Given Information:
Number of slots = 24
Number of turns = 40
Flux per pole = 0.060 Wb
Speed of rotation of magnetic field = 1800 rev/min
Required Information:
a) Frequency = ?
b) Phase and Terminal voltage = ?
Answer:
a) Frequency = 60 Hz
b) Phase voltage = 2560 V
Terminal voltage = 4434 V
Explanation:
(a)What is the frequency of the voltage produced in this winding?
The relation between frequency of the voltage produced and the speed of rotation of magnetic field is given by
[tex]f = \frac{nP}{120}[/tex]
Where n is the speed of rotation of magnetic field and P is the number of poles in the winding.
[tex]f = \frac{1800\times 4}{120}\\\\f = \frac{7200}{120}\\\\f = 60 \: Hz[/tex]
(b)What are the resulting phase and terminal voltages of this stator?
The phase voltage is given by
[tex]E = \sqrt{2} \cdot \pi\cdot N\cdot \phi\cdot f[/tex]
Where N is the number of turns, Ф is the flux per pole and f is the frequency calculated in part a.
[tex]E = \sqrt{2} \cdot \pi\cdot 40\cdot \ 0.060\cdot 60\\\\E = 639.77\\\\E = 640 \:V\\\[/tex]
There are total 24 slots so each phase has 24/3 = 8 slots
We know that the number of poles are 4 so that means each phase has 4 sets of coils.
So the voltage in each phase is
Vp = 4*640
Vp = 2560 V
Since it is a Y-connected machine, The terminal voltage is will be
[tex]V_T = \sqrt{3} V_p\\\\V_T = \sqrt{3} \cdot2560\\\\V_T = 4434 \: V\\\\[/tex]
A person jumps out a fourth-story window 14 m above a firefighter safety net. The survivor stretches the net 1.8 m before coming to rest. what was the deceleration experienced by the survivor? Use g = 9.8 m/s2 Calculate to one decimal.
Answer:
The deceleration is [tex]a = - 76.27 m/s^2[/tex]
Explanation:
From the question we are told that
The height above firefighter safety net is [tex]H = 14 \ m[/tex]
The length by which the net is stretched is [tex]s = 1.8 \ m[/tex]
From the law of energy conservation
[tex]KE_T + PE_T = KE_B + PE_B[/tex]
Where [tex]KE_T[/tex] is the kinetic energy of the person before jumping which equal to zero(because to kinetic energy at maximum height )
and [tex]PE_T[/tex] is the potential energy of the before jumping which is mathematically represented at
[tex]PE_T = mg H[/tex]
and [tex]KE_B[/tex] is the kinetic energy of the person just before landing on the safety net which is mathematically represented at
[tex]KE_B = \frac{1}{2} m v^2[/tex]
and [tex]PE_B[/tex] is the potential energy of the person as he lands on the safety net which has a value of zero (because it is converted to kinetic energy )
So the above equation becomes
[tex]mgH = \frac{1}{2} m v^2[/tex]
=> [tex]v = \sqrt{2 gH }[/tex]
substituting values
[tex]v = 16.57 m/s[/tex]
Applying the equation o motion
[tex]v_f = v + 2 a s[/tex]
Now the final velocity is zero because the person comes to rest
So
[tex]0 = 16.57 + 2 * a * 1.8[/tex]
[tex]a = - \frac{16.57^2 }{2 * 1.8}[/tex]
[tex]a = - 76.27 m/s^2[/tex]
As SCUBA divers go deeper underwater, the pressure from the weight of all the water above them increases tremendously which compresses the gases in their blood. What happens to the volume of gas in their blood as the diver rises quickly to the surface?
Answer:
The volume of gas in an early diving bell full of air at sea level is halved at 10 m according to Boyle’s law
Explanation:
;at 20 m pressure is 300 kPa absolute and the gas is compressed into one third the volume.
