An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in and multiples of g of this point at full rpm? (d) What is the total distance travelled by a point 9.5 cm from the axis of rotation of the ultracentrifuge?
Answers
The total distance travelled by a point 9.50 cm from the axis of rotation is 119,275 meters.
How can we find arc length of a point rotating in an ultracentrifuge?(a) To find the average angular acceleration, we can use the formula:
α = (ωf - ωi)/t
where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity (which is zero in this case since the ultracentrifuge starts from rest), and t is the time taken.
We're given that the final angular velocity is 100,000 rpm, but we need to convert this to radians per second (since the units of α are radians per second squared).
1 rpm = 2π/60 rad/s, so 100,000 rpm = (100,000*2π)/60 rad/s = 10,471 rad/s.
Substituting the values into the formula, we get:
α = (10,471 - 0)/120 = 87.26 rad/s^2.
So the average angular acceleration is 87.26 rad/s^2.
(b) The tangential acceleration of a point at a distance r from the axis of rotation can be found using the formula:
at = rα
where α is the angular acceleration we found in part (a).
Substituting r = 9.50 cm (which we convert to meters by dividing by 100) and α = 87.26 rad/s^2, we get:
at = (9.50/100)(87.26) = 8.23 m/s^2.
So the tangential acceleration of a point 9.50 cm from the axis of rotation is 8.23 m/s^2.
(c) The centripetal acceleration of a point at a distance r from the axis of rotation can be found using the formula:
ac = rω^2
where ω is the angular velocity in radians per second.
At full rpm, the angular velocity is 10,471 rad/s (which we found in part (a)), and r = 9.50 cm. Substituting these values into the formula, we get:
ac = (9.50/100)(10,471)^2 = 10,338 m/s^2.
To express this in terms of multiples of g, we divide by the acceleration due to gravity, which is approximately 9.81 m/s^2:
ac/g = 10,338/9.81 = 1053.
So the centripetal acceleration of a point 9.50 cm from the axis of rotation at full rpm is 10,338 m/s^2 or 1053 g.
(d) The total distance travelled by a point 9.50 cm from the axis of rotation can be found using the formula for the arc length of a circle:
s = rθ
where θ is the angle through which the point has rotated.
At full rpm, the angular velocity is 10,471 rad/s, so in 2.00 min (or 120 s), the point rotates through an angle of:
θ = ωt = 10,471*120 = 1,256,520 radians.
Substituting r = 9.50 cm (which we convert to meters by dividing by 100) and θ = 1,256,520 radians, we get:
s = (9.50/100)(1,256,520) = 119,275 meters.
So the total distance travelled by a point 9.50 cm from the axis of rotation is 119,275 meters.
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Related Questions
A golf ball is hit horizontally off the edge of a 30 m high cliff and lands a distance of 25 m from the edge of the cliff. What was the initial vertical velocity of the golf ball?At what time did the golf ball hit the ground?What was the initial horizontal velocity of the golf ball? What was the final horizontal velocity of the golf ball?
Answers
Answer:
V₀y = 0 m/s
t = 2.47 s
V₀ₓ = 61.86 m/s
Vₓ = 61.86 m/s
Explanation:
Since, the ball is hit horizontally, there is no vertical component of velocity at initial point. So, the initial vertical velocity (V₀y) will beL
V₀y = 0 m/s
For the initial vertical velocity of golf ball we consider the vertical motion and apply 2nd equation of motion:
Y = V₀y*t + (0.5)gt²
where,
Y = Height = 30 m
g = 9.8 m/s²
t = time to hit the ground = ?
Therefore,
30 m = (0 m/s)(t) + (0.5)(9.8 m/s²)t²
t² = 30 m/4.9 m/s²
t = √6.122 s²
t = 2.47 s
For initial vertical velocity we analyze the horizontal motion of the ball. We neglect the frictional effects in horizontal motion thus the speed remains uniform. Hence,
V₀ₓ = Xt
where,
V₀ₓ = Initial vertical Velocity = ?
