Answer:
the medium through which it travels
Explanation:
Two children are throwing a ball back-and-forth straight across the back seat of a car. The ball is being thrown 7 mph relative to the car, and the car is travelling 45 mph down the road. If one child doesn't catch the ball and it flies out the window, in what direction does the ball fly (ignoring wind resistance)
Answer:
the ball will fly in AX direction, making angle of 8.84° from the motion of the car
Explanation:
Given the data in the question and as illustrated in the diagram below;
Now, Lets assume line AB represent the movement of the car,
AC is the movement of the ball been thrown back and forth in the back seat
Ax is the motion of the ball it flies off the window
so from the diagram, We can see triangle ABC
where AB is 45 mph and AC = 7 mph
and angle ∠CAB = 90°
using SOH CAH TOA
TOA; tanθ = Opposite / Adjacent
tanθ = Opposite / Adjacent
tan( ∠ ABC ) = AC / AB
we substitute
tan( ∠ ABC ) = 7 / 45
tan( ∠ ABC ) = 0.15555
( ∠ ABC ) = tan⁻¹ 0.15555
( ∠ ABC ) = 8.84°
Therefor, angle ( ∠ ABC ) is 8.84°
Meaning angle ( ∠ XAA' ) is also 8.84°
Therefore, the ball will fly in AX direction, making angle of 8.84° from the motion of the car
The tension in a pulley belt is 31 N when stationary. Calculate power in watts transmitted when the belt is on the point of slipping on the smaller wheel. the wheel is 379 mm diameter and the coefficient of friction is 0.3. The angle of lap is 1610. The wheel speed is 1,547 rev/min.
Answer:
P = 756.84 Watts
Explanation:
As the tension is stationary or innitial, T₀ = 31 N, the mean would be:
T₁ + T₂ / 2 = T₀ (1)
T₁ + T₂ = 2 * 31 = 62 N
Now, with the following expression we can determine the linear speed:
V = πWD (2)
W: angular speed of the wheel (rev/s)
D: diameter of the wheel (in meters)
W = 1547 rev/min * (1 min/60 s) = 25.78 rev/s
V = π * 25.78 * 0.379 = 30.695 m/s
We also know that:
T₁ / T₂ = exp (μθ)
T₁ = T₂ exp(μθ) (3)
We already have those values so replacing:
T₁ = T₂ exp(0.3 * 161 * π/180)
T₁ = 2.32T₂ (4)
We can now replace (4) in (1) like this:
T₁ + T₂ = 62 N
2.32T₂ + T₂ = 62
3.32T₂ = 62
T₂ = 18.67 N
Which means that T₁:
T₁ = 2.32(18.67)
T₁ = 43.33 N
Finally, the power can be determined using the following expression:
P = (T₁ - T₂)V (5) Replacing we have:
P = (43.33 - 18.67)*30.695
P = 756.84 WattsHope this helps
A person slaps her leg with her hand, which results in her hand coming to rest in a time interval of 2.65 ms from an initial speed of 5.25 m/s . What is the magnitude of the average contact force exerted on the leg, assuming the total mass of the hand and the forearm to be 1.75 kg
Answer:
the magnitude of the average contact force exerted on the leg is 3466.98 N
Explanation:
Given the data in the question;
Initial velocity of hand v₀ = 5.25 m/s
final velocity of hand v = 0 m/s
time interval t = 2.65 ms = 0.00265 s
mass of hand m = 1.75 kg
We calculate force on the hand F[tex]_{hand[/tex]
using equation for impulse in momentum
F[tex]_{hand[/tex] × t = m( v - v₀ )
we substitute
F[tex]_{hand[/tex] × 0.00265 = 1.75( 0 - 5.25 )
F[tex]_{hand[/tex] × 0.00265 = 1.75( - 5.25 )
F[tex]_{hand[/tex] × 0.00265 = -9.1875
F[tex]_{hand[/tex] = -9.1875 / 0.00265
F[tex]_{hand[/tex] = -3466.98 N
Next we determine force on the leg F[tex]_{leg[/tex]
Using Newton's third law of motion
for every action, there is an equal opposite reaction;
so, F[tex]_{leg[/tex] = - F[tex]_{hand[/tex]
we substitute
F[tex]_{leg[/tex] = - ( -3466.98 N )
F[tex]_{leg[/tex] = 3466.98 N
Therefore, the magnitude of the average contact force exerted on the leg is 3466.98 N
How many spoonfuls of water did it take for your sponge to be 100% saturated?
