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
A ball tossed vertically upward from the ground next to a building passes the bottom of a window 1.7 s after being tossed and passes the top of the window 0.30 s
later. The window is 2.0 m high from top to bottom. What was the ball's initial velocity? How far is the bottom of the window from the launch position? How high does the ball rise above the launch position?
The initial velocity of the ball is v₀ = (2*2.0)/0.30 = 13.3 m/s. and the height of the ball above the launch position is h = (13.3*1.7) - (0.5*9.81*(1.7)²) = 15.1 m.
What is initial velocity?Initial velocity is the speed and direction of an object at the start of its motion. It is usually designated by vector notation, with the direction of motion indicated by an arrow.
The initial velocity of the ball can be calculated using the equation v₀ = (2h)/t, where h is the height of the window (2.0 m) and t is the time it took for the ball to reach the top of the window (0.30 s).
Thus, the initial velocity of the ball is v₀ = (2*2.0)/0.30 = 13.3 m/s.
The bottom of the window is 1.7 m above the launch position.
The height of the ball above the launch position can be calculated using the equation h = v₀t - 0.5gt².
Here, v₀ is the initial velocity (13.3 m/s),
t is the time it took for the ball to pass the bottom of the window (1.7 s),
and g is the acceleration due to gravity (9.81 m/s²).
Thus, the height of the ball above the launch position is h = (13.3*1.7) - (0.5*9.81*(1.7)²) = 15.1 m.
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Sandra who is a Level 200 student of SoE and also a snowboarder starts from rest at the top of a double black diamond hill. As she rides down the slope, GPS coordinates are used to determine her displacement as a function of time: x=0.5t3 + 6t2 +3t where x is in metres and t is in seconds. where x and t are expressed in feet and seconds, respectively. a) Determine the position of the boarder when t = 4 s b) Determine the velocity of the boarder when t = 4s c) Determine the acceleration of the boarder when t = 4s 2021/22
Explanation:
a) To determine the position of the snowboarder when t = 4 seconds, we can substitute t = 4 into the equation x = 0.5t^3 + 6t^2 + 3t:
x = 0.5 * 4^3 + 6 * 4^2 + 3 * 4
x = 64 + 96 + 12
x = 172
So when t = 4 seconds, the snowboarder's position is 172 meters.
b) To determine the velocity of the snowboarder when t = 4 seconds, we'll need to find the first derivative of the displacement function x = 0.5t^3 + 6t^2 + 3t with respect to time:
dx/dt = 3 * 0.5 * t^2 + 2 * 6 * t + 3
Next, we can substitute t = 4 into this expression to find the velocity when t = 4 seconds:
dx/dt = 3 * 0.5 * 4^2 + 2 * 6 * 4 + 3
dx/dt = 72 + 48 + 3
dx/dt = 123
So the velocity of the snowboarder when t = 4 seconds is 123 meters per second.
c) To determine the acceleration of the snowboarder when t = 4 seconds, we'll need to find the second derivative of the displacement function x = 0.5t^3 + 6t^2 + 3t with respect to time:
d^2x/dt^2 = 6 * 0.5 * t + 2 * 6
Next, we can substitute t = 4 into this expression to find the acceleration when t = 4 seconds:
d^2x/dt^2 = 6 * 0.5 * 4 + 2 * 6
d^2x/dt^2 = 24 + 12
d^2x/dt^2 = 36
So the acceleration of the snowboarder when t = 4 seconds is 36 meters per second squared.
A rope of length L is clamped at both ends. Which one of thefollowing is not a possible wavelength for standing waves on thisrope?
a. L/2
a. 2L/3
c. L
d. 2L
e. 4L
If rope of length L is clamped at both ends then, 4L is not a possible wavelength for standing waves on this rope.
A string's shortest wavelength is L = λ/2. There is a node where the rope is clamped; at this point, the rope is fixed at zero and cannot travel up or down. Therefore, this is λ/2 if the rope's midsection is oscillating up and down. There are two visible loops if there is a node in the middle of the rope, which indicates that there are 2λ/2. The options are 3λ/2, 4λ/2, etc. So, aside from b, all other methods work.
