Answer:
The speed of the second toy car after collision is [tex]v_2 = 0.155 \ m/s[/tex]
Explanation:
Let movement to the right be positive and the opposite negative
From the question we are told that
The mass of the car is [tex]m_1 = 15 \ g = \frac{15}{1000} = 0.015 \ kg[/tex]
The initial velocity of the car is [tex]u_1 = 24 \ cm /s = 0.24 m/s[/tex]
The mass of the second toy car [tex]m_2 = 21 g = 0.021 \ kg[/tex]
The initial velocity of the car is [tex]u_2 = 31 \ cm/s =- 0.31 m/s[/tex]
The final velocity of the first car is [tex]v = 41cm/s = - 0.41 m/s[/tex]
From law of momentum conservation we have that
[tex]m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2[/tex]
substituting values
[tex](0.015* 0.24) +( 0.021 * -0.31) = (0.015 * -0.41 ) + 0.021 v_2[/tex]
[tex]-0.00291 = -0.0615 + 0.021 v_2[/tex]
[tex]v_2 = 0.155 \ m/s[/tex]
The resistivity of a metal increases slightly with increased temperature. This can be expressed as rho=rho0[1+α(T−T0)], where T0 is a reference temperature, usually 20∘C, and α is the temperature coefficient of resistivity. Part A First find an expression for the current I through a wire of length L, cross-section area A, and temperature T when connected across the terminals of an ideal battery with terminal voltage ΔV. Then, because the change in resistance is small, use the binomial approximation to simplify your expression. Your final expression should have the temperature coefficient α in the numerator. Express your answer in terms of L, A, T, T0, ΔV, rho0, and α.
Answer:
I = ΔVA[1 - α (T₀ - T)]/Lρ₀
Explanation:
We have the following data:
ΔV = Battery Terminal Voltage
I = Current through wire
L = Length of wire
A = Cross-sectional area of wire
T = Temperature of wire, when connected across battery
T₀ = Reference temperature
ρ = Resistivity of wire at temperature T
ρ₀ = Resistivity of wire at reference temperature
α = Temperature Coefficient of Resistance
From OHM'S LAW we know that;
ΔV = IR
I = ΔV/R
but, R = ρL/A (For Wire)
Therefore,
I = ΔV/(ρL/A)
I = ΔVA/ρL
but, ρ = ρ₀[1 + α (T₀ - T)]
Therefore,
I = ΔVA/Lρ₀[1 + α (T₀ - T)]
I = [ΔVA/Lρ₀] [1 + α (T₀ - T)]⁻¹
using Binomial Theorem:
(1 +x)⁻¹ = 1 - x + x² - x³ + ...
In case of [1 + α (T₀ - T)]⁻¹, x = α (T₀ - T).
Since, α generally has very low value. Thus, its higher powers can easily be neglected.
Therefore, using this Binomial Approximation, we can write:
[1 + α (T₀ - T)]⁻¹ = [1 - α (T₀ - T)]
Thus, the equation becomes:
I = ΔVA[1 - α (T₀ - T)]/Lρ₀
Convert 45m/s to mph. Choose the best answer to two significant figures.
101mph
45mph
200mph
24mph
Explanation:
45 m/s × (3.28 ft/m) × (1 mi / 5280 ft) × (3600 s/h) = 101 mph
This is actually 3 significant figures. To write in 2 significant figures, you must use scientific notation:
1.0×10² mph
Consider an atom. Which contributes most to the size of the atom?
Answer:
Protons contribute the most to the size of the atom
Answer:
Protons
Explanation:
Protons contribute more to both the mass and size of an atom. Protons contribute more to an atom's mass while electrons contribute more to its size.
The dial of a scale looks like this: 00.0kg. A physicist placed a spring on it. The dial read 00.6kg. He then placed a metal chain on the scale, it read 02.1kg. The physicist, then decided to test Einstein’s equation, and compressed the spring and tied it with the chain and placed it on the scale. It read 02.7kg. Which of the following conclusions is the most likely the physicist will come to?
a. Einstein's equation has an error
b. The scale is broken
c. Compressing the spring didn't add energy
d. The scale's resolution is too low to read the change in mass
Answer:
d. The scale's resolution is too low to read the change in mass
Explanation:
If we want to find the change in energy of the spring, we will have to use the Hooke's Law. Hooke's Law states that:
F = kx
since,
w = Fd
dw = Fdx
integrating and using value of F, we get:
ΔE = (0.5)kx²
where,
ΔE = Energy added to spring
k = spring constant
x = displacement
The spring constant is typically in range of 4900 to 29400 N/m.