Answer:
19
Explanation:
I legit did this and it took 19.
Besides ethical considerations, what is another reason why Milgram’s experiment may be difficult to duplicate?
To increase the energy of an electromagnetic wave, which property should
you increase?
A. Shift
B. Frequency
o
C. Wavelength
D. Speed
Answer:
B. Frequency
Explanation:
Two electromagnetic waves are traveling through empty space. The wave with the greater wavelength is also characterized by _____.
a. the lower frequency
b. the higher frequency
c. the faster speed
d. the slower speed
How can a tennis ball and a bowling ball have the same momentum ?
A tennis ball and a bowling ball can have the same momentum. This is because, it depends upon both the mass of object and velocity of object.
What is Momentum?Momentum can be defined as the mass in motion. All objects which have mass so, if an object is moving in space, then it has some amount of momentum which has its mass in motion. The amount of momentum which an object has depend upon two variables which include how much stuff is moving that is the mass of object and how fast the stuff is moving that is the speed.
A fast-moving tennis ball may have the same momentum as a slow-bowling ball. It is important to understand here that the momentum of an object which depends on the product of the mass and velocity of an object, but not the mass or the velocity alone.
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A physics student mounts two thin lenses along a single optical axis (the lenses are at right angles to the line connecting them, and they appear concentric when viewed from either end). The lenses are identical, each with a positive (converging) focal length of 14.8 cm. They are separated by a distance of 39.4 cm. Lens 1 is to the left of Lens 2.
Required:
a. What is the final image's distance (in cm) from Lens 2?
b. Where is the final image located?
c. What is the overall magnification of the lens pair, considered as a single optical instrument?
Answer:
A) q₂ = 75.98 cm, B) q₂' = 115.38 cm, C)
Explanation:
A) This is an exercise in geometric optics, as the two lenses are separated by a greater distance than their focal lengths from each lens, they must be worked as independent lenses.
Lens 1. More to the left
let's use the constructor equation
[tex]\frac{1}{f} = \frac{1}{p} + \frac{1}{q}[/tex]
where f is the focal length, p and q are the distance to the object and the image, respectively,
We must assume a distance to the object to perform the calculation, suppose that the object is 50 cm from lens 1 that is further to the left of the system.
[tex]\frac{1}{q_1} = \frac{1}{f} - \frac{1}{p}[/tex]
[tex]\frac{1}{q_1} = \frac{1}{14.8} - \frac{1}{50}[/tex]
1 / q₁ = 0.04756
q₁ = 21.0227 cm
this image is the object for the second lens that has f₂ = 14.8 cm
the distance must be measured from the second lens
p₂ = 39.4 -q₁
p₂ = 39.4 -21.0227
p₂ = 18.38 cm
let's use the constructor equation
1 / q₂ = 1 / f - 1 / p2
[tex]\frac{1}{q_2} = \frac{1}{14.8} - \frac{1}{18.38}[/tex]
[tex]\frac{1}{q_2}[/tex] = 0.01316
q₂ = 75.98 cm
measured from the second lens
B) the position of the final image with respect to the first lens is
q₂’= q₂ + 39.4
q₂'= 75.98 +39.4
q₂' = 115.38 cm
C) the magnification of a lens is
m = - q / p
in this case the image measured from lens 2 is q2 = 75.98 cm
the distance to the object from the first lens is p1 = 50cm
m = - 75.98 / 50
m = -1.5 X
the negative sign indicates that the image is inverted
What are the functionssss of non-geostationary satellite?