You would have 2/3 of a wavelength if b were accurate. One of the nodes would have to be moving up and down as a result.
Every circle in my lovely image is a node; they appear every half-wavelength. Note that the square, which is at a wavelength of 2/3, is not a node. A standing wave cannot contain wavelengths that are divided into thirds.
Only standing waves whose length is an integral multiple of half wavelength can occur in a string that is fixed at both ends.
L = n* (λ/2)
Only in instance (e) is n = 1/2, and that is unacceptable.
(e) is the proper response.
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A 1. 20-gram sample of a hydrated salt is heated to a constant mass of 0. 80 gram. What was the percent by mass of water contained in the original sample?.
Water has a mass of 1.20 - 0.80 = 0.40 gram.
The water percentage is (0.40 / 1.20) * 100 = 33 1/3%
Evaporation is the physical process through which water transitions from a liquid to a gaseous state and then returns to the atmosphere as steam. Water in solid form (snow or ice) can also move straight to steam, a process known as sublimation. The word must be defined in a broad sense, including sublimation, to consequences of predicting evaporation losses in a region. Solar radiation supplies the energy required for water molecules to shift states.
Calculations:
Initial mass - ultimate mass of evaporated water
Evaporated water: 1.2 g - 0.8 g
0.4 g = evaporated H20
100% 1.2 g total mass
0.4 g of H20 --> 33.33 %
The initial sample has 33.33% of its mass in water.
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3. Suppose the speed of light were 1000 mi/h. You are traveling on a flight from Los Angeles to Boston, a distance of 3000 mi. The plane’s speed is a constant 600 mi/h. You leave Los Angeles at 10:00 am, as indicated by your wrist watch and by a clock in the airport. (a) According to your watch, what time is it when you land in Boston? (b) In the Boston airport is a clock that is synchronized to read exactly the same time as the clock in the Los Angeles airport. What time does that clock read when you land in Boston
The clock will read 5.88 hours when you land in Boston. If the speed of light were 1000mi/h when traveling in a flight from Los Angeles to Boston.
TimeIt is assumed that,
The speed of light, c, is equal to 1000 mph.
D = 2900 mi for distance
A plane's speed is 510 miles per hour.
(A) Assume that the time on your watch is and the time on the clock in the Los Angeles airport is, respectively. Using Einstein's theory of relativity, it can be calculated as follows: t= t0/1- v2/c
t= d/v and t0 = t1 - v2/c
.............(1)
t=2900 mi/510 mi/hr t=5.68 hrs
Equation (1) is transformed to: t0= 5.681-5102/1000 t0= 4.88 hours.
(b) According to a clock at the Los Angeles airport, the time was: t= 2900 miles/510 miles per hour; t= 5.68 hours.
Therefore, this is the necessary solution.
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A light wave has a frequency of 5.4*10^14 cycles per second and a wavelength of 5.5*10^-17 meter. What is the approximate speed of the wave?
A light wave has a frequency of 5.4 x 10⁻¹⁴cycles per second and a wavelength of 5.5 x 10⁻¹⁷ meter so the speed of the wave is 29.7 x 10⁻³m/s.
How to find the speed of the wave?v=λf, or velocity = wavelength x frequency, can be used to calculate a wave's speed. The distance a wave covers in a certain amount of time, such as the number of meters it covers every second, is known as its wave speed.
The formulae of the speed of the wave are,
v=λf, or velocity = wavelength x frequency
Frequency = 5.4 x 10⁻¹⁴ hertz
Wavelength = 5.5 x 10⁻¹⁷ m
v = 5.5 x 10⁻¹⁷x 5.4 x 10⁻¹⁴
= 29.7 x 10⁻³ m/s
Therefore, the speed of the wave is 29.7 x 10⁻³m/s.
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Newton's universal law of gravitation states that response area objects attract each other with a force response area proportional to the product of their masses and response area proportional to the square of the distance between their centers. When considering objects on the surface of the earth, the force is directly proportional to the product of the mass of the object and the response area due to response area at the earth's surface. Since the earth is response area than any object under consideration, the object is drawn response area the earth.
