Consider a spinning plate is dropped onto a stationary plate (which is itself at rest on a frictionless surface). Both plates have a radius of 30cm and a mass of 1kg. The spinning plate is initially spinning at a rate of 0.7 revolutions per second. Hint: This is like a totally-inelastic collision.
Required:
a. After a sufficiently long time, what is the angular velocity of the initially-spinning plate? What about the initially-stationary plate?
b. Assume that the period of velocity matching happens over a course of 2 seconds. Further, assume that the torque exerted by each plate on the other is constant over time. In that case, what is the magnitude of the acceleration that each plate feels during those two seconds? Hint: Use the rotational impulse-momentum theorem.
Answers
Answer:
The final angular velocity is \(w_f = 2.1994 rad/sec\)
The angular acceleration is \(\alpha = 1.099 \ rad/sec^2\)
Explanation:
From the question we are told that
The radius of each plate is \(r = 30 \ cm = \frac{30}{100} = 0.3 \ m\)
The mass of each plate is \(m_p = 1 \ kg\)
The angular speed of the spinning plate is \(w = 0.7 \ rev \ per \ sec = 0.7 * 2 \pi = 4.3988 \ rad/sec\)
From the law of conservation of momentum
\(L_i = L_f\)
Where \(L_i\) is the initial angular momentum of the system (The spinning and stationary plate ) which is mathematically represented as
\(L_i = I_1 w + 0\)
here \(I_1\) is the moment of inertia of the spinning plate which mathematically represented as
\(I_1 = \frac{m_pr^2}{2}\)
and the zero signify that the stationary plate do not have an angular momentum as it is at rest at the initial state
\(L_f\) is the final angular momentum of the system (The spinning and stationary plate) , which is mathematically represented as
\(L_f = (I_1 + I_2 ) w_f\)
Where
\(I_2\) is the moment of inertia of the second plate (This was stationary before but now it spinning due to the first pate ) and is equal to \(I_1\)
and \(w_f\) is the final angular speed
So we have
\(I_1 w = (I_1 + I_2)w_f\)
\(\frac{m_p r^2}{2} * w = 2 * \frac{m_p r^2}{2} * w_f\)
\(w = 2 * w_f\)
substituting values
\(4.3988 = 2 * w_f\)
\(w_f = \frac{4.3988 }{2}\)
\(w_f = 2.1994 rad/sec\)
The the rotational impulse-momentum theorem can be mathematially represented as
\(\tau * \Delta t = 0.09891\)
Where \(\tau\) is the torque and \(\Delta t\) is the change in time
So at \(\Delta t = 2 \ sec\)
\(\tau = \frac{0.09891}{2}\)
\(\tau = 0.0995 \ Nm\)
now the angular acceleation is mathematically represented as
\(\alpha = 2 * \frac{\tau}{m_p * r^2 }\)
substittuting values
\(\alpha = 2 * \frac{0.0995}{1 * 0.3^2}\)
\(\alpha = 1.099 \ rad/sec^2\)
Related Questions
A lad, waiting for his friend walks in the sidewalk, in front of her house, from the front door, first, he moves towards the Positive x-axis, 5 m, then goes back, 6 m. What is his total displacement from his original position? Displacement is a vector quantity whilst, distance is a scalar quantity.
Answers
His total displacement from his original position is -1 m
We know that total displacement of an object from a position x to a position x', d = final position - initial position.
d = x' - x
If we assume the lad's initial position in front of her house is x = 0 m. The lad then moves towards the positive x-axis, 5 m. He then ends up at x' = 5 m. He then finally goes back 6 m.
Since displacement = final position - initial position, and his displacement is d' = -6 m (since he moves in the negative x - direction or moves back) from his initial position of x' = 5 m.
His final position, x" after moving back 6 m is gotten from
x" - x' = -6 m
x" = -6 + x'
x" = -6 + 5
x" = -1 m
Thus, his total displacement from his original position is
d = final position - initial position
d = x" - x
d = -1 m - 0 m
d = -1 m
So, his total displacement from his original position is -1 m
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The main functions of the skin are:
ОА.
To protect the human body from foreign bodies from the outside environment.
ОВ.
A sensory organ for the brain.
Ос.
Shock absorption
OD
All of the above
Reset
Next
Answers
Answer:To protect the human body from foreign bodies from the outside environment.
Explanation:
What happens to the mechanical advantage of a machine if the output force is less than the input force? What must happen to output distance? Give an example of a machine that does this?