Answer:
A communication system comprising a set of non-geostationary satellites provides communication links between ground stations and terminals, a communication link from a particular station via a satellite terminating at associated terminals in a limited geographical era including the station and providing a.Explanation:
Hopes this helps. Mark as brainlest plz!Geostationary satellites orbit around the Earth at the same rate as the Earth rotates so that the satellites are over the same spot on Earth all the time.
They are called geostationary due to their movement.
Geostationary satellites are a key tool for scientists to monitor and observe the Earth's atmosphere.
What is Ship Handling, an art or a science? Why?
Ship handling is both a science and an art. Science because it requires knowledge of various forces acting on the ship. Art because it requires the skills of an experienced navigator to use these forces in his favour. We may learn the science part from the various ship handling courses.
please give brainliest
The lens labelled (B) has radius 16.5cm on the curved side. Using the shape of the lens to assign the sign of the radius, calculate the focal length of the lens. Give your answer with the correct positive or negative sign using the usual convention for lenses.
Answer:
convex f = 33 cm
concave f = -33 cm
Explanation:
In geometric optics the focal length of a lens is given by
[tex]\frac{1}{f} = ( n-1) \ (\frac{1}{R_2} - \frac{1}{R_1} )[/tex]
where n is the refractive index of the medium, R₁ and R₂ are the focal lengths on each side of the lens.
In this case one of the sides is flat so its focal length is infinite, if the lens is convex the focal length is positive, convergent lens and if it is concave the focal length is negative, divergent lens.
[tex]\frac{1}{f} = (n-1) \ \frac{1}{R}[/tex]
the refractive index of the glass is n = 1.5
let's calculate
1 / f = (1.5 -1) 1 / 16.5
1 / f = 0.03030
f = 33 cm
convex f = 33 cm
concave f = -33 cm
A 620 nm light falls on a photoelectric surface and electrons with the maximum kinetic energy of 0.14 eV are emitted. (a) Determine the work function (in eV). eV (b) Determine the cutoff frequency of the surface (in THz). THz (c) What is the stopping potential (in V) when the surface is illuminated with light of wavelength 420 nm
Answer:
(a) The work function is 1.86 eV.
(b) The cut off frequency is 450 THz.
(c) The stopping potential is 1.16 V.
Explanation:
incident wavelength = 620 nm
Kinetic energy, K = 0.14 eV
According to the photoelectric equation
E = W + KE
where, W is the work function, KE is the kinetic energy.
(a) Let the work function is W.
[tex]W = E - KE\\W = \frac{h c}{\lambda }- KE\\W =\frac{6.63\times 10^{-34}\times3\times 10^{8}}{620\times 10^{-9}\times 1.6\times 10^{-19}}-0.14\\\\W =1.86 eV[/tex]
(b) Let the cut off frequency is f.
W = h f
[tex]1.86\times 1.6\times 10^{-19} = 6.63\times 10^{-34}\times f\\f = 4.5\times 10^{14} Hz =450 THz[/tex]
(c) Let the stopping potential is V.
[tex]E = W + eV\\\frac{6.63\times 10^{-34}\times 3\times 10^{8}}{420\times 10^{-9}\times 1.6\times 10^{-19}}=1.8 + eV\\\\V = 1.16 V[/tex]
a person is sitting on the last bench can see clearly see things written on book but cannot see them distinctly on board. what types of lens is this concave or convex
Answer:
I think concave
Explanation:
un auto si muove lungo una strada rettilinea
Answer:
Un'auto si muove lungo un percorso rettilineo con velocità variabile come mostrato in figura. Quando l'auto è in possesso di A, la sua velocità è 10 ms-1 e quando è in posizione B, la sua velocità è 20 ms-1. Se l'auto impiega 5 secondi per spostarsi da A a B, trova l'accelerazione dell'auto.