So if we take the extreme case of 29400 N/m and lets say we assume an unusually, extreme case of 1 m compression, we get the value of energy added to be:
ΔE = (0.5)(29400 N/m)(1 m)²
ΔE = 1.47 x 10⁴ J
Now, if we convert this energy to mass from Einstein's equation, we get:
ΔE = Δmc²
Δm = ΔE/c²
Δm = (1.47 x 10⁴ J)/(3 x 10⁸ m/s)²
Δm = 4.9 x 10⁻¹³ kg
As, you can see from the answer that even for the most extreme cases the value of mass associated with the additional energy is of very low magnitude.
Since, the scale only gives the mass value upto 1 decimal place.
Thus, it can not determine such a small change. So, the correct option is:
d. The scale's resolution is too low to read the change in mass
You are working in a biology lab and learning to use a new ultracentrifuge for blood ts. The specifications for the centrifuge say that a red blood cell rotating in the ultracentrifuge moves at 470 m/s and has a radial acceleration of 150,000 g's (that is, 150,000 times 9.8 m/s2). The radius of the centrifuge is 0.15 m. You wonder if this claim is correct.
What is the radial acceleration of the ultra-centrifuge using calculations ?
Answer:
The radial acceleration is [tex]a_r = 1472667 \ m/s^2[/tex]
Explanation:
From the question we are told that
The velocity of the red blood cell is [tex]v_r = 470 \ m/s[/tex]
The radial acceleration of the red blood cell is [tex]a_r = 150000g = 150000*9.8 = 1470000 \ m/s^2[/tex]
The radius of the centrifuge is [tex]r = 0.15 \ m[/tex]
Generally radial acceleration is mathematically represented as
[tex]a_r = \frac{v^2}{r}[/tex]
substituting values
[tex]a_r = \frac{470^2}{0.15}[/tex]
[tex]a_r = 1472667 \ m/s^2[/tex]
A substance that produces H+ ions in solution is a.
A)soap
B)acid
C)salt
D)base
Based on the information in the table, which two elements are most likely in the same group, and why?
A table with 5 columns and 5 rows labeled facts about 4 elements. The first column labeled element has entries bismuth (B i), nitrogen (N), oxygen (O), sodium (N a), thallium (T l). The second column labeled atomic mass (a m u) has entries 209, 14, 16, 23, 204. The third column labeled total electrons has entries 83, 7, 8, 11, 81. The fourth column labeled valence electrons has entries 5, 5, 6, 1, 3. The fifth column labeled year isolated has entries 1753, 1772, 1772, 1807, 1861.
bismuth and thallium, because their atomic masses are very similar
nitrogen and oxygen, because they were both first isolated in the same year
sodium and thallium, because their names both end in the same suffix: -ium
bismuth and nitrogen, because they have the same number of valence electrons
Answer: bismuth and nitrogen, because they have the same number of valence electrons
Explanation:
Elements are distributed in groups and periods in a periodic table.
Elements that belong to same groups will show similar chemical properties because they have same number of valence electrons.
The number of valence electrons in Bismuth and nitrogen are 5 and thus thus they will show similar chemical properties and thus belong to the same group.
The atomic masses of elements in a group will differ drastically.
The group number has got nothing to be the isolation year.
Thus bismuth and nitrogen belong to same group because they have the same number of valence electrons
Answer:
D
Explanation:
i got it right in my test
50 POINTS
What happens to kinetic energy of a moving object of the velocity decreases? (Look at photo multiple choice)
Answer: A Answers. Assuming that the terminal velocity doesn't change during the fall, then the kinetic energy would remain constant. However the terminal velocity decreases during the fall since the air becomes denser at lower altitudes.
Explanation:
What happens to the KE of an object when it slows down and heats up? - Quora. The kinetic energy goes down and the loss of the kinetic energy is through the production of heat energy. In real world this is due to friction, or an opposing force that decelerates the object, or a combination of both.