HOPE THIS HELPS i did this before
Coulomb's law for the magnitude of the force FFF between two particles with charges QQQ and Q′Q′Q^\prime separated by a distance ddd is
|F|=K|QQ′|d2|F|=K|QQ′|d2,
where K=14πϵ0K=14πϵ0, and ϵ0=8.854×10−12C2/(N⋅m2)ϵ0=8.854×10−12C2/(N⋅m2) is the permittivity of free space.
Consider two point charges located on the x axis: one charge, q1q1q_1 = -15.0 nCnC , is located at x1x1x_1 = -1.660 mm ; the second charge, q2q2q_2 = 34.5 nCnC , is at the origin (x=0.0000)(x=0.0000).
What is the net force exerted by these two charges on a third charge q3q3q_3 = 47.0 nCnC placed between q1q1q_1 and q2q2q_2 at x3x3x_3 = -1.240 mm ?
Your answer may be positive or negative, depending on the direction of the force.
Answer:
Explanation:
Force between two charges of q₁ and q₂ at distance d is given by the expression
F = k q₁ q₂ / d₂
Here force between charge q₁ = - 15 x 10⁻⁹ C and q₃ = 47 x 10⁻⁹ C when distance between them d = (1.66 - 1.24 ) = .42 mm
k = 1/ 4π x 8.85 x 10⁻¹²
putting the values in the expression
F = 1/ 4π x 8.85 x 10⁻¹² x - 15 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 9 x 10⁹ x - 15 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 35969.4 x 10⁻³ N .
force between charge q₂ = 34.5 x 10⁻⁹ C and q₃ = 47 x 10⁻⁹ C when distance between them d = ( 1.24 - 0 ) = 1.24 mm .
putting the values in the expression
F = 1/ 4π x 8.85 x 10⁻¹² x 34.5 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 9 x 10⁹ x - 34.5 x 10⁻⁹ x 47 x 10⁻⁹ /( .42 x 10⁻³)²
= 82729.6 x 10⁻³ N
Both these forces will act in the same direction towards the left (away from the origin towards - ve x axis)
Total force = 118699 x 10⁻³
= 118.7 N.
A 25kg box in released on a 27° incline and accelerates down the incline at 0.3 m/s2. Find the friction force impending its motion? What is the coefficient of kinetic friction?
A block is given an initial speed of 3m/s up a 25° incline. Coefficient of friction
Answer:
a) μ = 0.475 , b) μ = 0.433
Explanation:
a) For this exercise of Newton's second law, we create a reference system with the x-axis parallel to the plane and the y-axis perpendicular to it
X axis
Wₓ - fr = m a
the friction force has the expression
fr = μ N
y Axis
N - [tex]W_{y}[/tex] = 0
let's use trigonometry for the components the weight
sin 27 = Wₓ / W
Wₓ = W sin 27
cos 27 = W_{y} / W
W_{y} = W cos 27
N = W cos 27
W sin 27 - μ W cos 27 = m a
mg sin 27 - μ mg cos 27 = m a
μ = (g sin 27 - a) / (g cos 27)
very = tan 27 - a / g sec 27
μ = 0.510 - 0.0344
μ = 0.475
b) now the block starts with an initial speed of 3m / s. In Newton's second law velocity does not appear, so this term does not affect the result, the change in slope does affect the result
μ = tan 25 - 0.3 / 9.8 sec 25
μ = 0.466 -0.03378
μ = 0.433
Photons of light scatter off molecules, and the distance you can see through a gas is proportional to the mean free path of photons through the gas. Photons are not gas molecules, so the mean free path of a photon is not equal to that of a molecule, but its dependence on the number density of the gas and on molecular radius is the same. Suppose you are in a smoggy city and can barely see buildings 500 m away.
(a) How far would you be able to see if all the molecules around you suddenly doubled in volume?
(b) How far would you be able to see if the temperature suddenly rose from 20◦C to a blazing hot 1500◦C with the pressure unchanged?
Answer:
a) 315 m
b) 3025.6 m
Explanation:
The picture attached shows the full explanation for the problem.