Explanation:
two spheres of radii 5cm and 3cm are given charges on risk volume and 50 calling respectively and then connected by a wire calculate the loss of energy after connection
Answer:
Solution given:
Radius of small sphere[r]=5cm=0.05m
Radius of large sphere[R]=10cm=0.1m
capacitance of small sphere[c]=4πε0r
=[tex]4π*8.85×10^{-12}×0.05=5.56*10^{-12}F[/tex]
Charge for small sphere[Q1]=100C
Charge for small sphere[Q2]=50C
Potential difference [V1]=[tex] \frac{charge}{capacitance}=\frac{100}{5.56*10^{-12}}=1.8×10^{13}[/tex]V
.
again
capacitance of small sphere[C]=4πε0R
=[tex]4π*8.85×10^{-12}×0.1=1.11*10^{-11}F[/tex]
Potential difference [V2]=[tex] \frac{charge}{capacitance}=\frac{50}{1.11*10^{-11}}=4.5×10^{12}[/tex]V
Now
Loss of energy:
[tex] \frac{cC(V1-V2)^{2}}{2(c+C)}[/tex]
=[tex] \frac{5.56*10^{-12}*1.11*10^{-11}(1.8*10^{13}-4.5*10^{12})^{2}}{2(5.56*10^{-12}+1.11*10^{-11})}[/tex]
=25Joule
When the palmaris longus muscle in the forearm is flexed, the wrist moves back and forth. If the muscle generates a force of 53.5 N and it is acting with an effective lever arm of 2.25 cm , what is the torque that the muscle produces on the wrist
Answer:
1.20Nm
Explanation:
Given data
Force= 53.5N
Perpendicular distance= 2.25cm= 2.25/100= 0.0225m
The expression for the torque is given as
Torque= Force* Perpendicular distance
Torque= 53.5*0.0225
Torque= 1.20Nm
Hence the toque produced is 1.20Nm
A uniform electric field exists everywhere in the x,y plane. The electric field has a magnitude of 3500 N/coil, and is directed in the positive x direction. A point charge of -9.0 x 10-9 coil is placed at the origin. Determine the magnitude of the net electric field at: (a) x
Answer:
5525 N/C
Explanation:
Magnitude of electric field ( E ) = 3500 N/c
Direction of electric field : positive X axis
point charge ( q ) = -9.0 * 10^-9
Calculate the Magnitude of the net electric field at (a) x = -0.20 m
Magnitude = 5525 N/C
Electric field due to q = ( 9 * 10^9 * 9 * 10^-9 ) / ( -0.2 )^2
= 81 / 0.04 = 2025 N/c
Therefore the magnitude of the net electric field
= 2025 + 3500
= 5525 N/C
How strong is the repulsive force exerted on two point charges that each carry 1.0 E-6 C of negative charge and are 0.30 meters apart?
Coulomb's Constant is 9.0 E9 N*m2/C2
Remember to identity all of your data, write the equation, and show your work.
F = Kq₁q₂/(r)²
K is a constant
R is the distance between them
F = 9.0 E9 × 1.0 E-6 × 1.0 E-6/(0.30)²
= 9.0E-3/0.30² = 9.0E-3/0.09 = 0.1 N
The electrostatic force of repulsion between two charges can be determined using Coulomb's law of electrostatic force. The force of repulsion between the point charges of magnitude 1 ×10 ⁻⁶ C separated by 0.30 m is 0.1 N.
What is Coulomb's law of electrostatic forces?According Coulomb's law of electrostatic forces, the force between two charges q1 and q2 separated by a distance of r meters is given by the expression:
F = K q1 q2/r²
Where, K is Coulomb's Constant equal to 9.0 ×10⁹ Nm²/C²
Given q1 = q2 = 1 ×10 ⁻⁶ C
r = 0.30 m
k = 9.0 ×10⁹ Nm²/C².
Then the electrostatic force of repulsion between the two point charges is calculated as follows:
F = 9.0 ×10⁹ Nm²/C² × 1 ×10 ⁻⁶ C × 1 ×10 ⁻⁶ C/ (0.30 m )²
= 0.1 N.
