Answers
Answer:
The additional weight and mass needed for lifting the other piston slowly is 2500 N and 254.92 kg, respectively.
Explanation:
By means of the Pascal's Principle, the hydraulic lift can be modelled by the following two equations:
Hydraulic Lift - Before change
\(P = \frac{F}{A}\)
Hydraulic Lift - After change
\(P + \Delta P = \frac{F + \Delta F}{A}\)
Where:
\(P\) - Hydrostatic pressure, measured in pascals.
\(\Delta P\) - Change in hydrostatic pressure, measured in pascals.
\(A\) - Cross sectional area of the hydraulic lift, measured in square meters.
\(F\) - Hydrostatic force, measured in newtons.
\(\Delta F\) - Change in hydrostatic force, measured in newtons.
The additional weight is obtained after some algebraic handling and the replacing of all inputs:
\(\frac{F}{A} + \Delta P = \frac{F}{A} + \frac{\Delta F}{A}\)
\(\Delta P = \frac{\Delta F}{A}\)
\(\Delta F = A\cdot \Delta P\)
Given that \(\Delta P = 100\,Pa\) and \(A = 25\,m^{2}\), the additional weight is:
\(\Delta F = (25\,m^{2})\cdot (100\,Pa)\)
\(\Delta F = 2500\,N\)
The additional mass needed for the additional weight is:
\(\Delta m = \frac{\Delta F}{g}\)
Where:
\(\Delta F\) - Additional weight, measured in newtons.
\(\Delta m\) - Additional mass, measured in kilograms.
\(g\) - Gravitational constant, measured in meters per square second.
If \(\Delta F = 2500\,N\) and \(g = 9.807\,\frac{m}{s^{2}}\), then:
\(\Delta m = \frac{2500\,N}{9.807\,\frac{m}{s^{2}} }\)
\(\Delta m = 254.92\,kg\)
The additional weight and mass needed for lifting the other piston slowly is 2500 N and 254.92 kg, respectively.
Related Questions
A laboratory measurement finds 200 μg of hemoglobin per μL of blood. Hemoglobin, the blood protein that transports oxygen, has a molecular weight of 64 kDa or 64,000 u , where 1 dalton ( Da ) = 1 atomic mass unit ( u ) = 1.66×10^−24g . Estimate the number of hemoglobin proteins in one red blood cell. Express your answer in hemoglobin per red blood cell.
Answers
One red blood cell contains an estimated 251 molecules of haemoglobin, according to our estimation.
What size does a red blood cell typically have?The average red blood cell has a diameter of 6 to 8 micrometres, according to the American Society of Haematology, and a volume of 113-268 μm³ or 113-268x10⁻¹² L.
Let's first change the haemoglobin concentration from grammes per litre to grammes per litre so that it has the same units as the molecular weight:
200 μg/μL x 1 g/1000 μg x 10⁶ μL/L = 0.2 g/L
Next, let's translate hemoglobin's molecular weight from kDa to grammes per molecule:
64 kDa x 1000 Da/kDa x 1.66x10⁻²⁴ g/Da = 1.06x10⁻²⁰ g/molecule
Using Avogadro's number, we can now determine how many haemoglobin molecules are present in a single litre of blood (\(6.022*10^{23}\) molecules/mol): 0.2 g/L x 1 mol/1.06x10⁻²⁰ g x \(6.022*10^{23}\) molecules/mol = 1.13x10¹⁵ molecules/L.
Divide the total number of molecules in 1 litre of blood by the volume of red blood cells to get the amount of haemoglobin molecules per red blood cell. The typical red blood cell count range, according to the American Society of Haematology, is between 4.5-5.5 million cells/L, which translates to 4.5-5.5x10¹² cells/L.
When we divide the quantity of red blood cells in 1 L by the quantity of haemoglobin molecules, we get:
1.13x10¹⁵ molecules/L / 4.5x10¹² cells/L = 251 Red blood cell haemoglobin molecules, rounded to the closest integer.