Newton's Law of Universal Gravitation says that every particle in the cosmos attracts every other particle with a force directly equal to the product of their masses and inversely proportional to the square of their distance.
To detect the gravitational force of attraction between any two objects, at least one of them on Earth must have an exceptionally massive mass. We cannot detect such forces because no object on Earth has an enormously big mass.
Newton's universal law of gravitation states that all objects attract each other with a force (i) away from directly proportional to the product of their masses and (ii) gravity proportional to the square of the distance between their centers. When considering objects on the surface of the Earth, the force is (iii) directly proportional to the product of the mass of the object and the (iv) acceleration due to (v) smaller at the Earth's surface. Since the Earth is (vi) larger than any object under consideration, the object is drawn (vii) towards the Earth.
The two items in a room do not move towards one other since the gravitational force of attraction between them is extremely minimal due to their modest masses. According to the universal law of gravity, every object exerts a gravitational force on every other thing. The gravitational force is directly proportional to the product of masses and inversely proportional to the square of their distances, according to the universal law of gravitation.
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Complete Question:
Fill in the blanks with the appropriate option:
Newton's universal law of gravitation states that all objects attract each other with a force (i) _____ proportional to the product of their masses and (ii) ____ proportional to the square of the distance between their centers. When considering objects on the surface of the Earth, the force is (iii) _____ proportional to the product of the mass of the object and the (iv) ____ due to (v) _____ at the Earth's surface. Since the Earth is (vi) ____ than any object under consideration, the object is drawn (vii) ______ the Earth.
Options:
acceleration, away from directly, directly, gravity, inversely, larger, smaller, some, toward.
When a skydiver falls which force is acting in the opposite direction to gravity?
When a skydiver falls, air resistance, or drag, is the force that acts in the opposite direction to gravity.
As the skydiver falls through the atmosphere, air molecules collide with their body, creating a force that opposes the direction of motion. The magnitude of the air resistance force depends on the speed of the skydiver, the surface area of their body, and the density of the air.
Initially, when the skydiver jumps out of the plane, the force of gravity pulls them downward, and they start accelerating towards the ground. As they gain speed, the air resistance force gradually increases until it becomes equal in magnitude to the force of gravity. At this point, the skydiver stops accelerating and falls at a constant velocity, known as the terminal velocity.
The air resistance force is proportional to the velocity of the skydiver, which means that increasing the velocity increases the air resistance force. At high velocities, the air resistance force becomes so strong that it eventually overcomes the force of gravity, allowing the skydiver to slow down and eventually land safely on the ground.
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How much energy is transferred when the potential difference is 230v and the charge is 200c?.
Answer:
Explanation: E = QV, the energy transferred by the quantity of electric charge by a potential difference of V volts.
Car A is driving 21.4 m/s in the positive x-direction according to an observer standing stationary on the side of the road. Car B is driving on the same road with a velocity of 27.4 m/s, as observed by a passenger in Car A. What is Car B's velocity as observed by the person on the side of the road?
Car B's velocity as observed by the person on the side of the road is -6.0 m/s, which means that it is moving in the negative x-direction.
explain about velocity ?
Velocity is a physical quantity that describes the rate of change of an object's position with respect to time. In other words, it is the speed and direction of an object's motion. Velocity is a vector quantity, which means that it has both a magnitude (or size) and a direction.
the relative velocity formula, which gives the velocity of one object as observed by another object or observer:
velocity of B with respect to observer = velocity of B with respect to A + velocity of A with respect to observer
In this problem, we have:
velocity of A with respect to observer = +21.4 m/s (positive because it is in the positive x-direction)
velocity of B with respect to A = -27.4 m/s (negative because it is in the opposite direction to A's velocity)
(Note that we use a negative sign for the velocity of B with respect to A because they are moving in opposite directions.)
Using the formula, we get:
velocity of B with respect to observer = -27.4 m/s + 21.4 m/s = -6.0 m/s
Therefore, Car B's velocity as observed by the person on the side of the road is -6.0 m/s, which means that it is moving in the negative x-direction.