Therefore, the repulsive force exerted on two point charges that each carry 1.0 E-6 C of negative charge and are 0.30 meters apart is 0.1 N.
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In any given wave, when the frequency of the wave doubles (f = 2f), which of the following other changes would also take place?
A The wavelength would double (λ = 2λ).
B The velocity would double (v = 2v).
C The wavelength would be half (λ = λ/2).
D The velocity would be half (v = v/2).
Answer:
The correct answer is -
B. The velocity would double (v = 2v).
C. The wavelength would be half (λ = λ/2).
Explanation:
A wave has a speed or velocity that is related to the wavelength of the wave and the frequency of the wave and this relationship can be represented by the following equation-
Wave velocity V = Wavelength (λ) * Frequency (f)
Frequency (f) = Velocity (V) / Wavelength(λ).
The frequency and wavelength are inversely proportional and frequency and velocity are directly proportional to each other.
So, if f = 2f then,
putting value in the formula,
2f = 2v/λ, which means, f = 2v and f = λ/2
when the frequency is doubled, the wavelength will be halved and velocity will be doubled.
An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed 13 V. What is the highest rms voltage that can be supplied to this component while staying below the voltage limit in the warning
Answer:
9.2 V
Explanation:
The RMS value of an AC is the effective value of a varying voltage or current in DC, that is the equivalent value of the AC which produces the same effect as an DC. For example if a motor is supplied by a 9V RMS voltage, it will rotate as if the voltage applied was 9V DC.
The RMS value is given by:
RMS voltage = Peak voltage * 1/√2
Given that the maximum voltage should not exceed 13 V, this means that the peak voltage is 13 V. The maximum RMS voltage is:
RMS voltage = Peak voltage * 1/√2 = 13 * 1/√2 = 9.2 V
Imagine observing a white light through two peices of glass, one red and the other blue directly behind it.
What color would the light appear to be?
It is well known that bullets and other missiles fired at Superman simply bounce off his chest. Suppose that a gangster sprays Superman's chest with 6.4 g bullets at the rate of 92 bullets/min, and the speed of each bullet is 400 m/s. Suppose too that the bullets rebound straight back with no change in speed. What is the magnitude of the average force on Superman's chest from the stream of bullets
Answer:
Magnitude of the average force = 7.85 N
Explanation:
Data given:
Mass of bullets, m = 6.4 g
Rate of bullets/min, r = 92 bullets/min
Speed of each bullet, v = 400 m/s
Change in momentum here, Δ B = Bf - Bi
where f is the final and i is the initial
Note that change in momentum = force X time
So, Δ B = m(vf - vi)
= 2mv
= 2 X 0.0064 kg X 400 m/s (convert g to kg)
= 5.12 kg.m/s (for one bullet)
so for the 92 bullets = 92 X 5.12 kg.m/s
= 471.04 kg.m/s
The force = Δ B ÷ Δt
where t = time measured in 60 seconds
= 471.04 kg.m/s ÷ 60 seconds
= 7.85 N
The photo shows falling water droplets.
Which quality of a drop of water increases as it gets closer to Earth's surface?