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a roller coaster start at a height of 40Meters and reached a height of 20meter. does mechanical energy change
Answers
Mechanical energy changes when a roller coaster starts at a height of 40 meters and reaches a height of 20 meters. The potential energy decreases, while the kinetic energy increases.
When a roller coaster starts at a height of 40 meters and reaches a height of 20 meters, mechanical energy changes. In physics, mechanical energy is the sum of potential and kinetic energy that is present in the objects. When an object is moved, it gains or loses energy, thus the mechanical energy changes. There are two forms of mechanical energy, namely kinetic energy and potential energy. Kinetic energy is the energy that a moving object possesses due to its motion, while potential energy is the energy that an object possesses due to its position or shape.
In the case of a roller coaster, when it starts at a height of 40 meters, it has potential energy that is equal to its mass multiplied by the acceleration due to gravity multiplied by its height. As it moves down the track, the potential energy gets converted into kinetic energy, which is the energy of motion. When the roller coaster reaches a height of 20 meters, it has a lower potential energy compared to when it started. The difference in potential energy is equal to the amount of work done by the force of gravity in bringing the roller coaster down from a height of 40 meters to a height of 20 meters. At the same time, the roller coaster has a higher kinetic energy than when it started, as it gained speed during the descent.
Therefore, in summary, mechanical energy changes when a roller coaster starts at a height of 40 meters and reaches a height of 20 meters. The potential energy decreases, while the kinetic energy increases.
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an ideal gas at 20centigree In a press 1.5×10pa and compress,a.isothamally,b.adaibatically until it volume in 1/3 in each case reversible.calculate in each case the final pressure and temperature of d gas (the ratio all specific capacity=Cp/Cv=1.4
Answers
a) The final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\) and 293 K, respectively, while b) the final pressure and temperature for the adiabatic compression are\(5.58*10^5 Pa\) and 515 K, respectively.
a. Isothermal compression:
For an isothermal process, the temperature remains constant. Therefore, we can use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.
Since the process is isothermal, we can write:
\(P_1V_1 = P_2V_2\)
where P1 and V1 are the initial pressure and volume, and\(P_2\)and\(V_2\)are the final pressure and volume.
We are given that the volume is compressed to 1/3 of its original volume, so\(V_2 = (1/3)V_1\). Substituting this into the equation above gives:
\(P_2 = (V_1/V_2)P_1 = 3P_1\) = \(4.5*10^5 Pa\)
To find the final temperature, we can use the ideal gas law again:
PV = nRT
Rearranging, we get:
T = PV/(nR)
Substituting the values we know, we get:
T = (\(1.5*10^5\)Pa)(V1)/(nR)
Since the process is isothermal, the temperature remains constant, so the final temperature is the same as the initial temperature:
T2 = T1 = 293 K
b. Adiabatic compression:
For an adiabatic process, there is no heat transfer between the gas and its surroundings. Therefore, we can use the adiabatic equation:
PV^γ = constant
where γ = Cp/Cv is the ratio of specific heats.
Since the process is adiabatic and reversible, we can write:
\(P_1V_1\)^γ = \(P_2V_2\)^γ
We are given that the volume is compressed to 1/3 of its original volume, so V2 = (1/3)V1. Substituting this into the equation above gives:
\(P_2 = P_1(V_1/V_2)\)^γ = \(P_1\)\((3)^{(1.4)\) = \(5.58*10^5 Pa\)
To find the final temperature, we can use the adiabatic equation again:
\(T_2 = T_1(P_2/P_1)\)^((γ-1)/γ) = T1(5.58/1.5)^(0.4) = 515 K
Therefore, the final pressure and temperature for the isothermal compression are \(4.5*10^5 Pa\)and 293 K, respectively, while the final pressure and temperature for the adiabatic compression are \(5.58*10^5\) Pa and 515 K, respectively.