Alan leaves Los Angeles at 8:00 A.M. to drive to San Francisco 400 mi away. He manages to travel at a steady 50 mph in spite of traffic. Beth leaves Los Angeles at 9:00 A.M. and surprisingly manages to also drive at a constant speed, in this case 60 mph. (Knight 2.1) a. Who gets to San Francisco first? (Beth) b. How long does the first to arrive have to wait for the second? (20 minutes)
Answer:
a) Beth will reach before Alan
b)Beth has to wait 20 min for Alan to arrive
Explanation:
let 'd' be distance b/w Los Angeles and San Francisco i.e 400 mi
considering ,
Alan's speed [tex]v_A[/tex]=50mph
Beth's speed [tex]v_B[/tex]=60mph
->For Alan:
The time required [tex]t_A[/tex]= d/[tex]v_A[/tex]= 400/50 => 8h
-> For beth:
The time required [tex]t_B=\frac{d}{v_B} =\frac{400}{60} =>6\frac{2}{3} h[/tex] => 6h 40m
Alan will reach at 8:00 a.m +8h = 4:00p.m.
Beth will reach at 9:00 a.m +6h 40m= 3:40p.m.
a) Beth will reach before Alan
b)Beth has to wait 20 min for Alan to arrive
Q1. What is the frequency of rotation of 1000 loop coil of area 20cm2 in a magnetic field of 5T to
generate an emf that has a maximum value of 15.7V?
Answer:
Explanation:
Emf e generated in a coil with no of turn n and area A rotating in a magnetic field B with angular speed of ω is given by the expression
e = e₀ sinωt
where e₀ = nωAB which is the maximum emf generated
Putting the given values
15.7 = 1000xω x 20 x 10⁻² x 5
ω = .0157
frequency of rotation
= ω / 2π
= .0157 / 2 x 3.14
= .0025 /s
9 rotation / hour .
In later years, motors improved and could be run directly from a 60 Hz power supply. As a result, 25 Hz power systems shrank and disappeared. However, there were many perfectly-good working 25 Hz motors in factories around the country that owners were not ready to discard. To keep them running, some users created their own 25 Hz power in the plant using motor-generator sets. A motor generator set consists of two machines connected on a common shaft, one acting as a motor and the other acting as a generator. If the two machines have different numbers of poles but exactly the same shaft speed, then the electrical frequency of the two machines will be different due to Equation (3-34). What combination of poles on the two machines could convert 60 Hz power to 25 Hz power?
Answer:
as in motor generaror are connected to same shaft then both machines are working with same speed
but number of poles are different with same speed means both machines are working with different frequencies
we know
frequency F = N*P/120
speed N = 82120F/P
given
motor speed = generator speed
120F1/P1 = 120F2/P2
F1/P1 = F2/P2
output frequency is 25 which is obtained from generator so F2=25
input frequency is 60 which is given to motor soF1=60
60/P1 = 25/P2
60/25 = P!/P2
P1/P2 = 12/5
multiply and divided by 2 becuase poles are even
P1/P2 = 12*2/5*2
=24/10
P1= 24 poles a
P2 =10 poles we get 25 hz frequency from 60 hz frequency
Pendulum clock. Your friend is trying to construct a clock for a craft show and asks you for some advice. She has decided to construct the clock with a pendulum. The pendulum will be a very thin, very light wooden bar with a thin, but heavy, brass ring fastened to one end. The length of the rod is 80 cm and the diameter of the ring is 10 cm. She is planning to drill a hole in the bar to place the axis of rotation 15 cm from one end. She wants you to tell her the period of this pendulum.