A. Resistance
B. Mass
C. Magnetism
D. Velocity
As part of a physics experiment, you carry a bathroom scale calibrated in newtons onto an elevator and stand on it. At rest, you check the scale and it reads 588 N. Then the elevator starts accelerating upward at 2.0 m/s2 and you check the reading again. Now what does the scale show
Answer: 708 N
Explanation:
Given
At rest, Elevator reads 588 N
When it starts moving upward at [tex]2\ m/s^2[/tex], apparent weight changes
i.e. weight can be given by
[tex]\Rightarrow W'=m(g+a)\\\Rightarrow W'=mg+mg\cdot \dfrac{a}{g}\\\\\Rightarrow W'=W\left(1+\dfrac{a}{g}\right)\\\\\Rightarrow W'=588\left(1+\dfrac{2}{9.8}\right)\\\\\Rightarrow W'=707.99\approx 708\ N[/tex]
The apparent weight is 708 N
A 1.80-kg monkey wrench is pivoted 0.250 m from its center of mass and allowed to swing as a physical pendulum. The period for small-angle oscillations is 0.940 s. (a) What is the moment of inertia of the wrench about an axis through the pivot
Answer:
[tex]I=0.0987kg.m^2[/tex]
Explanation:
From the question we are told that:
Mass [tex]M=1.80kg[/tex]
Deviation [tex]d=0.250[/tex]
Time [tex]t=0.940s[/tex]
Generally the equation for moment of inertia is mathematically given by
[tex]I=\frac{T}{2\pi}^2(mgd)[/tex]
[tex]I=\frac{0.94}{2.3.142}^2(1.80*9.8*0.250)[/tex]
[tex]I=0.0987kgm^2[/tex]
The load across a 12 V battery consists of a series combination of three resistors 34 Ω, 42Ω, and 30Ω. What is the total resistance of the load? Answer in units of Ω. What is the current in the circuit? Answer in units of A.
Answer:
The total resistance is 106 Ω and the current in the circuit is 0.11 A.
Explanation:
Given that,
Voltage of the battery, V = 12 V
Resistors 34 Ω, 42Ω, and 30Ω are connected in series.
The total resistance is given by :}
R = 34 + 42 +30
= 106Ω
Let I is the total current in the circuit. Using ohm's law to find it such that,
[tex]I=\dfrac{V}{R}\\\\I=\dfrac{12}{106}\\\\I=0.11\ A[/tex]
Hence, the total resistance is 106 Ω and the current in the circuit is 0.11 A.
Two horizontal strings are attached to a block, resting on a frictionless surface as shown
below.A force of 100N pulls on one string. The block does not move. Find the value o
force, F on the other string
ON
Answer:
100N in the opposite direction
Explanation:
as the block is not moving, we can apply the formula f=ma where the total force is equal to the mass times accelaration, since the block is not moving, the net force is zero meaning that the other force is completely cancelling out the force of 100N, or to put it in a maths equation, 100-force=0 as the block is stationary. we can therefore assume that the force cancelling the 100N out is equal to it and therefore 100N in the opposite direction
A block of mass m slides along a frictionless surface with kinetic energy Kiit collides with a block of mass 3m that is initially at rest, and the two blocks stick together and slide with total kinetic energy Kf . What is the ratio Kf:Ki
Answer:
the ratio Kf : Ki is 1 / 4 or 1 : 4
Explanation:
Given the data in the question;
Since this is a perfectly inelastic collision, momentum is conserved;
[tex]P_{initial[/tex] = [tex]P_{final[/tex]
Now for BLOCK 1
mass = M₁ = M
KE = K[tex]_i[/tex]
[tex]\frac{1}{2}[/tex]mv[tex]_i[/tex]₁² = K[tex]_i[/tex]
we solve for v[tex]_i[/tex]₁
mv[tex]_i[/tex]₁² = 2K[tex]_i[/tex]
v[tex]_i[/tex]₁ = √( 2K[tex]_i[/tex] / m )
for BLOCK 2
mass = M₂ = 3m and since its at rest v[tex]_i[/tex]₂ = 0
Now after the collision; Total mass = m + 3m = 4m
KE = K[tex]_f[/tex]
[tex]\frac{1}{2}[/tex]( 4m )v[tex]_f[/tex]² = K[tex]_f[/tex]
(2m)v[tex]_f[/tex]² = K[tex]_f[/tex]
v[tex]_f[/tex] = √(K[tex]_f[/tex] / 2m)
so since [tex]P_{initial[/tex] = [tex]P_{final[/tex]
[m₁ × v[tex]_i[/tex]₁] + [m₂ × v[tex]_i[/tex]₂] = ( m + 3m ) × v[tex]_f[/tex]
so
[ m₁ × √( 2K[tex]_i[/tex] / m ) ] + [ m₂ × 0 ] = ( m + 3m ) × [ √(K[tex]_f[/tex] / 2m) ]
[ m × √( 2K[tex]_i[/tex] / m ) ] = 4m × [ √(K[tex]_f[/tex] / 2m) ]
square both side
m² × 2K[tex]_i[/tex] / m = (4m)² × K[tex]_f[/tex] / 2m
m² × 2K[tex]_i[/tex] / m = 16m² × K[tex]_f[/tex] / 2m
m × 2K[tex]_i[/tex] = 8m × K[tex]_f[/tex]
2K[tex]_i[/tex] = 8K[tex]_f[/tex]
K[tex]_f[/tex] = 2K[tex]_i[/tex] / 8
K[tex]_f[/tex] / K[tex]_i[/tex] = 2 / 8
K[tex]_f[/tex] / K[tex]_i[/tex] = 1 / 4
Therefore, the ratio Kf : Ki is 1 / 4 or 1 : 4
The ratio of the final kinetic energy to initial kinetic energy of the blocks is determined as 1:4.