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When a "full" moon rises, the size appears to be larger than when it is directly overhead. Why?
Answers
The reason we perceive the moon to be bigger when its a full moon is because it is farther away, making our brains think it is larger. One interpretation is that the horizon might appear more distant than the sky, making space of the moon look more flattened and dome like instead of a round sphere.
The highness or lowness of a sound is perceived as
a.
compression.
c.
ultrasound.
b.
wavelength.
d.
pitch.
Answers
Answer:
i think its D
Explanation:
Answer:
The highness or lowness of a sound is perceived as pitch. Pitch is a perceptual property of sound that allows us to distinguish between sounds that have the same loudness and duration, but differ in their frequency content. The pitch of a sound is determined by the frequency of the sound wave, with higher frequencies producing higher pitches and lower frequencies producing lower pitches. The pitch is what makes a sound distinguishable and is important in music, language, and communication.
A 70.0 kg
ice hockey goalie, originally at rest, has a 0.110 kg
hockey puck slapped at him at a velocity of 43.5 m/s.
Suppose the goalie and the puck have an elastic collision, and the puck is reflected back in the direction from which it came. What would the final velocities goalie
and puck
of the goalie and the puck, respectively, be in this case? Assume that the collision is completely elastic.
Answers
The final velocity of the goalie is -0.613 m/s (indicating that he moves backwards), and the final velocity of the puck is 30.2 m/s (indicating that it moves forwards).
What does mechanics' collision mean?When particles, collections of particles, or solid bodies move in the same direction and get close enough to each other, they collide and generate mutual force.
This issue can be resolved by applying the laws of motion and kinetic energy conservation.
momentum conservation
Before the collision:
Total momentum = 0 (since the goalie is at rest)
After the collision:
Total momentum = m_goalie * v_goalie + m_puck * v_puck
Conservation of kinetic energy:
Before the collision:
Total kinetic energy = 0
After the collision:
Total kinetic energy = (1/2) * m_goalie * v_goalie² + (1/2) * m_puck * v_puck^2
We can use these two equations to solve for the final velocities of the goalie and the puck.
First, let's use the conservation of momentum equation to solve for v_goalie:
0 = m_goalie * v_goalie + m_puck * v_puck
v_goalie = - m_puck * v_puck / m_goalie
Now, we can substitute this expression for v_goalie into the conservation of kinetic energy equation:
(1/2) * m_puck * v_puck² = (1/2) * m_goalie * (- m_puck * v_puck / m_goalie)² + (1/2) * m_puck * 43.5²
Simplifying this equation and solving for v_puck, we get:
v_puck = 2 * (m_oalie / (m_goalie + m_puck)) * 43.5
v_puck = 30.2 m/s
Finally, we can substitute this value for v_puck back into the equation for v_goalie
v_goalie = - m_puck * v_puck / m_goalie
v_goalie = -0.613 m/s
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Why did Izzy fall when playing tug of war? Responses he tripped he tripped balanced forces balanced forces he was pushed he was pushed unbalanced forces
Answers
Answer:
he tripped ballanced forces ballanced forces
what is a shargaff rule
Answers
According to Chargaff's rule, the amounts of adenine (A), thymine (T), and guanine (G) in the DNA molecule are equal to each other. The amounts of cytosine (C) and guanine (G) are also equal.
Who is Chargaff ?Erwin Chargaff was a biochemist, author, Bucovinian Jew who immigrated to America during the Nazi era, and professor of biochemistry at Columbia University's medical school.
Chargaff found patterns among the four bases, or chemical building blocks, of DNA, which are directly related to DNA's function as the genetic material of living things.
He was born in Austria-Hungary. Heraclitean Fire: Sketches from a Life Before Nature, an autobiography he penned, received positive reviews.
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If 10 waves pass one dock every 16.0 seconds, determine the frequency of the wave.