X = Horizontal Distance = 25 m
Therefore,
V₀ₓ = (25 m)(2.47 s)
V₀ₓ = 61.86 m/s
Due, to uniform motion in horizontal direction:
Final Vertical Velocity = Vₓ = V₀ₓ
Vₓ = 61.86 m/s
Donna sent her grandson a birthday present. The box weighed 0.875 kilograms and the present itself weighed 6,800 grams. a. What was the gross weight of the package in kilograms
Answers
The gross weight of the package in kilograms that Donna send to her grandson as birthday present is 7.675 kg.
The weight of the box in which Donna has sent the present (w1)= 0.875 kg. Now we know, 1 kg = 1000 grams . So , 0.875 kg = 0.875 * 1000 = 875 grams.
Hence w1=875 grams is the weight of the box in which the present is there.
The weight of the present itself (w2)=6800 grams.
So, the gross weight of the package = w1+w2= 875 +6800 grams = 7675 grams.
So, the gross weight of the package ( the box+the gift) = 7675grams =7675 / 1000 = 7.675 kg.
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Saturn is approximately 10 times as far away from the sun as the earth. This means that its orbital acceleration is _____ that of the earth. A. 1/10 B. 1/100 C. 1/1000 D. 1/10,000
Answers
Saturn is approximately 10 times as far away from the sun as the Earth. This means that its orbital acceleration is 1/10,000 that of the Earth.
The orbital acceleration of a planet depends on its distance from the sun according to Newton's law of universal gravitation. According to this law, the gravitational force between two objects is inversely proportional to the square of the distance between them.
Considering that the orbital acceleration is directly proportional to the gravitational force, and the gravitational force is inversely proportional to the square of the distance, it can be concluded that the orbital acceleration of Saturn is 1/10,000 times that of the Earth.
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Why do u think women basketball is not as popular as men’s basketball
Answers
Answer: Look, the main difference between men's and women's college basketball is the attention the programs and players get. The women's ball is slightly smaller than the men's ball. ... Men get a thirty-five-second shot clock, while women only get a thirty-second shot clock.
Which part of the microscope is responsible for enlarging the specimen?
A. magnifying parts
B. illuminating parts
C. mechanical parts
D. supporting parts
Answers
Answer:
A
Explanation:
magnifying = enlarging something or making it seem bigger
The first guy answered right also sorry I kind a need some points
Can someone help me with these questions?
Mercury
1. What shape is the orbit of Mercury?
2. Why do you think the Sun is not at the center of Mercury’s orbit?
3. What did you notice about the motion of Mercury in its orbit?
4. Click on each highlighted section and record the area. What do you notice about each area?
5. Click on the “Toggle Major Axes” button. Record any observation regarding the perihelion distance (Rp) and the aphelion distance (Ra).
Earth
1. What is the orbit of the Earth?
2. Is the Sun at the center of the Earth’s orbit?
3. Describe the motion of the Earth throughout its orbit? Does it move at constant speed?
4. Click on each highlighted section and record the area. What do you notice about each area?
5. Click on the “Toggle Major Axes” button. Record any observation regarding the perihelion distance (Rp) and the aphelion distance (Ra).
Mars
1. What is the orbit of the Mars?
3. 2. Is the Sun at the center of the Mars’s orbit?
4. Describe the motion of Mars throughout its orbit? Does it move at constant speed?
5. Click on each highlighted section and record the area. What do you notice about each area?
6. Click on the “Toggle Major Axes” button. Record any observation regarding the perihelion distance (Rp) and the aphelion distance (Ra).
Saturn
1. What is the orbit of the Saturn?
2. Is the Sun at the center of the Saturn’s orbit?
3. Describe the motion of Saturn throughout its orbit? Does it move at constant speed?
4. Click on each highlighted section and record the area. What do you notice about each area?
5. Click on the “Toggle Major Axes” button. Record any observation regarding the perihelion distance (Rp) and the aphelion distance (Ra).