Answer:
Kinetic energy stays the same
The speed of light changes when it goes from ethyl alcohol (n = 1.361) to carbon tetrachloride (n = 1.461). The ratio of the speed of light in carbon tetrachloride to the speed in ethyl alcohol is
Answer:
The ratio of the speed of light in carbon tetrachloride to the speed in ethyl alcohol is 0.93
Explanation:
The formula for the refractive index of a medium is given as:
n = c/v
where,
n = refractive index of the medium
c = speed of light in vacuum
v = speed of light in that medium
FOR CARBON TETRACHLORIDE:
n = n₁ = 1.461
v = v₁
Therefore,
1.461 = c/v₁
v₁ = c/1.461 ----- equation (1)
FOR ETHYL ALCOHOL:
n = n₂ = 1.361
v = v₂
Therefore,
1.361 = c/v₂
v₂ = c/1.361 ----- equation (2)
Now, dividing equation (1) by equation (2), we get:
v₁/v₂ = (c/1.461) / (c/1.361)
v₁/v₂ = 1.361/1.461
v₁/v₂ = 0.93
Hence, the ratio of the speed of light in carbon tetrachloride to the speed in ethyl alcohol is 0.93
Two fledglings leave a nest which is 2.50 m off the ground. One drops from rest and then 0.10 s later the second charges out of the nest with a velocity with horizontal and
downward components of 1.00 and 1.50 m/s, respectively.
1. Which fledgling hits the ground first (first or second)?
2. With what speed, in m/s, does the first fledgling hit the ground?
3. With what speed, in m/s, does the second fledgling hit the ground?
4. Which fledgling travels the greater displacement?
5. How far does a parent bird have to travel on the ground between the two fledglings, in m, to make sure they are alright?
t Answer:
1) the time of the pigeon 1 is less, so it comes first
2) v = - 6,997 m / s , 3) v = 10.15 m / s ,
4) the displacement of the second point in greater
5) x = 0.883 m
Explanation:
For this exercise we will use the kinematics equations
1) ask which chick reaches the ground first
we calculate for the first chick that has zero initial velocity
y = y₀ + v₀ t - ½ g t²
0 = yo - ½ g t²
t = √ 2 y₀ / g
let's calculate
t = √ (2 2.50 / 9.8)
t = 0.714 s
We calculate the time it takes for the second chick that has velocity v = (1 i ^ - 1.5 j⁾ m / s
y = y₀ + v₀t - ½ g t²
0 = 2.5 - 1.5 t - ½ 9.8 t²
4.9 t² + 1.5 t - 2.5 = 0
t² + 0.306 t - 0.510 = 0
we solve the quadratic equation
t = [0.306 ± √ (0.306² - 4 (-0.510))] / 2
t = [0.306 ± 1.46] / 2
The results are
t₁ = -0.577 s
t₂ = 0.883 m / s
we take positive time as correct
the time of the pigeon 1 is less, so it comes first
2) the speed of the first chick is
v = v₀ - g t
we can see that
v = -gt
v = - 9.8 0.714
v = - 6,997 m / s
the negative sign indicates that the speed is down
3) the speed of the other bird is
v = -1.5 - 9.8 0.883
v = 10.15 m / s
4) which chick has the greatest displacement. The first point falls vertically and its displacement is y₀
The second point describes a parabola and its displacement is
d = √ (x² + y₀²)
therefore we see that the displacement of the second point in greater
5) calculate the horizontal displacement of the second point
x = vx t
x = 1 0.883
x = 0.883 m
Whale sharks swim forward while ascending or descending. They swim along a straight-line path at a shallow angle as they move from the surface to deep water or from the depths to the surface. In one recorded dive, a shark started 50 m below the surface and swam at 0.85 m/s along a path tipped at a 13° angle above the horizontal until reaching the surface.
Required:
a. What was the horizontal distance between the shark's starting and ending positions?
b. What was the total distance that the shark swam?
c. How much time did this motion take?
Answer:
a)217m
b)222m
c)261s
Explanation:
Considering the figure in the attachment
depth 'h'=50m
speed 'v'=0.85m/s
angle 'θ'=13°
a) we have
[tex]\frac{h}{x}[/tex]=tanθ
x = h / tanθ => 50/tan13°
x=216.57≈217m
b)we have
[tex]\frac{h}{d}[/tex]=sinθ
d=h / sinθ => 50 / sin13°
d=222.27≈222m
c)Time needed = d / v = 222/0.85
261.18≈261s
An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary, the tension in the cable was 6000 N. When the craft was lowered or raised at a steady rate, the motion through the water added an 1800 N drag force. What was the tension in the cable when the craft was being lowered to the seafloor?