Answers
The frequency of the wave is 0.625 waves per second, calculated by dividing the number of waves (10) by the time (16.0 seconds).
To determine the frequency of a wave, you need to divide the number of waves (in this case, 10) by the time it takes for those waves to pass a certain point (in this case, a dock) within 16.0 seconds.
Frequency is usually measured in Hertz (Hz), which represents the number of cycles or events per second. So, to find the frequency, we calculate 10 waves / 16.0 seconds = 0.625 waves per second or 0.625 Hz.
This means that every second, 0.625 waves pass by the dock, giving you the frequency of the wave.
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Suppose the width of your fist is 4.1 inches and the length of your arm is 35.4 inches. Based on these measurements, what will be the angular width (in degrees) of your fist held at arm’s length?
Answers
Answer:
7 degree
Explanation:
given data
width = 4.1 inches
length = 35.4 inches
solution
we consider as per fig
O is mid point of BC
so OB = 2.05 inches
and
AB = \(\sqrt{OB^2 + OA^2}\)
AB = \(\sqrt{2.05^2 + 35.4^2}\)
AB = 35.078 inches
so
\(sin \frac{\alpha }{2} = \frac{OB}{AB}\)
\(sin \frac{\alpha }{2} = \frac{2.05}{35.078}\)
\(\alpha = 7 degree\)
which items are matter?
Answers
Answer:
which items are matter?
battery , mobile phone
The period of a pendulum is measured 16 times. The average value of the period over these 16 trials is calculated to be 1.50 seconds, whereas the standard deviation is found to be 0.24 seconds. The standard error (or standard deviation of the mean) therefore is 0.24 seconds divided by the square root of 16, yielding 0.06 seconds. Assuming that the uncertainty of this period arises solely from random error for these 16 trials, about how many additional trials would need to be completed to reduce the standard error to 0.03 seconds? ______________
Answers
Answer:
The additional trials needed is 48 trials
Explanation:
Given;
initial number of trials, n = 16 trials
the standard deviation, σ = 0.24 s
initial standard error, ε = 0.06 s
The standard error is given by;
\(\epsilon = \frac{\sigma}{\sqrt{n} }\)
To reduce the standard error to 0.03 s, let the additional number of trials = x
\(0.03= \frac{0.24}{\sqrt{n+x} } \\\\0.03= \frac{0.24}{\sqrt{16+x} }\\\\0.03\sqrt{16+x} = 0.24\\\\\sqrt{16+x} = \frac{0.24}{0.03} \\\\\sqrt{16+x} = 8\\\\16+x = 8^2\\\\16+x = 64\\\\x = 64 -16\\\\x = 48 \ trials\)
Therefore, the additional trials needed is 48 trials.
Convert 15000kg/m cube
into gm/cm cube
please write the process also
Answers
Answer:
15000 Kilograms/Cubic Meters (kg/m3) = 15 Grams/Cubic Centimeters (g/cm3)
Explanation:
1 g/cm3 is equal to 1000 kilogram/cubic meter. To convert 100 gram into kg then divide it by 1000 i.e. 100/1000 = 0.1 kg. To convert any value of gm/cm3 into kg/m3 then multiply it by 1000.
15000 kg / m^3 =
15000 × 10^3 g / m^3 =
15000 × 10^3 × 10^3 mg / m^3 =
15 × 10^9 mg / m^3 =
15 × 10^9 × 10^(-3) mg / dm^3 =
15 × 10^9 × 10^(-3) × 10^(-3) mg / cm^3 =
15 × 10^9 × 10^(-6) mg / cm^3 =
15 × 10^( 9 - 6 ) mg / cm^3 =
15 × 10^3 mg / cm^3 =
15000 mg / cm^3 =
Look : We found the exact thing we had ...
WoW ...