Answer:
The time period for this pendulum is 1.68 seconds
Explanation:
Solution
Given that:
The length of the pendulum is measured from the axis of rotation to the center of mass of the bob of the pendulum
Now,
In this case, the length becomes:
L= 80 - 15+5
L = 70 cm
The time period = T = 2π √L/g
T = 2* 3.14 *√0.7/9.8
= 1.68 seconds
Note: Kindly find an attached work to the part of the solution of the given question
Mr. Dunn drives 64.8km from work at a speed of 48km/h. Mrs. Dunn drives 81.2km from work
at a speed of 58km/h. They both leave work at the same time. Show complete working to secure
full credits. [4]
i. Who arrives home first?
ii. How many minutes later is it before the second person gets home?
iii. A Coyote is chasing its meal (the Road Runner). Unfortunately, the Coyote has difficulty
adjusting to the Road Runner’s speed but we have a good idea of what it is.
plz help me i will mark you as brainliest
Answer:
i) Mr. Dunn arrives to home first.
ii) 3 min
Explanation:
i. To find who arrives first to home you calculate the time, by using the following formula:
[tex]t=\frac{x}{v}[/tex]
x: distance
v: velocity
Mr. Dunn:
[tex]t=\frac{64.8km}{48km/h}=1.35h[/tex]
Mrs. Dunn:
[tex]t=\frac{81.2km}{58km/h}=1.4h[/tex]
Hence, Mr. Dunn arrives to home first.
ii. To calculate the difference in minutes, you convert hours to minutes:
[tex]1.35h*\frac{60min}{1h}=81min\\\\1.40h*\frac{60min}{1h}=84min\\\\\Delta\ t=(84-81)min=3min[/tex]
the difference between the times is 3min
(i) Mr. Dunn takes less time so he arrives at home first.
(ii) The second person arrives 3 min late.
Time taken to arrive home:
(i) We have to calculate the time taken to reach home by Mr. Dunn and Mrs. Dunn.
t = x/v
where x is the distance
and v is the velocity
Time taken by Mr. Dunn:
distance x = 64.8 km
speed v = 48 km/h
t = 64.8 / 48
t = 1.35 h
Time taken by Mrs. Dunn:
distance x = 81.2 km
speed v = 58 km/h
t' = 81.2 / 58
t' = 1.4 h
Hence, Mr. Dunn arrives at home first.
(ii) To calculate the difference in minutes, you convert hours to minutes:
The time taken by Mr. Dunn in minutes is:
t = 1.35×60 = 81 minutes
The time taken by Mrs. Dunn in minutes is:
t' = 1.4×60 = 84 minutes
the difference between the times is 3min
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A firearms company is testing a new model of rifle by firing a 7.50-g lead bullet into a block of wood having a mass of 17.5 kg. The bullet embeds into the block and the collision generates heat. As a consequence, the temperature rises by 0.040°C, as measured with a high-precision thermometer. Assuming that all the kinetic energy of the bullet goes into heating the system, what is the bullet’s speed when it enters the block? The initial temperatures of bullet and wooden block can be considered identical and the specific heats of lead and wood are cPb = 130 J/(kg ⋅ C°) and c wood = 1700 J/(kg ⋅ C°), respectively.
Answer:
Explanation:
Let the bullets speed be V .
Kinetic energy = 1/2 mV² where m is mass of bullet
This energy is converted into heat Q which raises the temperature of target by Δ T .
Q = mc Δ T , m is mass , c is specific heat and Δ T is rise in temperature .
heat absobed by bullet
= .0075 x 130 x .040
= .039 J
heat absorbed by block of wood
= 17.5 x 1700 x .04
= 1190 J
Total heat absorbed
= 1190.039 J
So kinetic energy = heat absobed
= 1/2 x .0075 x V² = 1190.039
V² = 317343.73
V = 563.33 m /s
Which of the following is not true about of the use of MRI in medicine?
1) It produces no negative side-effects on the human body
2) It produces high resolution images of soft tissues
3) It is very cheap
4) It requires very strong magnetic fields
Answer:
3) False. It is expensive since it requires sophisticated equipment and very low temperatures
Explanation:
Nuclear magnetic resonance imaging measurements consist of magnetic resonance imaging to analyze tissues by the transition of the unpaired electron at carbon 13, giving information on the structure and composition of tissues. This information is processed in computers and transformed into images.