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what is life? can you explain in please
Why is it that, relative humidity does not tell us how much water is actually in the air, but tells us how close the air is to being saturated?
The reason why relative humidity does not tell us how much water is actually in the air is because the amount of water vapor that air can hold depends on its temperature and pressure.
What is Relative humidity?
Relative humidity is a measure of the amount of water vapor in the air compared to the maximum amount of water vapor that the air can hold at a given temperature and pressure. It is expressed as a percentage and provides information about how close the air is to being saturated with water vapor.
armer air can hold more water vapor than colder air, and air at higher pressure can hold more water vapor than air at lower pressure. Therefore, the same amount of water vapor in the air can result in different relative humilities depending on the temperature and pressure.
For example, on a humid day with a relative humidity of 90%, there may be more water vapor in the air than on a dry day with a relative humidity of 30%. However, the air on the dry day is still capable of holding more water vapor before it becomes saturated. This is because the amount of water vapor that air can hold increases with temperature, so if the dry day is hotter than the humid day, the air may be able to hold more water vapor even though the relative humidity is lower.
In summary, relative humidity is a useful measure of how close the air is to being saturated with water vapor, but it does not provide information about the actual amount of water vapor in the air, which depends on the temperature and pressure.
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The mass of Jupiter is 1/1047 of the Sun's mass (that's 0.000955). We want to confirm this using Newton's version of Kepler's Third Law, following the examples in Lecture 7. We'll use the approximate data for two different moons of Jupiter to see how close the results are. Pick the closest answer in each case: (a) Ganymede is the third moon from the inside. It has an orbital period around Jupiter of approximately 0.0194 Earth years. Its semimajor axis is 0.0071 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data → [Select ] 0.000951 (b) Europa is the second moon from the inside. It has an ork 0.000989 approximately 0.0096 Earth years. Its semimajor axis is 0.0045 AU. Which of these comes closest to the mass of Jupiter (in solar masses) when using these data? [Select] Hint: See also example 3.4 in the textbook.
These come closest to the mass of Jupiter as (a) 0.000951; (b) 0.000955.
what is Kepler's law?Kepler's laws describe the motion of planets in their orbits around the sun.
This question involves using Newton's version of Kepler's Third Law to calculate the mass of Jupiter. Kepler's Third Law states that the square of the period of revolution of a planet/moon around a central object is proportional to the cube of the semimajor axis of the orbit. Newton's version of the law introduces the masses of the two objects in the equation, allowing us to solve for the mass of the central object (in this case, Jupiter) if we know the period and semimajor axis of a moon's orbit around it.
For part (a), we are given the period and semimajor axis of Ganymede's orbit and asked to select the closest answer for the mass of Jupiter when using this data. By plugging the values into Newton's version of Kepler's Third Law and solving for Jupiter's mass, we get an answer of 0.000951 solar masses.
For part (b), we are given the period and semimajor axis of Europa's orbit and asked to select the closest answer for the mass of Jupiter when using this data. Again, by plugging the values into the equation and solving for Jupiter's mass, we get an answer of 0.000989 solar masses.
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A startled deer runs 520 m at 20.0° north of east for half a minute, then turns and runs 380 m at 55.0° north of west for 15.0 seconds and stops. What is the average velocity of the deer during this time?
Answerbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Explanation:
A startled deer runs 520 m at 20.0° north of east for half a minute, then turns and runs 380 m at 55.0° north of west for 15.0 seconds and stops. Therefore, 60m/s is the average velocity of the deer during this time.
What is average velocity?Motion may be defined using physical quantity concepts such as speed, velocity, duration, displacement, as well as acceleration. Sir Isaac Newton provided the correct explanation of motion.
All of these quantities are explained in terms of a single quantity, time. In this section, we will look at average velocity, its mathematical representation, and its graphical depiction.
average velocity = 520 m+ 380 m / 15=60m/s
Therefore, 60m/s is the average velocity of the deer during this time.