We got a point ;
Remember from now on :
kg / m^3 = mg / cm^3
A. 65-year old emmetrope wearing +2.50D readers has a near point of accommodation of 25cm.what is his near point of accommodation without glasses? B. The patient above wishes to have glasses for reading material at 50cm. what should the appropriate power of the reading spectacles be?
Answers
If he does not use the lenses, his near point will be 66.7 cm. For him to read a material at 50 cm, he has to use a lens of 2.0D.
What is the near point?The near point is the nearest area which a person can see or have distinct vision. The focal length of the lens is f = 100/2.5 = 40cm
Then;
1/40 = -1/v + 1/25
1/v = 1/25 - 1/40
v = 66.7 cm
Also, for the purpose of reading at 50 cm
1/f = -1/50 + 1/25
1/f = 1/25 - 1/50
f = 50cm
The power of this lens is;
100/50 cm = 2 D
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An analog-to-digital converter is a device that can be used with a microphone to take in an audio wave (an analog signal). The device then converts the information to a digitized form that can be stored and used by a computer. The image below shows the steps in the digitization process. The question mark in the image represents how the data is stored after it is processed by the analog-to-digital converter.
How is the information from the audio wave stored after it is processed by the analog-to-digital converter?
A.
It is stored as graphs because it was converted to base ten data.
B.
It is stored as a table of ones and twos because it was converted to a radio wave.
C.
It is stored as a series of ones and zeros because it was converted to binary data.
D.
It is stored as images because it was converted to mathematical equations.
Reset
Answers
Answer:
Answer C It is stored as a series of ones and zeros because it was converted to binary data.
Explanation:
After the Analog to Digital Converter (ADC) the data is stored in a series of numbers encoded in binary mode (combinations of Zeros and Ones).
This agrees with answer labeled as C) in the list of options.
Answer: C
Explanation: Study Island correct
If a 15kg mass weighs 372 N on Jupiter, what is Jupiter's gravitational acceleration?
Answers
Answer:
The mass of Jupiter is 1.9 x 1027 kg. It is hard to fully understand a number that large, so here are a few comparisons to help. It would take 318 times Earth's mass to equal Jupiter's.
Explanation:
Given the two vectors A =i+ j and B = j + k, find the following.
(a) A + B and |A + B|
(b) 3A - 2B
(c) A • B
(d) AxB and |AxB|
Answers
a) The value of the vector A + B is i + 2j + k and |A + B| is √6 units.
Given:
A = i + j
B = j + k
A + B = i + j + j + k
= i + 2j + k
|A + B| is the magnitude of the vectors A and B
|A + B| = √(1² + 2² + 1²)
= √(1 + 4 +1)
= √6
b) The vector 3A - 2B has the value of 3i + j -2k
Given:
A = i + j
3A = 3i + 3j
B = j + k
2B = 2j + 2k
3A - 2B = 3i + 3j - 2j - 2k
= 3i + j -2k
c) The scalar product of the vector that is A • B is equal to 3 units
The scalar product is calculated as follows:
A • B = i + j • j + k
= 1 + 1 * 1 + 1
= 1 + 1 + 1
= 3 units
d) The vector product or A x B is i - j + k and the magnitude of the same is √3 units.
i j k
A 1 1 0
B 0 1 1
The vector product is calculated as follows:
A x B = (1 * 1 - 1 * 0) i + (0 * 0 - 1 * 0) j + (1 * 1 - 0 * 1) k
= (1 - 0) i + (0 - 1) j + (1 - 0) k
= i - j + k
| A x B | = √(1² + (-1)² + 1²
= √1 + 1 + 1
= √3 units
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What is the magnitude of the displacement of
the mass hanger H after a 0.20-kilogram mass
is loaded on it? [Assume the hanger is at rest in
both positions.]
Answers
A spring has an energy of 10.0 joules when stretched 0.200 metres from its equilibrium point.
How can you determine a spring's magnitude?The formula for calculating the force a spring produces is Fs=kx F s = k x where k is indeed an experimentally determined number known as the spring constant that indicates the force the spring exerts per metre of stretch or compression or x is indeed the distance the spring is compressed or stretched from its initial position.