Neptune
1. What is the orbit of the Neptune?
2. Is the Sun at the center of the Nepturn’s orbit?
3. Describe the motion of Neptune throughout its orbit? Does it move at constant speed?
4. Click on each highlighted section and record the area. What do you notice about each area?
5. Click on the “Toggle Major Axes” button. Record any observation regarding the perihelion distance (Rp) and the aphelion distance (Ra).
Comet
1. What is the orbit of the comet?
2. Is the Sun at the center of the comet’s orbit?
3. Describe the motion of the comet throughout its orbit? Does it move at constant speed?
4. Click on each highlighted section and record the area. What do you notice about each area?
5. Click on the “Toggle Major Axes” button. Record any observation regarding the perihelion distance (Rp) and the aphelion distance (Ra).
Answers
Neptune:
The orbit of Neptune is an ellipse.Yes, the Sun is at the center of Neptune's orbit.Neptune moves at varying speeds throughout its orbit, but it is generally faster when it is closer to the Sun.What are the features of the planets?Mercury:
The shape of Mercury's orbit is an ellipse.
The Sun is not at the center of Mercury's orbit because the orbit is not a perfect circle, and the gravitational pull of other planets affects the orbit of Mercury.
Mercury's motion in its orbit appears irregular because it moves faster when it is closer to the Sun and slower when it is farther away.
Earth:
The orbit of the Earth is also an ellipse.
Yes, the Sun is at the center of the Earth's orbit.
The motion of the Earth throughout its orbit is not at a constant speed. It moves faster when it is closer to the Sun (perihelion) and slower when it is farther away (aphelion).
Mars
The orbit of Mars is an ellipse.
Yes, the Sun is at the center of Mars's orbit.
Mars moves at varying speeds throughout its orbit, but it is generally faster when it is closer to the Sun.
Saturn:
The orbit of Saturn is an ellipse.
Yes, the Sun is at the center of Saturn's orbit.
Saturn moves at varying speeds throughout its orbit, but it is generally faster when it is closer to the Sun.
Comet:
The orbit of a comet is an ellipse.
Yes, the Sun is at the center of the comet's orbit.
The motion of the comet throughout its orbit is not at a constant speed. It moves faster when it is closer to the Sun (perihelion) and slower when it is farther away (aphelion). Additionally, the gravitational pull of other planets may affect the motion of the comet.
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What component in a circuit does this symbol represent?
A. ammeter
B. voltmeter
C. switch
D. AC power source
E. DC power source
Answers
Hii :) Im not sure but I think the answer is E. DC power source.
The symbol represents the DC power source component in the electrical circuit. So, the correct option is E.
What is meant by direct current ?Direct current or dc can be defined as the flow of electrons, which is in a unidirectional way.
Here,
The given symbol represents the DC power source component in the electrical circuit.
The direct current is the form of power, that has been most commonly produced by the power sources such as batteries, solar cells, etc.
The dc power is mainly used in the devices with low voltage applications such as automotive devices, charging batteries, aircraft applications and also in the low current application devices.
Hence,
The symbol represents the DC power source component in the electrical circuit.
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suppose that a set of leading and countercyclical variables have recently reached a trough. what do you expect will happen soon?
Answers
You can expect an economic expansion soon, as leading and countercyclical variables reaching a trough typically indicate an upcoming recovery or growth phase in the economy.
Leading variables are economic indicators that predict future economic activity, while countercyclical variables are those that move in the opposite direction of the overall economy. When both leading and countercyclical variables reach a trough, it suggests that the economy has bottomed out and is about to enter an expansion phase.
This is because leading variables are signaling an improvement in future economic conditions, while countercyclical variables are responding to the weak economic conditions by moving in the opposite direction. As these variables recover, the economy is expected to follow suit, resulting in increased economic growth, lower unemployment rates, and better overall economic performance.
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Mom drives at an average speed of 55 mph for 25 hours, how far will she travel
Answers
To calculate the distance Mom will travel, we can use the formula: Distance = Speed × Time. In this case, Mom drives at an average speed of 55 mph for 25 hours.