Answer:
T = 4200N
Explanation:
When the submersible craft is at rest, the tension in the cable is 6000N.
With this information you can calculate the weight of the craft by summing the forces (the summation of the force is zero because the craft is at rest):
[tex]T-W=0\\\\W=T=6000N[/tex]
When the craft is going down with a constant speed, there is a drag force of 1800N. Then, by using the second Newton law you have:
[tex]T-W+F_d=0[/tex] (1)
Fd: drag force
The summation of the forces is zero because the craft moves with constant velocity, that is, there is no acceleration.
You calculate the new tension on the cable by solving the equation (1) for T:
[tex]T=W-Fd=6000N-1800N=4200N[/tex]
hence, the tension is 4200N
Suppose the electric field in problems 2 was caused by a point charge. The test charge is moved to a distance twice as far from the charge. What is the magnitude of the force that the field exerts on the test charge now ?
Answer:
it is reduced four times.
Explanation:
By definition, the electric field is the force per unit charge created by a charge distribution.
If the charge creating the field is a point charge, the force exerted by it on a test charge, must obey Coulomb´s Law, so, it must be inversely proportional to the square of the distance between the charges.
So, if the distance increases twice, as the force is inversely proportional to the square of the distance, and the square of 2 is 4, this means that the magnitude of the force exerted on the test charge must be 4 times smaller.
Helppppp please thanks
Answer:
It represents battery
Answer: I think #1 represent lights and #2 represent the battery
Complete the sentence below correctly.
A compression of a longitudinal wave is like a
of a transverse wave.
OA) crest
OB) trough
OC) rarefaction
OD) compression
Answer:
A. Crest
Explanation:
Longitudinal wave is a type of wave that is characterized by the particles of the medium's movement in a parallel direction in comparison to the direction in which wave travels, such that, in compression of longitudinal wave, the density of the wave medium is at its highest due to its closeness together than natural state, while in rarefaction, the density is at its lowest due to wave medium spread apart than normal.
Similarly, in Transverse wave, the crest of a wave implies the medium has reached the highest point while the trough of the wave depicts the lowest point the wave medium has reached.
Therefore, longitudinal wave's compression and rarefaction equates accordingly to the crest and trough of a transverse wave.
Hence, a compression of a longitudinal wave is like a CREST of a transverse wave.
Having successfully ransomed a nearby city with her rail gun, Prof. Marcia Grail is looking for new and exciting ways to wreck science based havok for profit. She constructs a device capable of creating a constant intensity of electromagnetic radiation of any frequency over a circular space of radius 50cm. In order to do the most damage to biological systems (e.g. make those filthy normal humans pay), what type of electromagnetic wave does she need to set the device for
Answer:
Gamma radiation
Explanation:
Electromagnetic radiations are waves that do not require material medium for their propagation, and they travel at the same velocity. When these waves are arranged with respect to increasing frequency or decreasing wavelength, it forms a spectrum.
Since Prof. Marcia Grail's device can create an electromagnetic radiation of any frequency, the appropriate radiation to achieve her goal would be gamma radiation.
Gamma radiation is a high penetrating radiation with lethal effects on exposed biological molecules, causing induction of cancer and genetic mutations even at low level.
If the molar mass of helium is 4.0 g/mol and the molar mass of neon is 20.2 g/mol, then
a. All the atoms have exactly the same velocity.
b. All the atoms have the same average speed.
c.The average speed of the helium atoms is greater than the average speed of the neon atoms.
d. The average speed of the neon atoms is greater than the average speed of the helium atoms.
e. The atoms diffuse from high temperature to low temperature.
In order for an external force to do work on a system, Question 9 options: a) there must be a component of the force perpendicular to the motion. b) there must be a component of force parallel to the motion of the object. c) the force can be at any angle relative to the motion of the object.
Answer:
b) there must be a component of force parallel to the motion of the object.
Explanation:
We know that work done on a body by an external force is calculated by the formula given below:
W = F.d = Fd Cos θ
where,
W = Work Done by the force on the body
F = Magnitude of force
d = displacement of the body
θ = The angle between the direction of motion of the body and the force applied
It is clear from the formula of the work done, that "F Cosθ" represents the component of the force, that is acting in the direction of motion of the object or parallel to the direction of motion of the object. So, if there is no component of force parallel to motion of object, then this factor will become zero. As a result, the work done will also be zero.
Therefore, the correct option will be:
b) there must be a component of force parallel to the motion of object.
