavelength of the light, wich corresponds to red.
In Ptolemy's Earth-centered model for the solar system, Venus's phase is never full as viewed from Earth because it always lies between Earth and the Sun. In reality, as Galileo first recognized, Venus is __________.
Explanation:
Galileo observed that Venus presented phases (such as those of the moon) together with a variation in size; observations that are only compatible with the fact that Venus rotates around the Sun and not around Earth.
This is because Venus presented its smaller size when it was in full phase and the largest size when it was in the new one, when it is between the Sun and the Earth.
In other words: When Venus is in its full phase it is not possible to observe it from the Earth because always in this phase, Venus, the Sun and the Earth are in conjunction (or aligned). This means the Sun is between Venus and Earth, in the orbit that both planets describe around this star.
Therefore, from the Earth, the Sun covers Venus.
This fact along with other discoveries were presented by Galileo to the Catholic Church (which supported the geocentric theory at that time) as a proof that completely refuted Ptolemy's geocentric system and affirmed Copernicus' heliocentric theory.
If the magnitude of the electric field in air exceeds roughly 3 ✕ 106 N/C, the air breaks down and a spark forms. For a two-disk capacitor of radius 54 cm with a gap of 3 mm, what is the maximum charge (plus and minus) that can be placed on the disks without a spark forming (which would permit charge to flow from one disk to the other)? The constant ε0 = 8.85 ✕ 10-12 C2/(N·m2).
The electric field inside a parallel plate capacitor is given by:
E = Q/(ε₀A)
E is the electric field, Q is the charge stored on one of the plates, and A is the area of one of the plates.
The plates are circular, so the area A of one of the plates is given by:
A = πr²
where r is the radius.
Therefore the electric field is given by:
E = Q/(ε₀πr²)
Given values:
E = 3×10⁶N/C (max E field allowed before breakdown occurs)
r = 54×10⁻²m
Plug in these values and solve for Q:
3×10⁶ = Q/(ε₀π(54×10⁻²)²)
Q = 2.4×10⁻⁵C
Marina is staring at an optical illusion where he sees a version of the American flag that is colored green, yellow, and black. When the flag is removed and she stares at a blank screen, she sees an afterimage of the flag that is red, white, and blue. Which theory best explains this illusion?
Explanation:
The reason why Marina sees the colour red, white and blue or the original colour of the American flag is that because of a phenomenon known as Afterimage. The retina in our eyes have mainly three receptors that are colour sensitive known as cones. These receptors can perceive the colour green, red and blue. Now when we look or stare at a particular colour for a long time, what happen is that our retina becomes tired and they ignore the colours that stared at. And now they work to form other colours at the retina just like the way when we produce other colour from the primary colour.
If the red receptor gets exhausted we will see the colour red. Likewise when we see the colour orange when we stare at the colour blue.
This explains the optical illusion of the American flag.
Final answer:
Marina's observation of a red, white, and blue afterimage after staring at a green, yellow, and black flag is explained by the opponent-process theory of color perception. This theory indicates that colors are perceived in opposing pairs, and overstimulation of certain color-sensitive cells can lead to the perception of their opposite colors when looking away.
Explanation:
The Opponent-Process Theory of Color Perception
The optical illusion experienced by Marina where she sees an afterimage of the American flag in red, white, and blue after staring at a flag colored green, yellow, and black can be explained by the opponent-process theory of color perception.
This theory suggests that color perception is controlled by the activity of two opposing sets of colors: red versus green, and blue versus yellow, plus a black versus white system. When Marina stares at the green, yellow, and black flag, the respective ganglion cells in her retina which are associated with these colors become fatigued.
After looking away and viewing a blank screen, these cells reduce their activity, resulting in Marina's brain interpreting the lack of those colors as their opposites, which are red, white, and blue. This means that the afterimage is not just a random occurrence but rather a direct consequence of the way our visual system works to perceive colors.
The opponent-process theory is supported by how the retinal ganglion cells and the neurons in the visual cortex process color signals, as well as experimental demonstrations like staring at a flag and observing the afterimage that appears.