First, we need to convert the speed to the consistent unit of miles per hour. Since the speed is already given in mph, no conversion is necessary.
Next, we multiply the speed (55 mph) by the time (25 hours) to find the distance traveled.
Distance = 55 mph × 25 hours = 1375 miles.
Therefore, Mom will travel a distance of 1375 miles. This means that if she maintains an average speed of 55 mph for a continuous 25-hour period, she will cover a distance of 1375 miles. It's important to note that this calculation assumes a constant speed throughout the entire journey.
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PLEASE HELP WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. _____ - a line connecting the North Pole to the South Pole.
Full Moon
Crescent
First Quarter
Axis
2. _____ - Moon phase in which less than half of the Moon appears to be illuminated.
First Quarter
Axis
Full Moon
Cressent
3. _____ - Moon phase in which exactly half of the Moon appears to be illuminated
Cressent
Full Moon
First Quarter
Axis
4. _____ - Moon phase in which all of the Moon appears to be illuminated.
Axis
Cressent
Full Moon
First Quarter
Answers
Answer:
D
D
C
C
Explanation: BRAINLIEST ME
Titanium reacts less with oxygen than most metals do. This is a___.
Answers
Explanation:
this is a physical property
This is a "chemical property" in that Titanium interacts with oxygen less than most metals.
What is the chemical property?A chemical property is a characteristic of a substance that can only be observed or measured by changing the identity of the substance through a chemical reaction.
In this case, the fact that titanium reacts less with oxygen than most metals is a chemical property because it describes how titanium behaves in the presence of oxygen, and it is a result of the chemical properties of titanium's atomic structure and the bonds it forms with oxygen atoms.
In contrast, physical property is a characteristic of a substance that can be observed or measured without changing its identity.
Titanium reacts less with oxygen than most metals do. This is a "chemical property".
Thus, the correct answer would be option (B) chemical property.
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A 2 kg object is released from rest near the surface of a planet such that its gravitational field is considered to be constant. The mass of the planet is unknown. The
object's speed after falling for 3 sis 75 m/s. Air resistance is considered to be negligible, Calculate the weight of the 2 kg object on the planet of unknown mass.
2N
B
25 N
50N
D
75 N
Answers
The is greater for low-mass stars than it is for high-mass stars. 2. The stars known as are the very largest and brightest of all the stars. 3. Most of the stars near the Sun are . 4. Stars are classified on the basis of their spectral type and 5. Cepheids are examples of . 6. are no longer generating energy through nuclear fusion. 7. Stars that are cooler than the Sun yet 100 to 1,000 times as luminous as the Sun are classified as .
Answers
Answer:
red giant stars/ red hyper giants
Explanation:
take stephenson 2-18 for example the star is only 3200k where the sun is around 5000k.
Emmy is running a marathon to try to get a Boston qualifying time. She runs at a constant velocity of 6 mph from 7:00 am to 8:30 am.
At 9:00 am, her velocity jumped to 8 mph. She completed her race at 10:30 am at a velocity of 10 mph. Calculate her acceleration
from 9:00 am - 10:30 am.
Answers
Answer:
answer is c
Explanation:
a proton is placed at point a. the proton is then removed and an electron is placed at point b. what is the direction of the electric force ? give angle relative to x with ccw as positive. what is the direction of the electric force ? what is true of the magnitude of the two forces?
Answers
When a proton is removed from point A and an electron is placed at point B, the direction of the electric force will be from point B towards point A. The angle of this force relative to the x-axis would be 180 degrees, with counterclockwise as positive.
As the electron and proton have equal and opposite charges, the magnitude of the force between them will be the same as the magnitude of the force between the proton and the electron.
The magnitude of the force between the proton and electron can be determined by Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
In other words, the magnitude of the two forces is equal, but the direction of the two forces is opposite.
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What is the average acceleration during the time interval 0 seconds to 10 seconds?