Consider the interference/diffraction pattern from a double-slit arrangement of slit separation d = 6.60 um and slit width a. The wavelength of the monochromatic light incident normally upon the slits is 2n = d/10 (in air). There is a filter (of negligible thickness) placed on slit 2, so that the magnitude of the EM wave emitted from it is half of that emitted from slit 1. The space between the slits and the screen is filled with water, whose index of refraction is n = 1.33 (you can take noir as 1.00).
(a) What is the wavelength 2 of the light in water?
(b) If a << 1, What is the phase difference between the waves from slits 1 and 2?
(c) For a << 2, Derive an expression for the intensity / as a function of O and other relevant parameters, including the intensity at the center of the screen (where 0 = 0).
(d) Now suppose a = d/3. Redo part (b) above. How many interference maxima are present within the central diffraction peak? (Do not count the "clipped" maxima, if any.) (4) — E -2 d E ) в /Б/ = 1/5 | TT
Answer:
(a) λ = 0.496 um (b) S =2π Δ d sinθ/ λ (c) I =gI₀ (d) For the central diffraction peak, a total of 5 interference maxima are present or available.
Note: find an attached copy of a part of the solution to the given question below.
Explanation:
Solution
Recall that:
d = 6.6 um
λ₀ =d/10
λ₀ = 6.6 um
Now,
(a) We find the wavelength λ of the light in water.
Thus,
λ water = (λ₀ )/n
= 0.66/1.33
So,
λ water = λ = 0.496 um
(b) We find the phase difference between the waves from slit 1 and 2
Now,
if a <<d and a<<λ
Then the path difference between the rays will be
Δ S₂N = Δ d sinθ
Thus, the phase difference becomes,
S = 2π Δ/λ is S= 2π Δ d sinθ/ λ
(c) The next step is to derive an expression for the intensity I as function of O and other relevant parameters.
Now,
Let p be the point where these two rays interfere with each other.
Thus,
The electric field vector coming out from slot and and slot 2 is
E₁= E₀₁ cos (ks₁ p - wt) i
E₂ = E₀₂ cos (ks₂ p - wt) i
Note: Kindly find an attached copy of a part of the solution to the given question below.
A television weighs 8.50 pounds. How many grams is this? (Hint: You need to
use two unit conversion fractions. 1 pound equals about 0.454 kg.)
Answer:
3859 grams
Explanation:
Given: Weight of a television = 8.50 pounds
To find: Weight of a television in grams
Solution:
1 pound = 0.454 kg and 1 kg = 1000 g
So,
1 pound = 0.454 × 1000 = 454 grams
8.50 pounds = 8.50 × 454 = 3859 grams
Therefore,
Weight of television in grams = 3859 grams
-
is a side effect of tobacco use.
A. Lightheadedness
B. Irritability
C. Dizziness
D. All of the above
Please select the best answer from the choices provided.
Answer:
D. all of the above
Explanation:
a block (mass 0.6kg) is released from rest at point A at the top of a ramp inclined at 36.9 degress above the horizontal. The block moves a distance of 4m along the ramp to point b at the bottom of the ramp. How much work is done by gravity as the block goes from a to b
The motion of a free falling body is an example of __________ motion
Answer:
uniformly accelerated motion
Explanation:
The motion of the body where the acceleration is constant is known as uniformly accelerated motion. The value of the acceleration does not change with the function of time.
Three Small Identical Balls Have Charges -3 Times 10^-12 C, 8 Times 10^12 C And 4 Times 10^-12 C Respectively. They Are Brought In Contact And Then Separated. Calculate Charge On Each Ball.
Answer:
The charge in each ball will be 3 * 10^-12 C
Explanation:
(Assuming the correct charge of the second ball is 8 * 10^-12)
When the balls are brought in contact, all the charges are split evenly among then.
So first we need to find the total charge combined:
(-3 * 10^-12) + (8 * 10^-12) + (4 * 10^-12) = 9 * 10^-12 C
Then, when the balls are separated, each ball will have one third of the total charge, so in the end they will have the same charge:
(9 * 10^-12) / 3 = 3 * 10^-12 C
So the charge in each ball will be 3 * 10^-12 C
There is an old physics joke involving cows, and you will need to use its punchline to solve this problem
A cow is standing in the middle of an open, flat field. A plumb bob with a mass of 1 kg is suspended via an unstretchable string 10 meters long so that it is hanging down roughly 2 meters away from the center of mass of the cow. Making any reasonable assumptions you like or need to, estimate the angle of deflection of the plumb bob from vertical due to the gravitational field of the cow.