Final speed of the blocks after collisionThe speed of the two blocks after collision is determined by applying the principle of conservation of linear momentum as follows;
m1u1 + m2u2 = v(m1 + m2)
mu1 + m2(0) = v(m + 3m)
mu1 = v(4m)
u1 = 4v
Ratio of the final kinetic energy to initial kinetic energy[tex]\frac{K.E_f}{K.E_i} = \frac{0.5(4m)v_f^2}{0.5(m)u_1^2} \\\\\frac{K.E_f}{K.E_i} = \frac{4(v_f)^2}{u_1^2} \\\\\frac{K.E_f}{K.E_i} = \frac{4v_f^2}{(4v_f)^2} = \frac{4v_f^2}{16v_f^2} = \frac{1}{4} = 1:4[/tex]
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A 70 kg human body typically contains 140 g of potassium. Potassium has a chemical atomic mass of 39.1 u and has three naturally occurring isotopes. One of those isotopes, 40K (potassium), is radioactive with a half-life of 1.3 billion years and a natural abundance of 0.012 %. Each 40K (potassium) decay deposits, on average, 1.0 MeV of energy into the body.
What yearly dose in Gy does the typical person receive from the decay of 40K (potassium) in the body? Express your answer using two significant figures.
Answer:
Gy = 3.14x10⁻⁴ Gy
Explanation:
To get the dose in Gy we need to use the following expression:
Gy = E / m (1)
Where:
Gy: dose
E: energy absorbed per atom
m: mass of the human body.
We don't have the energy per atom, but we can calculate that by following the next procedure.
First, let's determine the number of atoms of potassium in our body. For that we need to determine the moles in the 140 g of potassium, with the molecular mass and then, use the avogadro's number:
moles = m/MM
moles = 140 / 39.1 = 3.58 moles
N° atoms = 3.58 * 6.02x10²³ atoms = 2.16x10²⁴ atoms of K.
The abundance of the ⁴⁰K is 0.012% so the atoms of this isotope would be:
N = 2.16x10²⁴ * (0.012/100) = 2.59x10²⁰ atoms of ⁴⁰K.
With this number, and the half life rate, we can determine the number of decay atoms in a year (λ) using the following expression:
λ = ln2 / t(1/2)
λ = ln2 / 1.3x10⁹ = 5.33x10⁻¹⁰ year⁻¹
This number, multiplied by the number of atoms:
R = 5.33x10⁻¹⁰ * 2.59x10²⁰ = 1.38x10¹¹ atoms/year
Now, each atom of K gives an average energy of 1 MeV, so with the atoms we have:
E = 1.38x10¹¹ * 1x10⁶ eV = 1.38x10¹⁷ eV
This value can be expressed in Joules so:
E = 1.38x10¹⁷ eV * (1 J / 6.24x10¹⁸ eV) = 0.022 J
Finally, we can use (1) to get the dose in Gy:
Gy = 0.022 / 70
Gy = 3.14x10⁻⁴ GyHope this helps