This illusion occurs because while staring at the flag, the green, black, and yellow sensitive ganglion cells become overstimulated and when the gaze is moved to a white background, the decreased stimulation is interpreted as their opponent colors. This effect persists until the ganglion cells return to their normal activity state, at which point the afterimage will fade away.
Which of the following is also a form of electromagnetic waves like light? A. Microwaves B. Sound waves C. Thermal energy D. Alpha radiation
Microwaves is a form of electromagnetic waves like light.
Answer: Option A
Explanation:
Electromagnetic spectrum constitutes a broad classification of waves of different wavelength starting from radio waves to gamma rays. Microwaves are in the order of Giga hertz (i.e) 10^9 where it finds major applications like antennas used in the television, frequency of FM radio channels, cellular phones, e.t.c.
Their wavelength ranges from 1 meter to one millimeter. The sun is also capable of emitting microwaves where most of them are observed by the earth's atmosphere.
2. An engine's _______ contains the cylinder head, the valves, the valve train components, the manifolds, and the engine covers. A. lower end B. upper end C. bottom end D. back end
Answer:
B. upper end
Explanation:
An engine's upper end contains the cylinder head, the valves, the valve train components, the manifolds, and the engine covers.
Final answer:
The upper end of an engine contains important components such as the cylinder head, valves, and valve train components.
Explanation:
The answer to the question is B. upper end. The upper end of an engine refers to the components located above the engine block. This includes the cylinder head, valves, valve train components, manifolds, and engine covers. These components are responsible for controlling the flow of air and fuel into the cylinders and the expulsion of exhaust gases.
Ciara is swinging a 0.015 kg ball tied to a string around her head in a flat, horizontal circle. The radius of the circle is 0.70 m. It takes the ball 0.60 seconds to complete one full circle. Calculate the tension in the string and its direction that provides the centripetal force acting on the ball to keep it in the circular path.
A) 0.0077 N, toward the center of the circle
B) 1.2 N, toward the center of the circle
C) 0.0077 N, along the line tangent to the circle
D) 1.2 N, along the line tangent to the circle
Answer:
B) 1.2 N, toward the center of the circle
Explanation:
The circumference of the circle is:
C = 2πr
C = 2π (0.70 m)
C = 4.40 m
So the velocity of the ball is:
v = C/t
v = 4.40 m / 0.60 s
v = 7.33 m/s
Sum of the forces in the radial direction:
∑F = ma
T = m v² / r
T = (0.015 kg) (7.33 m/s)² / (0.70 m)
T = 1.2 N
The tension force is 1.2 N towards the center of the circle.
Answer:
1.2 N, toward the center of the circle
Explanation:
It is given that,
Mass of the ball, m = 0.015 kg
The radius of the circle, r = 0.7 m
Time taken by the ball to complete complete circle, t = 0.6 s
We need to find the tension in the string and its direction that provides the centripetal force acting on the ball to keep it in the circular path. Here, tension in the string balances the centripetal force so that the ball moves in circular path. So,
[tex]T=\dfrac{mv^2}{r}[/tex]
Since, [tex]v=\dfrac{2\pi r}{t}=\dfrac{2\pi \times 0.7}{0.6}=7.33\ m/s[/tex]
So, [tex]T=\dfrac{0.015\times (7.33)^2}{0.7}[/tex]
T = 1.15 N
or
T = 1.2 N
The direction of centripetal force is toward the center of circle. So, the correct option is (b).
A rope has one end tied to a vertical support. You hold the other end so that the rope is horizontal. If you move the end of the rope back and forth with a frequency of 4 Hz, the transverse wave you produce has a wavelength of 0.5 m. What is the speed of the wave in the rope?
a. 0.13 m/s
b. 8 m/s
c. 2 m/s
d. 4 m/s
Like any other wave, the speed of the wave on the rope is
Speed = (frequency) x (wavelength)
Speed = (4 Hz) x (0.5 m)
Speed = 2 m/s
Divers often inflate heavy duty balloons attached to salvage items on the sea floor. If a balloon is filled to a volume of 3.00 L at a pressure of 2.50 atm, what is the volume of the balloon when it reaches the surface?