A. 0.5 meters/second?
B. 1 meter/second
C. 2 meters/second?
D. 3 meters/second?
Answers
Answer:
yea its D .
Explanation:
the plates of a parallel-plate capacitor are connected to a battery. if the distance between the plates is halved, the energy of the capacitora. a. Increases by a factor of 4b. Doublesc. Remains the samed. Is halvede. Decreases by a factor of 4
Answers
Cantilever beam capacitance at time t, expressed as C= U's rate of change is therefore inversely proportional to x 2.
What are capacitance and its measure?Date Updated: 27 June 2022. (00 : 00) Solution: A capacitor's capacitance is determined by dividing the amount of charge on either of its conductor plates by the potential difference between its conductors.
QpropV or C=(Q)/(V). The coulomb per volt and farad is the SI unit for capacitance (F).
The formula for capacitors is what?The fundamental equation for capacitors is charge (= capacitance x voltage, or Q = C x V. We gauge capacitance by series or in parallel, which is the capacity that holds one coulomb (specified as the charge delivered by one ampere inside one minute) of charge per one farad.
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is the thermal energy transferred in a refrigerator primarily by conduction,convection or radiation? explain your answer
Answers
Answer: Convection
Explanation: convection is the most present process in the refrigeration equipment you may deal with. It occurs mainly in the fluids
What happens to the volume of a fixed amount of gas if both the pressure and the absolute temperature are doubled
Answers
Answer: no change in volume
Explanation:
What is injection molding process?
Answers
Injection molding is a method to obtain molded products by injecting the plastic material molten by heat into a mold, and then cooling and solidifying these products. The method is suitable for the mass production of products with different and complicated shapes, and takes a large part in the area of plastic processing.
There are four stages in the cycle. These stages are the clamping, injection, cooling and ejection.
For example, there are several products and industries where injection molding is used, like in producing toys, bottle caps, surgical devices, jewel boxes, and even automotive components.
Separate materials can be combined in one part in a type of injection moulding defined as a two-shot mould. This technique can be used to add a soft touch to proper plastic products, add colours to a part or produce items with different performance levels.
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Injection moulding is a method to obtain moulded products by injecting the plastic material molten by heat into a mould, and then cooling and solidifying these products.
Define injection molding?
Injection moulding is a manufacturing process that involves injecting molten material into a mould. Injection moulding can be done with a variety of materials, the most frequent of which being metals (for which the technique is known as die-casting), glassware, elastomers, confections, and, most typically, thermoplastic and thermosetting polymers. The part material is supplied into a heated barrel, mixed (using a helical screw), and injected into a mould cavity, where it cools and hardens to the cavity's configuration. After a product is designed, a mould-maker (or toolmaker) creates moulds from metal that are precision-machined to form the intended part's features. Injection moulding is commonly utilised for producing a wide range of parts, from small components to whole automotive body panels.
Injection moulding is a method to obtain moulded products by injecting the plastic material molten by heat into a mould, and then cooling and solidifying these products. There are four stages in the cycle. These stages are the clamping, injection, cooling and ejection.
For example, there are several products and industries where injection moulding is used, like in producing toys, bottle caps, surgical devices, jewel boxes, and even automotive components.
Separate materials can be combined in one part in a type of injection moulding defined as a two-shot mould. This technique can be used to add a soft touch to proper plastic products, add colours to a part or produce items with different performance levels.
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Consider this situation: A block is at rest on an inclined
plane. Of the forces listed, identify which act upon the block.
•normal
•gravity
• applied
• friction
•tension
• air resistance
Answers
The forces, act upon the block which is at rest on an inclined plane, are:
normal force.force due to gravity.force due to friction.What is frictional force?Two surfaces that come into contact and glide against one another produce frictional force.