So the physical measurement is the MRN
Now we can analyze the statements in the problem
1) True by itself a magnetic measurement is non-invasive
2) True. Measuring carbon transitions has information about the soft tissue of the body
3) False. It is expensive since it requires sophisticated equipment and very low temperatures
4) Right. The applied magnetic field is high to be able to induce carbon transaction
An object has a mass of 5 kg. What force is needed to accelerate it at 6 m/s?
Answer:30N
Explanation:
Mass=5kg
Acceleration=6m/s^2
Force=mass x acceleration
Force=5 x 6
Force=30N
Answer:
30n
Explanation:
Mass=5kg
Acceleration=6m/s^2
Force=mass x acceleration
Force=5 x 6
Force=30N
a) When we were examining the Electromagnetic Tab, we saw that a flow of electrons or a current as we say it, creates a magnetic field. What about the converse, can a magnetic field be involved in the creation of a flow of electrons/current? Therefore is it reasonable to suggest that we can create a magnetic field by having a flow of current and this can be used to make more current? Explain how this can occur
Answer:
Magnetic field can be used to produce current, infact a changing magnetic field can produce current.
A changing magnetic field in a loop causes the flux linked with the loop to change in turn generating a emf in the loop and therefore a current.
For a loop of area A and resistance R.
I =dPhi/dt/R
В. А
I = AcosФ/R .dB /dt
But it isn't reasonable to say that we can create a magnetic field by having a flow of current and this can be used to make more current because the current generated due to change in magnetic field created by increase/decrease in flow of current will be in a direction such that it will counter act the change in magnetic field caused by increase/decrease in current flow.(lenz's law).
We were unable to transcribe this image
Ф= В. А
I = Acos dB Rd
why are brother anoying
Answer:
because they want attention, and big brother loves his younger one
Explanation:
Which of these parameters is directly related to sound frequency?
Answer:Velocity
Explanation:
Velocity is directly proportional to the frequency of a wave.
Velocity=frequency x wavelength
I need help plz help me out 10 points!!!!!!!
Answer:
The answer is diffraction
Explanation:
Answer:
The answer is diffraction
Explanation:
I did the test! HOPE THIS HELPS!
A cube, 1 m on each edge, is held 0.75 m below the surface of a pool of water by a rope. The mass of the cube is 700 kg, and the weight distribution is such that one face remains parallel to the surface of the water. a. Find the tension in the rope. b. Assuming the rope is cut, how far will the cube protrude from the water
Answer:
Explanation:
The mass of cube = 700 kg
volume = 1 m³
density = 700 kg / m²
Its density is less than that of water so it will try to float on the surface .
Tension in rope will be equal to net upward force
upthrust = volume x density of water x g
= 1 x 10³ x 9.8
= 9800 N
weight of cube = mass x g
= 700 x 9.8
= 6860 N .
Net upward force = 9800 - 6860
= 2940 N.
Tension in the rope = 2940 N.
Rope will hold the cube inside and not allow it to go outside water .
b )
If rope is cut , cube being lighter , will float on surface of water .
Part of cube inside water while floating
= 6860 / 9800
= .7
.7 m will remain inside water
part floating outside
= 1 - 0.7
= 0.3 m .
Official (Closed) - Non Sensitive
MEF Tutorial 2 Q3
A train with a maximum speed of 29.17 m/s has an
acceleration rate of 0.25 m/s2 and a deceleration
rate of 0.7 m/s2. Determine the minimum running
time, if it starts from rest at one station and stops
at the next station 7 km away.
Answer:
The minimum running time is 319.47 s.
Explanation:
First we find the distance covered and time taken by the train to reach its maximum speed:
We have:
Initial Speed = Vi = 0 m/s (Since, train is initially at rest)
Final Speed = Vf = 29.17 m/s
Acceleration = a = 0.25 m/s²
Distance Covered to reach maximum speed = s₁
Time taken to reach maximum speed = t₁
Using 1st equation of motion:
Vf = Vi + at₁
t₁ = (Vf - Vi)/a
t₁ = (29.17 m/s - 0 m/s)/(0.25 m/s²)
t₁ = 116.68 s
Using 2nd equation of motion:
s₁ = (Vi)(t₁) + (0.5)(a)(t₁)²
s₁ = (0 m/s)(116.68 s) + (0.5)(0.25 m/s²)(116.68 s)²
s₁ = 1701.78 m = 1.7 km
Now, we shall calculate the end time and distance covered by train, when it comes to rest on next station.