Answer:
The angle of deflection will be "1.07 × 10⁻⁷°".
Explanation:
The given values are:
Mass of a cow,
m = 1100 kg
Mass of bob,
mb = 1 kg
The total distance between a cow and bob will be,
d = 2 m
Let,
The tension be "t".
The angle with the verticles be "[tex]\theta[/tex]".
Now,
Vertically equating forces
⇒ [tex]T\times Cos \theta =mb\times g[/tex] ...(equation 1)
Horizontally equating forces
⇒ [tex]T\times Sin \theta = G\times M\times \frac{mb}{d^2}[/tex] ...(equation 2)
From equation 1 and equation 2, we get
⇒ [tex]tan \thata=\frac{G\times M}{g\times d^2}[/tex]
O putting the estimated values, will be
⇒ [tex]\theta = tan(\frac{6.674\times 10^{-11}\times 1100}{9.8\times 2^2} )[/tex]
⇒ [tex]\theta = 1.07\times 10^{-7}^{\circ}[/tex]
The frames for a pair of eyeglasses have a radius of 2.14 cm at 20.0°C. Lenses with radius of 2.16 cm have to be inserted into these frames. To what temperature must the technician heat the frames to accommodate the lenses? The frames are made of a material whose thermal expansion coefficient is 1.30 10-4/°C.
Answer:
The technician must heat the frame to a temperature of T₂ = 0.0072°C
Explanation:
Change in one-dimension of an object upon heating is given by the following equation:
ΔL = α L ΔT
For the radius this equation can be re-written as follows:
ΔR = α R ΔT
where,
ΔR = Change in Radius = 2.16 cm - 2.14 cm = 0.02 cm
α = Thermal Expansion Coefficient = 1.3 x 10⁻⁴ /°C
R = Original Radius = 2.14 cm
ΔT = Change in Temperature = T₂ - 20°C
Therefore,
0.02 cm = (1.3 x 10⁻⁴ /°C)(2.14 cm)(T₂ - 20°C)
T₂ - 20°C = (0.02 cm)/(1.3 x 10⁻⁴ /°C)(2.14 cm)
T₂ = 0.0072°C + 20°C
T₂ = 20.0072°C
A boat crosses a 200m wide river at 3m/s, north relative to water. The river flows at 1m/s as shown. What is the velocity of the boat as observed by a stationary observer on the river back from the boat departed?
Answer:
The resultant velocity = 3.16 m/s
Explanation:
Since the boat is moving North of the direction of the riverflow, the river would either be flowing westward or Eastward. The two motions form a right angle triangle with the resultant velocity being the hypotenuse of the traingle.
The resultant velocity will be given as ;
R² = B² + r²
Where B is the velocity of the boat and r is the velocity of the river
R² = 3² + 1²
R² = 10
R = √10 = 3.16 m/s
Therefore, the resultant velocity = 3.16 m/s
A p-type Si sample is used in the Haynes-Shockley experiment. The length of the sample is 2 cm, and two probes are separated by 1.8 cm. Voltage applied at the two ends is 5 V. A pulse arrives at the collection point at 0.608 ms, and the separation of the pulse is 180 sec. Calculate mobility and diffusion coefficient for minority carriers. Verify it from the Einstein relation.