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You are asked to figure out the size of an air bladder (a balloon that inflate and deflate to change the buoyancy of a profiling float) a profiling float should have to be able to profile from 1000m to the surface should be (at least). To figure it out, you look at profiles of density from the region where you will be deploying the float (see attached figure) and compute the maximum difference in density (=1000+sigma_theta) between 1000m and the surface.
Your float is a perfect cylinder with 20cm in diameter and 1.5m in length. Figure out its volume, Figure out the mass it should have, without inflating the bladder, to match the largest density observed at 1000m, so it can be neutrally buoyant at that depth (neither sinking or floating).
Finally, given the above, how big should the air bladder be (in minimum and in ml=cm^3) to that when inflated the float will be buoyant at the surface for all conditions observed at that region?
The minimum size of the air bladder [tex](in ml=cm^3)[/tex] should be[tex]2*σθ * 706.5 cm^3[/tex] to make sure that when inflated, the float will be buoyant at the surface for all conditions observed at that region.
What is air bladder?An air bladder is a sac-like organ that is filled with air and is found in certain aquatic animals, such as fish, amphibians, and certain invertebrates. It is used for buoyancy control, allowing the animal to adjust its position in the water column.
Volume of perfect cylinder =[tex]πr^2h[/tex]
[tex]= 3.14 * (10cm/2)^2 * 1.5m= 706.5 cm^3[/tex]
Mass of the float at 1000m = Density at 1000m * Volume of the float
[tex]= (1000+σθ)* 706.5 cm^3= (1000+σθ) * 706.5 g[/tex]
Air bladder size (minimum) = Mass of the float at 1000m - Mass of the float at surface
[tex]= (1000+σθ) * 706.5 g - (1000-σθ) * 706.5 g= 2*σθ * 706.5 g= 2*σθ * 706.5 cm^3[/tex]
Therefore, the minimum size of the air bladder (in ml=cm^3) should be [tex]2*σθ * 706.5 cm^3[/tex] to make sure that when inflated, the float will be buoyant at the surface for all conditions observed at that region.
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Let E =3i^+1j^ and F =1i^−3j^.
A. Find the magnitude of E.
B. Find the magnitude of F.
C. Find the magnitude of G =E +F.
D. Find the magnitude of H =−E −2F.
The given vectors E and F are in Cartesian form. To find their magnitudes, we can use the formula:
|v| = √(vx² + vy²)
where vx and vy are the x and y components of the vector.
What is the Cartesian algebra?Cartesian algebra, also known as coordinate algebra or analytic geometry, is a branch of mathematics that deals with the use of algebraic equations to describe geometric shapes and their properties. It is named after the French philosopher and mathematician René Descartes, who developed the Cartesian coordinate system, which provides a way to describe the position of points in space using numbers.
A. Magnitude of E:
|E| = √((3i)² + (1j)²)
= √(9i² + 1j²)
= √(9 + 1)
= √(10)
Therefore, the magnitude of E is √(10).
B. Magnitude of F:
|F| = √((1i)² + (-3j)²)
= √(1 + 9)
=√(10)
Therefore, the magnitude of F is √(10).
C. Magnitude of G = E + F:
G = E + F = (3i + 1i) + (1j - 3j)
= 4i - 2j
|G| = √((4i)² + (-2j)²)
=√(16 + 4)
= √(20)
= 2√(5)
Therefore, the magnitude of G is 2√(5).
D. Magnitude of H = -E - 2F:
H = -E - 2F = (-3i - 2i) + (-1j + 6j)
= -5i + 5j
|H| = √(-5i)² + (5j)²)
= √(25 + 25)
= √(50)
= 5√(2)
Therefore, the magnitude of H is 5√(2).
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Two blocks are connected by a massless rope over a massless, frictionless pulley. The mass of block 2 is 2=12.1 kg, and the coefficient of kinetic friction between block 2 and the incline is =0.200 . The angle of the incline is 29.5° . If block 2 is moving up the incline at constant speed, what is the mass 1 of block 1?
The 3.3kg is the mass 1 of block 1 .
What is mass ?
The amount of matter in a body is referred to as its mass. The kilogramme is the kilograms, which is the SI unit of mass (kg). Mass is defined as: Mass = Density/Volume.