Answer: The volume of balloon when it reaches the surface is 7.5 L.
Explanation:
The normal pressure at the surface of sea is 1 atm.
To calculate the volume of balloon, we use the equation given by Boyle's law.
This law states that pressure of the gas is inversely proportional to the volume of the gas at constant temperature. The equation for this law follows:
[tex]P_1V_1=P_2V_2[/tex]
[tex]P_1\text{ and }V_1[/tex] are initial pressure and volume.
[tex]P_2\text{ and }V_2[/tex] are final pressure and volume.
We are given:
[tex]P_1=2.5atm\\V_1=3.00L\\P_2=1atm\\V_2=?L[/tex]
Putting values in above equation, we get:
[tex]2.5atm\times 3L=1atm\times V_2\\\\V_2=7.5L[/tex]
Hence, the volume of balloon when it reaches the surface is 7.5 L.
Which type of heat transfer can happen through empty space?
Explanation:
There are three ways in which the thermal transfer (heat) occurs:
1. By Conduction, when the transmission is by the direct contact.
2. By Convection, heat transfer in fluids (like water or the air, for example).
3. By Radiation, by the electromagnetic waves (they can travel through any medium and in vacumm or empty space)
Since outter space is vacuum (sometimes called "empty"), energy cannot be transmitted by convection, nor conduction. It must be transmitted by electromagnetic waves that are able to travel with or without a medium.
A commuter train passes a passenger platform at a constant speed of 40.4 m/s. The train horn is sounded at its characteristic frequency of 350 Hz. (a) What overall change in frequency is detected by a person on the platform as the train moves from approaching to receding? (Indicate whether the frequency increases of decreases with the sign of your answer.) The response you submitted has the wrong sign. Hz (b) What wavelength is detected by a person on the platform as the train approaches? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m
(a) -83.6 Hz
Due to the Doppler effect, the frequency of the sound of the train horn appears shifted to the observer at rest, according to the formula:
[tex]f' = (\frac{v}{v\pm v_s})f[/tex]
where
f' is the apparent frequency
v = 343 m/s is the speed of sound
[tex]v_s[/tex] is the velocity of the source of the sound (positive if the source is moving away from the observer, negative if it is moving towards the observer)
f is the original frequency of the sound
Here we have
f = 350 Hz
When the train is approaching, we have
[tex]v_s = -40.4 m/s[/tex]
So the frequency heard by the observer on the platform is
[tex]f' = (\frac{343 m/s}{343 m/s - 40.4 m/s})(350 Hz)=396.7 Hz[/tex]
When the train has passed the platform, we have
[tex]v_s = +40.4 m/s[/tex]
So the frequency heard by the observer on the platform is
[tex]f' = (\frac{343 m/s}{343 m/s + 40.4 m/s})(350 Hz)=313.1 Hz[/tex]
Therefore the overall shift in frequency is
[tex]\Delta f = 313.1 Hz - 396.7 Hz = -83.6 Hz[/tex]
And the negative sign means the frequency has decreased.
(b) 0.865 m
The wavelength and the frequency of a wave are related by the equation
[tex]v=\lambda f[/tex]
where
v is the speed of the wave
[tex]\lambda[/tex] is the wavelength
f is the frequency
When the train is approaching the platform, we have
v = 343 m/s (speed of sound)
f = f' = 396.7 Hz (apparent frequency)
Therefore the wavelength detected by a person on the platform is
[tex]\lambda' = \frac{v}{f'}=\frac{343 m/s}{396.7 Hz}=0.865m[/tex]
To solve these problems, use the Doppler Shift formula to calculate the change in frequency as the train moves from approaching to receding. Then, use the relationship between speed, frequency, and wavelength to find the wavelength of the sound as the train approaches.