Is there an equation for magnitude?|v| =(x2 + y2) is the formula to calculate the magnitude of the a vector (or two dimensions) v = (x, y). The Pythagorean theorem serves as the basis for this formula.
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A Geiger–Müller tube can be used to detect ionising radiation. The tube is filled with low pressure gas. How does this detect ionising radiation
Answers
Explanation:
the gas will be hit by high energy particles as the radioactive decay happens and the decaying nuclei are breaking apart. these particles energize the gas and cause electrons to move around the orbitals. the flow of electrons is detected by the sensor.
How many seconds will it take a 75 W motor to lift 5 kg of apples to a height of 3 meters?
Answers
Answer:
It is not possible to calculate the time it took to go up to 3 meters.
Explanation:
There are all forces that apply to this situation like gravity, friction, torque, and efficiency. To answer this question, I might need the specifications given before to answer this question.
Explain whether a particle moving in a straight line with constant speed does or does not have an acceleration. b) Explain whether a particle moving around a curve with constant speed does or does not have an acceleration.
Answers
Answer:
A: No because it is nor changing speed or direction
B: Yes because it changes direction even though the speed is constant
Please Give Brainliest
Two vectors have magnitudes 20 m and 44 m. Which of the following cannot possibly be the magnitude of the resultant of the two vectors ?
Answers
Answer:
44M 64M
Explanation:
Which statement is true for objects in dynamic equilibrium?
A.
Objects have zero acceleration.
B.
Objects have non-zero positive acceleration.
C.
Objects have non-zero negative acceleration.
D.
Objects can have positive as well as negative acceleration.
E.
Objects have forces which are not balanced in at least one direction.
Answers
Answer:d
Explanation:
I think I've done this
Answer:
A objects have zero acceleration
Explanation:
I did this on Plato and it was right
The dwarf planet Pluto orbits at an average distance from the Sun of 39.5 AU. By looking at your data, what would the average speed of Pluto be?
Answers
The average speed of Pluto in its orbit around the Sun is approximately 4.67 km/s.
How to determine average speed?To determine the average speed of Pluto, know the time it takes for Pluto to complete one orbit around the Sun.
Using Kepler's Third Law, find the orbital period of Pluto:
T² = (4π² / GM) × r³
where T = orbital period, G = gravitational constant, M = mass of the Sun, and r = average distance between Pluto and the Sun.
Plugging in the values:
T² = (4π² / (6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²) ) × (39.5 AU × 1.496 × 10¹¹ m/AU)³ / (1.989 × 10³⁰ kg)
T² = 905,594,481,160,410 s²
T = 30,105,559 s (or approximately 905.6 Earth years)
Now calculate the average speed of Pluto:
Average speed = Distance traveled / Time taken
Distance traveled = 2π × r (the circumference of Pluto's orbit)
Distance traveled = 2π × (39.5 AU × 1.496 × 10¹¹ m/AU)
Distance traveled = 7.44 × 10¹² m
Average speed = 7.44 × 10¹² m / (30,105,559 s × 365.25 days/year × 24 hours/day × 3600 s/hour)
Average speed = 4.67 × 10³ m/s
Therefore, the average speed of Pluto in its orbit around the Sun is approximately 4.67 km/s.
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Explain the light detection technique of photovoltaic detection
Answers
Answer:
Photovoltaic detection is a technique that converts light into electrical energy. It is a process that involves the use of a photovoltaic cell, which is made up of semiconductor materials, to generate an electric current when exposed to light.
The photovoltaic cell absorbs the photons of light, which then knock electrons out of their orbits, creating a flow of electricity. The amount of electricity produced is proportional to the intensity of the light. The photovoltaic cell is commonly used in solar panels to generate electricity from sunlight. The efficiency of the photovoltaic cell is dependent on several factors, including the type of semiconductor material used, the purity of the material, and the thickness of the cell.