We have:
Final Speed = Vf = 0 m/s (Since, train is finally stops)
Initial Speed = Vi = 29.17 m/s (The train must maintain max. speed for min time)
Deceleration = a = - 0.7 m/s²
Distance Covered to stop = s₂
Time taken to stop = t₂
Using 1st equation of motion:
Vf = Vi + at₂
t₂ = (Vf - Vi)/a
t₂ = (0 m/s - 29.17 m/s)/(- 0.7 m/s²)
t₂ = 41.67 s
Using 2nd equation of motion:
s₂ = (Vi)(t₂) + (0.5)(a)(t₂)²
s₂ = (29.17 m/s)(41.67 s) + (0.5)(- 0.7 m/s²)(41.67 s)²
s₂ = 607.78 m = 0.6 km
Since, we know that the rest of 7 km, the train must maintain the maximum speed to get to the next station in minimum time.
The remaining distance is:
s₃ = 7 km - s₂ - s₁
s₃ = 7 km - 0.6 km - 1.7 km
s₃ = 4.7 km
Now, for uniform speed we use the relation:
s₃ = vt₃
t₃ = s₃/v
t₃ = (4700 m)/(29.17 m/s)
t₃ = 161.12 s
So, the minimum running time will be:
t = t₁ + t₂ + t₃
t = 116.68 s + 41.67 s + 161.12 s
t = 319.47 s
in the figure calculates the acceleration of the block friction not today
Answer:
A fan pushes hot air out of a vent and into a room. The hot air displaces cold air in the room, causing the cold air to move closer to the floor.
The hot air displacing the cold air is an example of transfer by
Explanation:
also the answer is hit my dm on ig
Which of the following is the healthiest type of carbohydrate?
A Bread made with white flour
B Rice made with whole grains
C Cereal made with refined grains
D White rice
Answer:
C
Explanation:
Cereal made with refined grains is the healthiest type of carbohydrate.
What are carbohydrates?
A carbohydrate is defined as a bio-molecule which consists of carbon,hydrogen and oxygen atoms which are usually in the ratio of 2:1 with the empirical formula C[tex]_n[/tex](H₂O)[tex]_n[/tex].
This term is most commonly used in field of biochemistry as a synonym of saccharide which is a group of sugars, starch and cellulose.
They perform various functions in living organisms. They serve as an energy source and as well as structural components . They are a key component in providing nutrition and are found in wide variety of natural as well as processed foods.
Carbohydrates occur as cellulose in the cell walls of plants and is one of the components of insoluble dietary fibers.
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Under electrostatic conditions, the electric field just outside the surface of any charged conductor
A. is always zero because the electric field is zero inside conductors
B. can have non zero components perpendicular to and parallel to the surface of the conductor
C. is always perpendicular to the surface of the conductor
D. is always parallel to the surface
E. is perpendicular to the surface of the conductor only if it is a sphere, a cylinder, or a flat sheet.
Answer:
C. is always perpendicular to the surface of the conductor
Explanation:
On a charged conductor , electric charge is uniformly distributed on its surface . The lines of forces are also uniformly distributed on all directions . They repel each other so they emerge perpendicular to the surface so that they do nor cut each other and at the same time they remain at maximum distance from each other.
Which term defines the distance from crest to crest
Answer:
The horizontal distance between two adjacent crests or troughs is known as the wavelength.
Answer: Wavelength
Explanation:
From crest to crest, it is one full wavelength
Which of the following statements are true? a. Kinematics is the science that studies forces and motion of particles and bodies. b. Speed is a vector quantity. c. The units of velocity are length divided by time. d. The term deceleration is commonly used to describe a negative acceleration.