Answer:
Mobility of the minority carriers, [tex]\mu_{n} =1184.21 cm^{2} /V-sec[/tex]
Diffusion coefficient for minority carriers,[tex]D_{n} = 29.20 cm^2 /s[/tex]
Verified from Einstein relation as [tex]\frac{D_{n} }{\mu_{n} } = 25 mV[/tex]
Explanation:
Length of sample, [tex]l_{s} = 2 cm[/tex]
Separation between the two probes, L = 1.8 cm
Drift time, [tex]t_{d} = 0.608 ms[/tex]
Applied voltage, V = 5 V
Mobility of the minority carriers ( electrons), [tex]\mu_{n} = \frac{V_{d} }{E}[/tex]
Where the drift velocity, [tex]V_{d} = \frac{L}{t_{d} }[/tex]
[tex]V_{d} = \frac{1.8}{0.608 * 10^{-3} } \\V_{d} = 2960.53 cm/s[/tex]
and the Electric field strength, [tex]E = \frac{V}{l_{s} }[/tex]
E = 5/2
E = 2.5 V/cm
Mobility of the minority carriers:
[tex]\mu_{n} = 2960.53/2.5\\\mu_{n} =1184.21 cm^{2} /V-sec[/tex]
The electron diffusion coefficient, [tex]D_{n} = \frac{(\triangle x)^{2} }{16 t_{d} }[/tex]
[tex]\triangle x = (\triangle t )V_{d}[/tex], where Δt = separation of pulse seen in an oscilloscope in time( it should be in micro second range)
[tex]\triangle x = \frac{(\triangle t) L}{t_{d} } \\\triangle x = \frac{180*10^{-6} * 1.8}{0.608*10^{-3} }\\\triangle x =0.533 cm[/tex]
[tex]D_{n} = \frac{0.533^{2} }{16 * 0.608 * 10^{-3} }\\D_{n} = 29.20 cm^2 /s[/tex]
For the Einstein equation to be satisfied, [tex]\frac{D_{n} }{\mu_{n} } = \frac{KT}{q} = 0.025 V[/tex]
[tex]\frac{D_{n} }{\mu_{n} } = \frac{29.20}{1184.21} \\\frac{D_{n} }{\mu_{n} } = 0.025 = 25 mV[/tex]
Verified.
A motor vehicle has a mass of 1.8 tonnes and its wheelbase is 3 m. The centre of gravity of the vehicle is situated in the central plane 0.9 m above the ground and 1.7 m behind the front axle. When moving on the level at 90 km/h the brakes applied and it comes to a rest in a distance of 50 m.
Calculate the normal reactions at the front and rear wheels during the braking period and the least coefficient of friction required between the tyres and the road. (Assume g = 10 m/s2)
Answer:
normal reaction, front: 11,175 Nnormal reaction, rear: 6,825 Nminimum coefficient of friction: 0.625Explanation:
The speed in meters per second is ...
(90 km/h)(1000 m/km)(1 h/(3600 s)) = 25 m/s
The braking acceleration can be found from ...
a = v²/(2d) = (25 m/s)²/(2×50 m) = 6.25 m/s²
Then the braking force is ...
F = Ma = (1800 kg)(6.25 m/s²) = 11,250 N
The torque on the center of gravity is ...
T = (11,250 N)(0.90 m) = 10,125 N·m
__
If we let x and y represent the normal forces on the front and rear wheels, respectively, then we have ...
x + y = (10 m/s²)(1800 kg) = 18000 . . . . . newtons
1.7x -1.3y = 10,125 . . . . . . . . . . . . . . . . . . . newton-meters
The latter equation balances the torque due to the wheel normal forces with the torque due to braking forces.
Multiplying the first equation by 1.3 and adding that to the second, we have ...
3.0x = (1.3)(18,000) + 10,125
x = 33,525/3 = 11,175 . . . . . . . . . . . newtons normal force on front tyres
y = 18000 -11175 = 6,825 . . . . . . . .newtons normal force on back tyres
The least coefficient of friction is the ratio of horizontal to vertical acceleration, 6.25/10 = 0.625.
4. An electric iron has a
power rating of 750W
a. How many joules of
electric energy does it
change into heat energy
every second?
b. How many joules of
work can it do in 3
seconds
c. How long does it take
the iron to do 1500J of
work?
5. Use the kinetic particle
theory to explain why a
solid has a definite shape
and liquid has none.
Answer:
4.
a) W = 750 J
b) W = 2250 J
c) t = 2 sec
5. Answered in explanation
Explanation:
4.
The formula of power is given as:
P = W/t
where,
P = Power
W = Work Done
t = Time Taken
a)
Here,
P = 750 W
t = 1 sec
W = ?
Therefore,
750 W = W/1 sec
W = 750 J
b)
Here,
P = 750 W
t = 3 sec
W = ?
Therefore,
750 W = W/3 sec
W = (750 W)(3 sec)
W = 2250 J
c)
Here,
P = 750 W
t = ?
W = 1500 J
Therefore,
750 W = 1500 J/t
t = 1500 J/750 W
t = 2 sec
5.
According to Kinetic Particle Theory, the molecules are tightly packed with each other, by strong inter-molecular forces and they can only vibrate at their position. While, molecules or particles in liquids have lesser attractive forces among them. They can move in layers and can take the shape of any container. This is the reason why solid has a definite shape and liquid has none.