Explanation:To solve part (a) of the question regarding the overall change in frequency, we need to apply the formula for the Doppler Shift. Since the train passes the observer with a velocity of 40.4 m/s, and the speed of sound in air is about 343 m/s we can utilize these values. Add in the frequency of the horn, 350 Hz, once when the train is approaching (+ velocity) and again while receding (- velocity). This will give us the observed frequency in both scenarios. Subtract the frequency of the horn when it is receding from the frequency when it is approaching to get the overall change in frequency.
For part (b), we already know that the speed of sound v is 343 m/s and the frequency f (Doppler Shift) is 350 Hz from the given. We just need to apply these values into the equation relating speed, frequency, and wavelength (v = fλ). Solving for λ (wavelength) will give us the wavelength of the sound as it reaches the person on the platform.
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The formula of acetic acid is C2H4O2. How many atoms is acetic acid composed of? A. 6 B. 8 C. 4 D. 3
Acetic acid, with the chemical formula C2H4O2, is composed of B. 8 atoms.
What is acetic acid?Acetic acid is represented by the chemical formula C2H4O2. In this formula, there are 2 carbon atoms, 4 hydrogen atoms, and 2 oxygen atoms.
Each letter in the chemical formula corresponds to one atom, and the subscripts denote the number of atoms of each element present. By adding these numbers together (2 + 4 + 2), we obtain the total number of atoms in acetic acid, which is 8. Therefore, the correct option is B (8).
Acetic acid, with its molecular formula C2H4O2, consists of 8 atoms in total, comprising carbon, hydrogen, and oxygen.
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Nuclear energy comes from splitting atoms of __________ to generate heat.
Answer:
Nuclear energy originates from the splitting of uranium atoms – a process called fission. This generates heat to produce steam, which is used by a turbine generator to generate electricity. Because nuclear power plants do not burn fuel, they do not produce greenhouse gas emissions.
Explanation:
Nuclear energy primarily comes from the process of nuclear fission, specifically the splitting of Uranium-235 atoms. This process releases immense energy which is utilized to generate power in nuclear power plants.
Explanation:Nuclear energy, used feasible in power plants, comes primarily from the process of splitting atoms of Uranium-235, a process known as nuclear fission. In this process, a neutron collides with a Uranium atom, causing the atom to split and release more neutrons along with a large amount of energy. This energy, in the form of heat, is then used to produce steam which drives turbines, thereby generating electricity.
Thus, it's clear that the process of splitting large, complex atomic nuclei, particularly those of Uranium-235, not only induces a chain reaction (due to the release of more neutrons) but also provides us with a sophisticated method of generating power in the form of nuclear energy.
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A 200 N force is applied to an object (that is at the origin) at 30 degrees above the horizontal on the positive x axis. A second force is applied at 20 degrees below the horizontal on the negative x axis. In order for the object to be in equilibrium in the y direction, what must the magnitude of this force be?
Answer:
294.11 N
Explanation:
F1 = 200 N
Let the other force is F2 = F = ?
Resolve the components of F1 and F2.
As the object is in equilibrium in y direction, it means the net force in y direction is zero.
So, F1 Sin 30 = F2 Sin 20
200 x 0.5 = F x 0.34
F = 294.11 N
The magnitude of force is 294.11 N
Roberto and Laura are studying across from each other at a wide table. Laura slides a 2.2 kg book
toward Roberto. If the net force acting on the book is 1.6 N to the right, what is the book's acceleration?
Explanation:
Force = Mass × Acceleration
1.6 = 2.2 × a
a = 1.6/2.2
= 0.73 m/s^2
Note that the acceleration will be negative.
Answer: The acceleration of the book is [tex]0.73m/s^2[/tex]
Explanation:
Force is defined as the push or pull on an object with some mass that causes change in its velocity.
It is also defined as the mass multiplied by the acceleration of the object.
Mathematically,
[tex]F=ma[/tex]
where,
F = force exerted on the book = 1.6 N
m = mass of the book = 2.2 kg
a = acceleration of the book = ?