Answer:
true. b, c and d
Explanation:
Let's review each statement separately
a) False. The kinematics studies the position, speed and acceleration of the bodies, but not what causes these changes
b) True. Velocity is the displacement between time, displacement is a vector, and time is a scalar, so the division between them gives a vector
c) True. speed is the displacement that is a length between time, so its unit is length / time
d) true desaceleration = - aceleration
The current in the wires of a circuit is 60 milliamps. If the resistance of the circuit were doubled (with no change in voltage), then it’s new current would be _____ milliamps
Answer:30
Explanation:
Current=60 milliamps
Current=(voltage)/(resistance)
60=(voltage)/(resistance)
Doubling the resistance means multiplying both sides by 1/2
60x1/2=(voltage)/(resistance) x 1/2
30=(voltage)/2(resistance)
Therefore the resistance would be 30 milliamp if we double the resistance
A small object begins a free-fall from a height of =81.5 m at 0=0 s . After τ=2.20 s , a second small object is launched vertically up from the ground with an initial velocity of 0=40.0 m/s . At what height from the ground will the two objects first meet?
Answer:
33.2 m
Explanation:
For the first object:
y₀ = 81.5 m
v₀ = 0 m/s
a = -9.8 m/s²
t₀ = 0 s
y = y₀ + v₀ t + ½ at²
y = 81.5 − 4.9t²
For the second object:
y₀ = 0 m
v₀ = 40.0 m/s
a = -9.8 m/s²
t₀ = 2.20 s
y = y₀ + v₀ t + ½ at²
y = 40(t−2.2) − 4.9(t−2.2)²
When they meet:
81.5 − 4.9t² = 40(t−2.2) − 4.9(t−2.2)²
81.5 − 4.9t² = 40t − 88 − 4.9 (t² − 4.4t + 4.84)
81.5 − 4.9t² = 40t − 88 − 4.9t² + 21.56t − 23.716
81.5 = 61.56t − 111.716
193.216 = 61.56t
t = 3.139
The position at that time is:
y = 81.5 − 4.9(3.139)²
y = 33.2
The figure shows a crane whose weight is 12.5 kN and center of gravity in G. (a) If the crane needs to suspend the 2.5kN drum, determine the reactions on the wheel in A and B when the boom is in the position shown.(b) Considering the same situation illustrated, what is the value of the maximum weight that the crane can suspend without tipping over?
Answer:
(a) Ra = 9.25 kN; Rb = 5.75 kN
(b) 26.7 kN
Explanation:
(a) Draw a free-body diagram of the crane. There are four forces:
Reaction Ra pushing up at A,
Reaction Rb pushing up at B,
Weight force 12.5 kN pulling down at G,
and weight force 2.5 kN pulling down at F.
Sum of moments about B in the counterclockwise direction:
∑τ = Iα
-Ra (0.66 m + 0.42 m + 2.52 m) + 12.5 kN (2.52 m + 0.42 m) − 2.5 kN ((3.6 m + 0.9 m) cos 30° − 2.52 m) = 0
-Ra (3.6 m) + 12.5 kN (2.94 m) − 2.5 kN (1.38 m) = 0
Ra = 9.25 kN
Sum of moments about A in the counterclockwise direction:
∑τ = Iα
Rb (0.66 m + 0.42 m + 2.52 m) − 12.5 kN (0.66 m) − 2.5 kN ((3.6 m + 0.9 m) cos 30° + 0.66 m + 0.42 m) = 0
Rb (3.6 m) − 12.5 kN (0.66 m) − 2.5 kN (4.98 m) = 0
Rb = 5.75 kN
Alternatively, you can use sum of the forces in the y direction as your second equation.
∑F = ma
Ra + Rb − 12.5 kN − 2.5 kN = 0
Ra + Rb = 15 kN
9.25 kN + Rb = 15 kN
Rb = 5.75 kN
However, you must be careful. If you make a mistake in the first equation, it will carry over to this equation.
(b) At the maximum weight, Ra = 0.