What is speed ?
The rate of a directionally changing object's location. The SI unit of speed is created by combining the fundamental units of length and time. Meters per second (m/s) is the unit of speed in the metric system.
Therefore, The 3.3kg is the mass 1 of block 1 .
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For each of the following file extensions, select the correct file format from the drop-down menu. . Avi. Rtf. Pdf. Txt.
The following file extensions are
.avi: Audio Video Interleave file format
.rtf: Rich Text Format file format
.pdf: Portable Document Format file format
.txt: Text File format
File extensions are used by computer operating systems and applications to determine which program to use to open a file and how to handle it.
A file extension is a series of characters that follow the last period in a filename and indicates the format of the file. It is a way of identifying the type of data stored in a file, such as a text document, image, audio or video file, spreadsheet, or executable program.
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(a) A charge of -275e is uniformly distributed along a circular arc of radius 3.85 cm, which subtends an angle of 37°. What is the linear charge density along the arc?
1 C/m
(b) A charge of -275e is uniformly distributed over one face of a circular disk of radius 1.85 cm. What is the surface charge density over that face?
2 C/m2
(c) A charge of -275e is uniformly distributed over the surface of a sphere of radius 1.85 cm. What is the surface charge density over that surface?
3 C/m2
(d) A charge of -275e is uniformly spread through the volume of a sphere of radius 1.85 cm. What is the volume charge density in that sphere?
4 C/m3
Uniform distribution of charge a) [tex]-1.752 * 10^(-17) C/m[/tex] b) [tex]-4.038 * 10^(-16) C/m^2[/tex] c) [tex]-6.346 * 10^(-16) C/m^2[/tex] d) [tex]-4.580 * 10^(-13) C/m^3[/tex]
(a) To find the linear charge density along the arc, we divide total charge (-275e) by arc length. Arc length is product of radius (3.85 cm) by the angle (in radians) arc subtends. Convert angle to radians:
[tex]37 degree = (37/360) * 2\pi radians = 0.6435 radians[/tex]
The length of the arc is then:
length = radius x angle = (3.85 cm) x (0.6435) ≈ 2.477 cm
The linear charge density is then:
linear charge density = charge in total / length magnitude = (-275e) / (2.477 cm)
e: elementary charge.
Using charge value:
linear charge density = [tex]-1.752 * 10^(-17) C/m[/tex]
Therefore, linear charge density along the arc is [tex]-1.752 * 10^(-17) C/m.[/tex]
(b) To find the surface charge density over the face of the circular disk, we need to divide the total charge (-275e) by area of disk. Area of face of disk is [tex]\pi[/tex] times radius squared
area =[tex]\pi * (1.85 cm)^2 = 10.78 cm^2[/tex]
The surface charge density is then:
surface charge density = total value of charge / area magnitude = [tex](-275e) / (10.78 cm^2)[/tex]
e: elementary charge.
Using charge value:
surface charge density = [tex]-4.038 * 10^(-16) C/m^2[/tex]
Surface charge density over the face of the circular disk is [tex]-4.038 * 10^(-16) C/m^2[/tex].
(c) To get surface charge density over sphere surface, we divide total charge (-275e) by sphere surface area:
surface area = [tex]4\pi * (radius)^2[/tex]
The surface charge density:
surface charge density = total charge / surface area =[tex](-275e) / [4\pi * (1.85 cm)^2][/tex]
where e is the elementary charge.
Use charge value:
surface charge density ≈ [tex]-6.346 * 10^(-16) C/m^2[/tex]
Surface charge density over sphere is[tex]-6.346 * 10^(-16) C/m^2.[/tex]
(d) To get volume charge density in the sphere, we divide the total charge (-275e) by the volume of the sphere.
volume = [tex](4/3)\pi * (radius)^3[/tex]
The volume charge density is then:
volume charge density = total charge / volume = [tex](-275e) / [(4/3)\pi * (1.85 cm)^3][/tex]
e: elementary charge
Using value of the elementary charge:
volume charge density = [tex]-4.580 * 10^(-13) C/m^3[/tex]
Therefore, the volume charge density in the sphere is [tex]-4.580 * 10^(-13) C/m^3[/tex]
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Find the moment of inertia for the following objects:
A. A uniform disc of mass M and radius R rotating about its axis. Replace the sum in 3.31 by the appropriate integral and do the integral in polar coordinates.