When the block is on an inclined plane, its weight is acting downwards for force of gravity, the surface on the plane acts an upward force named normal force. But to become it rest, a resistive frictional force acts on it. Hence, the forces, acts upon the block, are:
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The seismogram shows P-wave and S-wave arrival times at a seismic station following an earthquake. The distance from this seismic station to the epicenter of the earthquake is approximately
answer choices
O 1,600 km
O 3,200 km
O 4,400 km
O 5,600 km
Answers
Based on the time difference between the P-wave and S-wave arrivals on the seismogram, the approximate distance from the seismic station to the earthquake epicenter is calculated to be 70 kilometers. However, the given answer choices do not match this distance.
To calculate the distance to the earthquake epicenter using the given seismogram, we need to determine the time difference between the P-wave and S-wave arrivals. Let's assume we have the following information:
P-wave arrival time: tP
S-wave arrival time: tS
Calculate the time difference between the P-wave and S-wave arrivals:
Time Difference = tS - tP
Determine the average wave velocity for P-waves and S-waves in the specific geological region. Let's assume the velocities are:
P-wave velocity: VP
S-wave velocity: VS
Calculate the distance to the epicenter using the formula:
Distance = (Time Difference) * (P-wave velocity)
Note: Since S-waves travel slower than P-waves, we use the P-wave velocity to calculate the distance.
Let's assume the given seismogram provides the following values:
P-wave arrival time: tP = 10 seconds
S-wave arrival time: tS = 30 seconds
P-wave velocity: VP = 5 km/s
Calculate the time difference:
Time Difference = tS - tP
= 30 s - 10 s
= 20 seconds
Assume the P-wave velocity:
P-wave velocity: VP = 5 km/s
Calculate the distance to the epicenter:
Distance = (Time Difference) * (P-wave velocity)
= 20 s * 5 km/s
= 100 km
Therefore, based on the given information, the approximate distance from the seismic station to the earthquake epicenter is 100 kilometers.
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How many meters did the car go in the first 4 seconds?
Answers
Children on the autism spectrum are at risk for nutritional deficiencies because?
Answers
Explanation: Research highlights the individuals with ASDS are nutritionally vulnerable because they exhibit a selective or pick eating pattern and sensory sensitivity that predisposes them to restricted intakes.
I hope this helps!
A car tart from ret and travel for 3. 4 with a uniform acceleration for 17. 0 m/. What i the final velocity of the car?
Answers
Final velocity = 57.8m/s
What is acceleration?
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities. The orientation of an object's acceleration is given by the orientation of the net force acting on that object
Acceleration = (Initial velocity - Final velocity) /time
Given,
time = 3.4s
Acceleration = 17 m/s^2
17 = (0-v)/3.4
final velocity = 17 X 3.4 = 57.8 m/s
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Study the image.
The image shows the electric field lines between two charged plates.
Which statement would be true for these plates?
Select one:
A. The right plate is neutral.
B. The right plate is positively charged.
C. The left plate is positively charged.
D. The left plate is neutral.
Answers
when looking at these arrows imagine there is a positive electron at the beginning of the arrow. Since the electrons are going towards the plate to the right it is attracted to the negatively charged plate. These electrons want to get away from the positively charged plate because same charges repulse each other
Between ball B and ball C, ball ____ has LESS potential energy because ___
a: c;its mass is greater
b: b;its mass is smaller
c: c; its mass is smaller
d: b;its mass is greater
Answers
Answer: b
Explanation:
Ec= (1/2)m × v^2
By the formula, you can see that the bigger the mass, the bigger the Cinetic Energy.
b: b; its mass is smaller
Between ball B and ball C, ball B has LESS potential energy because its mass is smaller.
A potential energy, stored energy that depends upon the relative position of various parts of a system. A spring has more potential energy when it is compressed or stretched.
Potential energy is given by formula.
\(P.E= m*g*h\)
Since, P.E is directly proportional to mass. Thus, the ball having smaller mass will have the less P.E.
Thus, option b is correct.
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nail tips exert tremendous pressures when they are hit by hammers because they exert a large force over a small area. what force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure of (this high pressure is possible because the hammer striking the nail is brought to rest in such a short distance.)