Answers
A is thrown up into the air with initial vem/s. How fast is the ball moving when it first reachemeters?
Answers
Once the ball is thrown, the only force acting on it is gravity, which means that it's acceleration is -9.81 m/s² (negative means downward).
List the known and unknown quantities from the question.
u = initial velocity = 20 m/s
v = final velocity = ? m/s
g = acceleration due to gravity = -9.81 m/s²
t = time interval = ? s
s displacement = 11 m
Before calculating the time it takes for the ball to reach 11 m, the final velocity needs to be calculated using the following kinematic equation.
v² = u² + 2gs
v = √(u² + 2gs)
= √((20 m/s)² + (2x-9.81 m/s² x 11 m)) = 13.57 m/s V=
Calculate the time it takes the ball to reach 11 m using the following kinematic equation.
V = u + gt
Solve for t.
t = (v-u)/g
t (13 57 m/s - 20 m/s)/(-981 m/s²) = 0.655 s
Which lists three organic biological molecules?
O carbohydrates, salts, metals
O salts, proteins, minerals,
O proteins, lipids, carbohydrates
O lipids, metals, minerals
Answers
Answer:
B
Explanation:
I'm learning it in science.
Answer:
its not b i just took the test and b was wrong
Explanation:
que estudia la estática?
Answers
QUESTION 13
Find the distance (m) that an object would have to fall to gain 18.32m/s of velocity.
Answers
Answer:
this is ez
Explanation:
so basically you gotta find the volume then divide by Density and the you got to figure out w
how many times it would go into the velocity, hope this helps have a great day
Which of the following correctly describes the relationship between current and voltage as the voltage of a battery increases? Responses As voltage increases, current decreases because current and voltage are directly proportional. As voltage increases, current decreases because current and voltage are directly proportional. As voltage increases, current increases because current and voltage are directly proportional. As voltage increases, current increases because current and voltage are directly proportional. As voltage increases, current decreases because current and voltage are inversely proportional. As voltage increases, current decreases because current and voltage are inversely proportional. As voltage increases, current increases because current and voltage are inversely proportional.
Answers
The correct statement is: "As voltage increases, current increases because current and voltage are directly proportional."
According to Ohm's Law, the relationship between current (I), voltage (V), and resistance (R) in a circuit can be described by the equation:
V = I * R
From this equation, we can see that voltage (V) and current (I) are directly proportional. When the voltage increases, assuming the resistance remains constant, the current will also increase. Similarly, if the voltage decreases, the current will decrease.
Therefore, as the voltage of a battery increases, the current flowing through a circuit connected to that battery will also increase, given that the resistance remains constant.
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CAN I HAVE SOME HELP PLEASE
give listing the law used the intensity of current carried by each lamp?
Answers
Answer:
By teh way is isn't it question of law or science and the picture is of what electric light or not I have read it so I was asking isn't is question of science
An object accelerates 3.0 m/s2 when a force of 6.0 N is applied to it. What is the mass of the object?
Answers
Answer:
2 kgExplanation:
The mass of the object can be found by using the formula
\(m = \frac{f}{a} \\ \)
f is the force
a is the acceleration
From the question we have
\(m = \frac{6}{3} \\ \)
We have the final answer as
2 kgHope this helps you
Which model below describes the processes of Gamma radiation?
A
B.
C.
D.
Answers
Answer:
C
Explanation:
Two cars approach each other from opposite directions each
with a velocity of 54 km/h. One of the cars emits a note of frequency 480 Hz. What will be the approximate frequency
heard in the other car before they cross each other?
Answers
Answer:524 Hz
Explanation:
Approximate frequency, heard in other car, when two car approaches each other, before they cross each other is 524 Hz.
What is frequency?Frequency of wave is the number of waves, which is passed thorough a particular point at a unit time.
For the two cars approaching each other the Doppler formula to find the frequency of second car is given as,
\(f_2=\dfrac{V_s+V_2}{V_s-V_1}f_1\)
Here, \(V_s\) is the speed of the sound.
Two cars approach each other from opposite directions.The velocity of car one is 54 km/h and the velocity of the car two is also 54 km/h.
Convert the unit of velocity of the car as,
\(\rm 54km/s=54\times\dfrac{5}{18}m/s\\\rm 54km/s=15m/s\)
As we know that the speed of the sound is 340 m/s and one of the cars emits a note of frequency 480 Hz.
Thus, putting the values in the above formula to find out the frequency heard in the other car before they cross each other as,
\(f_2=\dfrac{340+15}{340-15}480\\f_2=524.3\rm Hz\)
The approximate frequency heard in the other car before they cross each other is 524 Hz.