Putting values in above equation, we get:
[tex]1.6kg.m/s^2=2.2\times a\\\\a=\frac{1.6}{2.2}=0.73m/s^2[/tex]
Hence, the acceleration of the book is [tex]0.73m/s^2[/tex]
If you were to cut a small permanent bar magnet in half,A) None of these statements is true. B) one piece would be a magnetic north pole and the other piece would be a south pole.C) each piece would in itself be a smaller bar magnet with both north and south poles.D) neither piece would be magnetic.
Explanation:
According to classical physics, a magnetic field always has two associated magnetic poles (north and south), the same happens with magnets. This means that if we break a magnet in half, we will have two magnets, where each new magnet will have a new south pole, and a new north pole. However, the magnetic force of each magnet will be less than that of the original magnet.
This is because for classical physics, naturally, magnetic monopoles can not exist.
Nevertheless, according to quantum physics, magnetic monopoles do exist, which was predicted by Paul Dirac in 1981. This has led to several experiments and investigations, among which the most recent one so far (year 2014), is the experiment led by a group of scientists from the Amherst College (United States) and the University of Aalto (Finland), that reported having synthesized for the first time in a laboratory a magnet of a single magnetic pole.
The Kinetic energy, K, of an object with mass m moving with velocity v can be found using the formula - E_{\text{k}}={\tfrac {1}{2}}mv^{2}
. A scientist measured the velocity of a 5-kilogram object and a 20-kilogram object in an experiment. If the velocity of the 5-kilogram object was twice the velocity of the 20-kilogram object, what was the ratio of the kinetic energy of the 5 kilogram object to the kinetic energy of the 20-kilogram object?
Answer:
The ratio of kinetic energies of 5 kg object to 20 kg object is 1:1.
Explanation:
Kinetic energy is defined as energy possessed by an object due to its motion.It is calculated by:
[tex]K.E=\frac{1}{2}mv^2[/tex]
Kinetic energy of the 5 kg object.
Mass of object,m = 5 kg
Velocity of an object = v
[tex]K.E=\frac{1}{2}mv^2=\frac{1}{2}\times 5kg\times v^2[/tex]
Kinetic energy of the 20 kg object.
Mass of object,m' = 20 kg
Velocity of an object = v'
[tex]K.E=\frac{1}{2}mv^2=\frac{1}{2}\times 20kg\times v'^2[/tex]
The ratio of the kinetic energy of the 5 kilogram object to the kinetic energy of the 20-kilogram object:
[tex]\frac{K.E}{K.E'}=\frac{\frac{1}{2}\times 5kg\times v^2}{\frac{1}{2}\times 20kg\times v'^2}[/tex]
Given that, v = 2v'
[tex]\frac{K.E}{K.E'}=\frac{1}{1}[/tex]
The ratio of kinetic energies of 5 kg object to 20 kg object is 1:1.
When an object oscillating in simple harmonic motion is at its maximum displacement from the equilibrium position, which of the following is true of the values of its speed and the magnitude of the restoring force?
At maximum displacement (amplitude) in simple harmonic motion, the speed of the object is zero and the restoring force is at its maximum. This is because the object has momentarily stopped before changing direction to move back towards the equilibrium.
Explanation:When an object in simple harmonic motion is at its maximum displacement from the equilibrium position, its speed is zero and the magnitude of the restoring force is at its maximum. This is because at maximum displacement, the object has stretched the spring to its limit and hence the spring force (the restoring force) is at its peak. This force aims to pull the object back to the equilibrium position. However, at this point, the object has not yet started moving back, so its speed is zero.
Consider a scenario with a spring-object system: if the object is pulled max away from the equilibrium position (max displacement or amplitude), the spring force is at max (Hooke's law: F = -kx where F is the restoring force, k is the spring constant, and x is the displacement). Since the object is momentarily at rest before it starts moving back towards the equilibrium, its velocity or speed is zero.
Consequently, at maximum displacement (amplitude), the speed is zero while the restoring force is maximum.
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