B. A uniform solid sphere rotating about a diameter. Replace the sum in 3.31 by the appropriate integral and do the integral in spherical coordinates.
The moment of inertia of a uniform disc of mass M and radius R rotating about its axis is [tex](1/2) MR^2[/tex].
The moment of inertia of a uniform solid sphere of mass M and radius R rotating about a diameter is [tex](8/5) MR^2[/tex].
The moment of inertia of a uniform disc of mass M and radius R rotating about its axis can be found by integrating the moment of inertia of small elements of mass dm located at a distance r from the axis of rotation.
Using polar coordinates, we can write dm = (M/πR^2)rdrdθ, where r ranges from 0 to R and θ ranges from 0 to 2π.
The moment of inertia of each element is given by dI = dm r^2. Therefore, we have:
I = ∫dI
= ∫[tex]r^2 dm[/tex]
= ∫₀²π ∫₀ᴿ (M/πR^2)r³drdθ
= (M/πR^2) ∫₀²π [∫₀ᴿ r³dr] dθ
= (M/πR^2) ∫₀²π [(1/4)R^4] dθ
= (M/πR^2) (1/4)R^4 (2π)
= [tex](1/2) MR^2[/tex]
The moment of inertia of a uniform solid sphere of mass M and radius R rotating about a diameter can be found by integrating the moment of inertia of small elements of mass dm located at a distance r from the diameter. Using spherical coordinates, we can write dm = (M/4πR^3)r^2sinθdrdθdφ, where r ranges from 0 to R, θ ranges from 0 to π, and φ ranges from 0 to 2π. The moment of inertia of each element is given by dI = dm r^2sin^2θ. Therefore, we have:
I = ∫dI = ∫r^2sin^2θ dm = ∫₀²π ∫₀ᴾ ∫₀ᴿ (M/4πR^3)r^4sin^3θdrdθdφ
= (M/4πR^3) ∫₀²π ∫₀ᴾ [∫₀ᴿ r^4sin^3θdr] dθdφ
= (M/4πR^3) ∫₀²π ∫₀ᴾ [(2/5)R^5sin^3θ] dθdφ
= (2/5) MR^2 ∫₀²π [∫₀ᴾ sin^3θ dθ] dφ
= (2/5) MR^2 ∫₀²π [(-cosθ + (3/2)cos^3θ/3)|₀ᴾ] dφ
= (8/15) MR^2 ∫₀²π dφ
= (8/15) MR^2 (2π)
= (8/5) MR^2
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A man is standing on the shore of a beach, up to his knees in water. Every 5 seconds a wave breaks on him. What is the period of the wave?.
Answer:
The period of a wave refers to the time it takes for a complete wave cycle to occur, from crest to crest or from trough to trough. In this scenario, you have specified that every 5 seconds a wave breaks on the man, so the period of the wave is 5 seconds.
Explanation:
pls mark brainlist and np
Answer:
Explanation:
= 4 Hz
As an example, a wave with a period T = 0.25 s takes ¼ of a second to complete a full vibration cycle (crest - trough - crest) at a certain location and thus performs four vibrations per second. Hence its frequency is f = 4 Hz.
The diagram below shows three cubes of the same material and density. If the cubes all start out at 80°C, which cube will cool the most slowly?
Answer:
the cube that will slowly cool is 2
The cube 2 will cool the most slowly.
What is meant by cooling ?The removal of heat from a system is known as cooling, and it usually leads to a decrease in temperature or a change in phase.
Here,
Three cubes of same material and density are given in the diagram. They all are said to be cooling starting from 80°C.
The three cubes have different volumes.
We know that, as the volume of the cube increases, the surface area of the cube decreases accordingly. That means, the volume of a cube is inversely proportional to its surface area.