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Which sequence shows the chain of energy transfers that create surface currents on the ocean?
Answers
Answer:
The correct answer is A. The sun is the energy source of the surface currents in the ocean
The energy transfer starts from solar energy , then wind energy and finally wind energy is the cause of surface current .
What is surface current ?Surface currents are currents that are located in the upper feet of the ocean , they are simply how water moves from one place to another . Pattern of surface current are determined by wind direction .
Surface currents are formed by global wind system that are fueled by energy from the sun . Because of heating effect of sun , the earth's atmosphere gets warmed up . As we know , warm air is lighter then cool air , it rises up and create low pressure near the equator because of this wind causes surface currents the ocean .
hence , The energy transfer starts from solar energy , then wind energy and finally wind energy is the cause of surface current .
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An object–spring system undergoes simple harmonic motion. If the amplitude increases but the mass of the object is not changed, the total energy of the system:______.a. undergoes a sinusoidal change. b. decreases exponentially. c. decreases. d. doesn't change. e. increases.
Answers
Answer:
The correct answer is:
doesn't change (d)
Explanation:
The total energy in a system is the sum of Kinetic and Potential energies in a system, assuming that energy is not lost to an external procedure. Now, let us define what potential and kinetic energies are:
Potential Energy: this is energy at rest or stored energy
Kinetic Energy: this is energy in motion
In a simple harmonic motion of a mass-spring system, there is no dissipative force, hence the total energy is equal to the potential and kinetic energies. The total energy is not changed rather, it varies between potential and kinetic energies depending on the point at which the mass is. The kinetic energy is greatest at the point of lowest amplitude (highest velocity) and lowest at the point of greatest amplitude (lowest velocity), while potential energy is greatest at the point of highest amplitude (lowest velocity) and lowest at the point of smallest amplitude ( highest velocity). However, at every point, the sum of kinetic and potential energies equals total energy.
Suppose a 3000 cm3 container holds 7.0 g of nitrogen gas at a pressure of 200 kPa. The gas can be heated at constant pressure if a piston moves outward to let the gas expand as it's heated. Alternatively, the gas can be heated at constant volume if the piston is locked in place to prevent expansion. How does the heat required for one of these processes compare to the heat required for the other process?
1. What is the starting temperature of the gas?
2. With the piston locked in place, the gas is heated until the pressure doubles. What is the final temperature?
Answers
1) The starting temperature of the gas is 288 K
b) When the pressure is doubled, the temperature is 576 K
What is the temperature?We know that we have to use the ideal gas equation so as to be able to obtain the temperature of the starting of the gas and we know that;
Pressure = 200 kPa or 1.97 atm
Volume = 3000 cm3 or 3 L
Temperature = ?
Number of moles = mass/molar mass = 7 g/28 g/mol = 0.25 moles
Then we have;
PV = nRT
T = PV/nR
T = 1.97 * 3/0.25 * 0.082
T = 5.91/0.0205
T = 288 K
If the pressure doubles and we have;
P1/T1 = P2/T2
P1T2 = P2T1
T2 = 2(1.97) * 288/1.97
T2 = 576 K
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physical properties for soap
Answers
Answer:
there are germs in your hand and soap has chemicals that kill germs
Answer:
dino nuggies
Explanation:
cause whynot
a proton travelling along is x-axis is lowed by a niform electric field E. at x = 20.0 cm, the proton has a speed of 3.5x10^6 m/s and at 80.0 cm the speed is zero. Determine the magnitude and direction of e,
Answers
Answer:
Magnitude of electric field is 1.06 x \(10^5\) V/m along negative X-direction
Explanation:
Given: initial velocity of proton = u = 3.5 x \(10^6\) m/s
final velocity of proton = v = 0 m/s
initial point \(l_i\) = 0.2 m and final point is \(l_f\) = 0.8 m
According to conservation of energy:
change in in kinetic energy = change in potential energy of proton
⇒\(\frac{m}{2}(v^2-u^2 ) = qE(l_i - l_f)\)
where q and m is the charge and mass of proton E is the electric field , \(l_i\) and \(l_f\) is the initial and final position of proton
on substituting the respected values we get,
1.023 x \(10^-^1^4\) = 9.6 x \(10^-^2^0\) x E
⇒ E = 1.06 x \(10^5\) V/m
external force is opposite to the motion as velocity of proton decreases with distance.