The photovoltaic cell has many applications, including in solar power generation, telecommunications, and remote sensing. The technique of photovoltaic detection is an important area of research, as it has the potential to provide a clean and renewable source of energy that can help mitigate climate change.
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Find the period of oscillation of a pendulum with a length of 0.75 m.
Answers
Answer:
1.74 s
Explanation:
\(T=2\pi\sqrt\frac{L}{g}=2\pi\sqrt\frac{0.75}{9.81}\)
T = 1.74 s
What is 6 Fahrenheit in celcious
Answers
Answer:
6 Fahrenheit, converted over to Celsius, would be -14.444444
How did earth change about 2.5 billion years ago when many organisms began using photosynthesis to make food
A. The amount of oxygen in the atmosphere increased
B. Mass extinctions occurred
C. The oceans became larger
D. Rainfall increased
Answers
Assuming 100% efficient energy conversion, how much water stored behind a 50
centimeter high hydroelectric dam would be required to charge the battery?
Answers
Answer:
Explanation:
The power rating of the battery isn't provided. But let us assume that it is one of the common batteries with ratings of 12 V and 50 A.h
Potential energy possessed by water at that height = mgh
m = mass of the water = ρV
ρ = density of water = 1000 kg/m³
V = volume of water = ?
g = acceleration due to gravity = 9.8 m/s²
h = height of water = 50 cm = 0.5 m
Potential energy = ρVgh = 1000 × V × 9.8 × 0.5 = (4900V) J
Energy of the battery = qV
q = 50 A.h = 50 × 3600 = 180,000 C
V = 12 V
qV = 180,000 × 12 = 2,160,000 J
Energy = 2,160,000 J
At a 100% conversion rate, the energy of the water totally powers the battery
(4900V) = (2,160,000)
4900V = 2,160,000
V = (2,160,000/4900)
V = 440.82 m³
Hence, with our assumed power ratings for the battery (12 V and 50 A.h), 440.82 m³ of water at the given height of 50 cm would power the battery.
Incase the power ratings of the battery in the complete question is different, this solution provides you with how to obtain the correct answer, given any battery power rating.
Hope this Helps!!!
An applied frictional force on this wheel (not shown) causes it to slow down until it comes to a complete stop after a time interval Δt, where: |ωo| = 34.28 rad/s, R = 0.29 m, |α| = 1.77 rad/s2.
a) Solve for the time interval needed for the wheel to come to a complete stop.
19.37s
b) Solve for total angular distance traveled (in radians, not meters) by the wheel during this time interval.
Answers
We can use the formula for angular deceleration to find the time interval needed for the wheel to come to a complete stop:
α = (ωf - ωo) / Δt
where ωf is the final angular velocity, ωo is the initial angular velocity, and Δt is the time interval. Rearranging the formula, we get:
Δt = (ωf - ωo) / α
Since the wheel comes to a complete stop, the final angular velocity is zero:
ωf = 0
Substituting the given values, we get:
Δt = (0 - 34.28) / (-1.77) ≈ 19.37 s
What is the r total angular distance traveled?The formula for angular displacement is:
θ = ωo t + (1/2) α t^2
where θ is the angular displacement, ωo is the initial angular velocity, α is the angular acceleration, and t is the time interval. When the wheel comes to a complete stop, the final angular velocity is zero, so the formula simplifies to:
θ = ωo t + (1/2) α t^2
Substituting the given values, we get:
θ = (34.28 rad/s)(19.37 s) + (1/2)(-1.77 rad/s^2)(19.37 s)^2 ≈ -2003.9 rad
The negative sign indicates that the wheel has rotated in the opposite direction of its initial motion.
To get the total angular distance traveled by the wheel during this time interval, we take the absolute value of θ:
|θ| = |-2003.9 rad| = 2003.9 rad
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