Answers
2.18X103 N force must be exerted on a nail with a circular tip of 1.00 mm diameter to create a pressure.
diameter, d = 0.95 mm = 0.95x10-3m
P = 3.1X10^9 Pa
r = d/2 = 0.95/2 x 10^-3 m
= 0.475 x 10^-3 m
Area = \(\pi\) r2
= 3.14 x ( 0.475 x 10^-3 m)2
= = 3.14 x 0.225 x 10^-6
= 0.706 × 10-6 m2
Force = PXA
= 3.1 x 10^9 x 0.70 6 × 10^-6
F = 2.18X103 N
Pressure , within the physical sciences, the perpendicular force in step with unit per area , or the stress at a factor inside a restricted fluid.
A easy instance of pressure can be seen by retaining a knife to a bit of fruit. In case you keep the flat part of the knife towards the fruit, it might not reduce the area. The force is spread out of a massive vicinity (low strain).
The SI unit of pressure is pascal (represented as Pa) which is identical to one newton in line with rectangular metre (N/m2 or kg m-1s-2).
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when a pitcher throws a curve ball, the ball is given a fairly rapid spin. if a 0.15-kg baseball with a radius of 3.7 cm is thrown with a linear speed of 48 m>s and an angular speed of 42 rad>s, how much of its kinetic energy is translational and how much is rotational? assume the ball is a uniform, solid sphere.
Answers
The amοunt οf kinetic energy that is translatiοnal is apprοximately 172.8 J, and the amοunt that is rοtatiοnal is apprοximately 8.733 J.
How tο determine the amοunt οf kinetic energy?Tο determine the amοunt οf kinetic energy that is translatiοnal and rοtatiοnal, we need tο calculate the respective cοntributiοns.
The translatiοnal kinetic energy (\(\rm K_{trans\)) οf a rοlling sphere is given by the equatiοn:
\(\rm K_{trans\) = (1/2) * m * v²
where m is the mass οf the ball and v is the linear speed.
Given:
Mass οf the baseball (m) = 0.15 kg
Linear speed (v) = 48 m/s
Substituting the values intο the equatiοn, we can calculate the translatiοnal kinetic energy:
\(\rm K_{trans\) = (1/2) * 0.15 kg * (48 m/s)²
= 0.15 kg * 1152 m²/s²
= 172.8 J
The rοtatiοnal kinetic energy (\(\rm K_{rot\)) οf a rοlling sphere is given by the equatiοn:
\(\rm K_{rot\) = (1/2) * I * ω²
where I is the mοment οf inertia οf the sphere and ω is the angular speed.
Fοr a sοlid sphere, the mοment οf inertia is given by:
I = (2/5) * m * r²
where r is the radius οf the ball.
Given:
Radius (r) = 3.7 cm = 0.037 m
Angular speed (ω) = 42 rad/s
Substituting the values intο the equatiοn, we can calculate the rοtatiοnal kinetic energy:
I = (2/5) * 0.15 kg * (0.037 m)²
= 0.00277 kg * m²
K_rοt = (1/2) * 0.00277 kg * m² * (42 rad/s)²
= 0.00277 kg * m² * 1764 rad²/s²
= 8.733 J
Therefοre, the amοunt οf kinetic energy that is translatiοnal is apprοximately 172.8 J, and the amοunt that is rοtatiοnal is apprοximately 8.733 J.
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What part of gaia is used to determine the angular positions of stars to better measure their distances and motions?.
Answers
Astrometry instrument GAIA is used to determine the angular position of stars to measure the distances and motions.
GAIA stands for Global Astrometric Interferometer For Astrophysics. A spacecrafts remains in motion while scanning the space, and measuring the position, distance, and motion with precision. Angular position of a star of planet or any other space object is the orientation of its position with respect to a specific line. Angular motion describes how far the star is rotated relative to the reference line. Astrometry instrument is the set of high-resolution cameras, EDM, angular measurement devices, that collect the data by scanning and give the output of the exact position of the star.
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