Therefore, magnitude of electric field is 1.06 x \(10^5\) V/m along negative X-direction
A lighter particle moving with a speed of 19 m /s collides with an object of quadruple its mass moving in the opposite direction with a third of its speed. Assume that the collision is a one-dimensional elastic collision. What will be the speed of both particles after the collision?
Answers
Answer:
Speed of lighter particle = -21.53 m/s
Speed of other particle = 3.8 m/s
Explanation:
Let mass of the lighter object be m
Thus mass of heavier object = 4m
Speed of lighter particle = 19 m/s
Speed of second particle with opposite direction = - ⅓(19) m/s = -19/3 m/s
Now, from the formulas of momentum before collision = momentum after collision, and also kinetic energy before collision = Kinetic Energy after collision, we have;
v_bf = [2m_a/(m_a + m_b)]v_ai + [(m_b - m_a)/(m_a + m_b)]v_bi
Now, in this question;
m_a = m
m_b = 4m
v_ai = 19
v_bi = -19/3 m/s
Thus;
v_bf = [2m/(m + 4m)]19 + [(4m - m)/(m + 4m)](-19/3)
Simplifying to get;
v_bf = 19(2m/5m) - (19/3)(3m/5m)
>> v_bf = 38/5 - 19/5
>> v_bf = 19/5 m/s
>> v_bf = 3.8 m/s
Similarly;
v_af = [(m_a - m_b)/(m_a + m_b)]v_ai + [2m_b/(m_a + m_b)]v_bi
v_af = 19((m - 4m)/(m + 4m)) - (19/3)((2 × 4m)/(m + 4m))
This gives;
v_af = 19(-3m/5m) - (19/3)(8m/5m)
v_af = -(57/5) - (152/15)
v_af = -323/15
v_af = -21.53 m/s
4. A tankful of liquid has a volume
of 0.2m3. What is the volume in (a)
lities (b) cm3 (c)ml
Answers
Explanation:
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Displacement is the slope of a velocity vs. time graph.
True or false
Answers
Answer: false
Explanation:
The slope of a velocity–time graph is the acceleration.
How many phase conductors are installed between the switch and the light fixture shown in the figure? A. Four
B. Three
C. Two
D. Five
Answers
Answer:
TWO
Explanation:
WILL GIVE BRAINLIEST PLS HELP!!
A student taking an Earth Science class tries to move a rock with a weight of 10,000 N. He strains and huffs and puffs but fails to budge the rock. How much work did your friend do?
Answers
Answer:
zero
Explanation:
zero, because no displacement
A student moves from a region that has short, cool summers and very cold winters to a region that has hot and
humid summers but short, cold winters
Both regions are located within which climate?
O dry
O highlands
O temperate marine
temperate continental
Answers
Answer:B
Explanation:
Answer:
(D) temperate continental
Explanation:
A rocket fires two engines simultaneously. One produces a thrust of 725Ndirectly forward while the other gives a 513N thrust at 32.4° above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant force which these engines exert on the rocket.
Answers
The magnitude of the resultant force, F = 1,190.3 acting at a direction X = 13.35°.
What is the resultant force the two engines exert on the rocket?The resultant force on the rocket is calculated thus:
The 513N thrust is resolved into vertical and horizontal components;
Horizontal component: 513N cos(32.4°) = 433.14 N
Vertical component: 513N sin(32.4°) = 274.88 N
Total forward force on the rocket = 725 N + 433.14 N = 1,158.14 N
Total force at right angles:
0 + 274.88 N = 274.88 N
The resultant force (F) is then given as follows:
F² = a² + b²
F² = (1158.14 N)² + (274.88 N)²
F = √1,416,847.27
F = 1,190.3
To find the direction:
tan X 274.88 N / 1,158.14 N
X = tan⁻¹ 0.237346089419241
X = 13.35°
Therefore, the magnitude of the resultant force, F = 1,190.3 acting at a direction X = 13.35°.
In conclusion, the resultant force is obtained by resolving the forces into vertical and horizontal components.
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What is the cost per month to operate an A.C. 10hours per day whose power is 3kW and 1KWH cost 79francs
Answers
The cost of operation for an A.C for 10 hours per day for a month will be 71,100 francs.
What is Power?Power is the amount of energy transferred or converted per unit time. The unit of power is the watt, equal to one joule per second. Power is a scalar quantity.