Sum of the moments about B in the counterclockwise direction:
∑τ = Iα
12.5 kN (2.52 m + 0.42 m) − F ((3.6 m + 0.9 m) cos 30° − 2.52 m) = 0
12.5 kN (2.94 m) − F (1.38 m) = 0
F = 26.7 kN
A 3.6 kg block moving with a velocity of 4.3 m/s makes an elastic collision with a stationary block of mass 2.1 kg.
(a) Use conservation of momentum and the fact that the relative speed of recession equals the relative speed of approach to find the velocity of each block after the collision. 1.1315 m/s (for the 3.6 kg block) 5.43 m/s (for the 2.1 kg block)
(b) Check your answer by calculating the initial and final kinetic energies of each block. 33.282 J (initially for the 3.6 kg block) J (initially for the 2.1 kg block) J (finally for the 3.6 kg block) J (finally for the 2.1 kg block) Are the two total kinetic energies the same?
Answer:
a) Velocity of the block of mass 3.6 kg after collision = 1.13 m/s
Velocity of the block of mass 2.1 kg after collision = 5.43 m/s
b) Initial energy of the 3.6 kg block = 33.282 J
Final energy of the 3.6 kg block = 2.3 J
Initial energy of the 2.1 kg block = 0J
Final energy of the 2.1 kg block = 30.96 J
The two total kinetic energies are the same = 33.30 J
Explanation:
Check the attached files for the complete solution and explanations.
The uniform slender bar of mass m and length l is released from rest in the vertical position and pivots on its square end about the corner at O. (a) If the bar is observed to slip when 30 , find the coefficient of static friction s between the bar and the corner. (b)If the end of the bar is notched so that it cannot slip, find the angle at which contact between the bar and the corner ceases.
Answer:
A) 0.188
B) 53.1 ⁰
Explanation:
taking moment about 0
∑ Mo = Lo∝
mg 1/2 sin∅ = 1/3 m L^2∝
note ∝ = w[tex]\frac{dw}{d}[/tex]∅
forces acting along t-direction ( ASSUMED t direction)
∑ Ft = Ma(t) = mr∝
mg sin ∅ - F = m* 1/2 * 3g/2l sin∅
therefore F = mg/4 sin∅
forces acting along n - direction ( ASSUMED n direction)
∑ Fn = ma(n) = mr([tex]w^{2}[/tex])
= mg cos∅ - N = m*1/2*3g/1 ( 1 - cos∅ )
hence N = mg/2 ( 5cos∅ -3 )
A ) Angle given = 30⁰c find coefficient of static friction
∪ = F/N
= [tex]\frac{\frac{mg}{4}sin30 }{\frac{mg}{2}(5cos30 -3) }[/tex] = 0.188
B) when there is no slip
N = O
= 5 cos ∅ -3 =0
therefore cos ∅ = 3/5 hence ∅ = 53.1⁰
Minority group
A shared identity based on
cultural elements such as
heritage, language, and
religion
Ethnicity
A socially constructed
group of people who share
physical characteristics
that are considered
significant by a society
and that are used to
distinguish them from
other groups
Majority group
People who are singled
out for unequal treatment
and who regard
themselves as objects of
collective discrimination
Race
A group's subset that
consists of more than half
of the entire group's
members
Answer:
Minority group - People who are singled out for unequal treatment and who regard themselves as objects of collective discrimination.
Ethnicity - A shared identity based on cultural elements such as heritage, language, and religion.
Majority group - A group's subset that consists of more than half of the entire group's members.
Race - A socially constructed group of people who share physical characteristics that are considered significant by a society and that are used to distinguish them from other groups.
Explanation:
To better understand the above-mentioned definitions we would use some examples:
Elder people can be considered as a minority group in the United States because of their reduced status as a consequence of popular discrimination and prejudice against them. In contrast to them, young men consisting of more than half the population in the age category is an example of the majority group.
Groups of people like Hispanic Americans, Jews, Italian America, Irish are some examples of people belonging to different ethnic backgrounds residing in the U.S.
African Americans who are distinguished based on their skin color is an example of race.