Cost of operation for 10 hours a day;
Daily consumption = 3kW x 10 hours
Daily Consumption = 30kW
Since 1kWH = 79 francs;
Daily consumption amount = 30 x 79 francs
Daily consumption amount = 2,370 francs
Therefore, the monthly consumption (using 30days) will be;
2,370 francs x 30 = 71,100 francs
In conclusion, 71,100 francs will be spent in a month (30 days) to run the 3kW rated A.C for 10 hours a day at 1kWH.
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at one instant, a 15.0-kg sled is moving over a horizontal surface of snow at 4.50 m/s. after 8.70 s have elapsed, the sled stops. use a momentum approach to find the magnitude of the average friction force acting on the sled while it was moving.
Answers
The force acting on the moving sled is equal to F = 7.76 N while it was moving.
What are momentum and speed?Momentum and velocity are different in that momentum is a measurement of an object's amount of motion, whereas velocity is a measurement of an object's speed with direction. Velocity is one of the components of momentum since momentum is equal to an object's mass multiplied by its speed.
What, for instance, is friction force?Walking - When we walk on the ground or a surface, our feet are kept firmly planted by frictional force. We frequently slip on icy or slippery surfaces because there is less friction present.
Given,
Mass of sled = 15.0 Kg
speed of snow on horizontal surface = 4.50 m/s
time taken to stop = 8.70 s
initial momentum
= m U
= 15.0 x 4.50 = 67.5 Kg.m/s
final momentum
final velocity = 0 m/s
final momentum = 0
impulse = change in momentum
impulse = force x time
equating both the formula of impulse
F x t = 67.5 - 0
F x 8.70 = 67.5
F = 7.76 N
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Compared to its weight on Earth, a 5kg object on the moon will weigh
The same amount
Less
More
Answers
Answer:
Less
Explanation:
Weight is a force measurement. The object's mass is 5kg not its weight. To find its weight you have to take the mass of an object and multiply it by the acceleration of gravity. The acceleration of gravity is greater on earth than on the moon so therefore the object will weigh less on the moon.
2. A Spring-Loaded gun shoots a plastic ball with a launch speed of 2.0 m/s. If the Spring is replaced with a new Spring having twice the spring-constant (but still compressed the same distance), the ball’s launch speed will be, a) 1.0 m/s b) 2.o m/s c) 2.8 m/s d) 4.0 m/s e) 16.0 m/s
Answers
When the spring constant is twice, the ball’s launch speed will be 2.8 m/s.
option C is the correct answer.
What is the launch speed when the compression of the spring is twice?
The launch speed when the compression of the spring is twice is calculated by applying the principle of conservation of energy as follows;
K.E = U
¹/₂mv² = ¹/₂kx²
mv² = kx²
v²/k = x²/m
where;
v is the launch speedk is the spring constantm is the mass of the springx is the extension of the springv₁²/k₁ = v₂²/k₂
v₂² = k₂(v₁²/k₁)
when the new Spring is twice the spring-constant of the first;
v₂² = (2k₁) x (v₁²/k₁)
v₂² = 2v₁²
v₂ = v₁√2
v₂ = 2 m/s x √2
v₂ = 2.8 m/s
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In an attempt to deliver a parcel on time, the dispatch rider had to ride 10km 15 degrees SE, he then rode 11 km 30 degrees NE and then takes a shortcut at 22km W .find the rider's displacement
Answers
The total displacement of the dispatch rider is calculated as 43km.
Data;
10km 15 degrees SE11km 30 degrees NE22km WTotal DisplacementTo calculate the total displacement of the dispatch rider, we can simply add up the total distance covered by the rider.
This becomes;
\(10+11+22 = 43km\)
The total displacement of the dispatch rider is calculated as 43km.
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What If? Fluoride ions (which have the same charge as an electron) are initially moving with the same speed as the electrons from part (a) through a different uniform electric field. The ions come to a stop in the same distance d. Let the mass of an ion be M and the mass of an electron be m. Find the ratio of the magnitude of electric field the ions travel through to the magnitude of the electric field found in part (a). (Use the following as necessary: d, K, m, M, and e for the charge of the electron.)
Answers
Answer:
E₁ / E₂ = M / m
Explanation:
Let the electric field be E₁ and E₂ for ions and electrons respectively .
Force on ions = E₁ e where e is charge on ions .
Acceleration on ions a = E₁ e / M . Let initial velocity of both be u . Final velocity v = 0
v² = u² - 2as
0 = u² - 2 x E₁ e d / M
u² = 2 x E₁ e d / M
Similarly for electrons
u² = 2 x E₂ e d / m
Hence
2 x E₁ e d / M = 2 x E₂ e d / m
E₁ / E₂ = M / m