V ∝ 1/A
According to the principle of cooling, the rate of cooling is directly proportional to the surface area. That means, the rate of cooling is higher for objects with higher surface area and slower for those with lower surface area.
So, the cube 2 is having the lowest volume among the three cubes and thus the highest surface area.
Therefore, it will take more time to cool down.
Hence,
The cube 2 will cool the most slowly.
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Consider a ball on a circular track. The ball is slowly coming to a stop which takes 15.0 seconds. At the start, the ball was moving around with 9.13 rad/s. Calculate the angular deceleration if the ball traveled across 90 radians.
The answer should be -0.42 rad/s2
I don't know how to solve it
The angular deceleration of the ball is -0.42 rad/s².
What is angular acceleration?Angular acceleration is a measure of the rate of change of angular velocity of an object rotating about an axis. When an object rotates, its angular velocity (ω) can change as a result of various factors, such as the application of an external torque or the redistribution of mass in the object.
We can use the formula for angular acceleration:
α = (ωf - ωi) / t
where
α is the angular acceleration
ωi is the initial angular velocity
ωf is the final angular velocity (which is zero in this case since the ball comes to a stop)
t is the time it takes for the ball to come to a stop
To find the initial and final angular positions, we can use the formula:
θf - θi = ωi * t + (1/2) * α * t²
where
θi is the initial angular position (0 in this case)
θf is the final angular position (90 radians in this case)
Substtuting the given values, we have:
θf - θi = ωi * t + (1/2) * α * t²
90 - 0 = (9.13 rad/s) * 15 s + (1/2) * α * (15 s)²
Simplifying and solving for α, we get:
α = -0.42 rad/s²
Therefore, the angular deceleration of the ball is -0.42 rad/s².
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A frictionless ramp forms a 20.0° angle with the horizontal. A 5.00 kg
load rests on the ramp. Calculate the magnitude of the force that will hold
the load stationary on the ramp, and then determine the ideal mechanical
advantage of the ramp using this information.
The force of approximately 16.9 N is needed to hold the load stationary on the ramp.
What is friction?Friction is the force that prevents two solid objects from rolling or sliding over one another.
Although frictional forces, such the traction required to walk without slipping, may be advantageous, they can provide a significant amount of resistance to motion.
Since the ramp is frictionless, the only forces acting on the load are its weight (mg) and the normal force (N) exerted by the ramp perpendicular to the surface.
We can break the weight into two components: one parallel to the ramp (mg sin θ) and one perpendicular to the ramp (mg cos θ).
To keep the load stationary on the ramp, the force applied parallel to the ramp (call it F) must balance the component of the weight parallel to the ramp:
F = mg sin θ
Substituting the given values, we get:
F = (5.00 kg) * (9.81 [tex]m/s^2[/tex]) * sin 20.0° ≈ 16.9 N
Therefore, a force of approximately 16.9 N is needed to hold the load stationary on the ramp.
The ideal mechanical advantage (IMA) of the ramp is the ratio of the length of the ramp (L) to its height (h):
IMA = L/h
Let's say the ramp has a height of h and a base of b. Then:
h = b sin θ
L = b cos θ
Substituting the given angle, we get:
h = b sin 20.0°
L = b cos 20.0°
Dividing L by h, we get:
IMA = L/h = (b cos 20.0°) / (b sin 20.0°) = cos 20.0° / sin 20.0° ≈ 1.16
Thus, the ideal mechanical advantage of the ramp is approximately 1.16.
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A student is playing with a magnetic compass near a bar magnet. At a range of 10 cm, they notice that the compass needle is pulled slightly towards the magnet. What would they see if the compass was moved to 8 cm?
A. The needle would not move from its original deflection.
B. The needle would be pushed in the opposite direction.
C. The needle would be pulled more towards the magnet.
D. The needle would return closer to its normal position.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As the boy moves the bar magnet towards the magnetic compass, the needly is pulled slightly towards the bar magnet, so if he deduct the separation to 8 cm, most probably the needle would be pulled more towards the bar magnet.
Hence, the correct choice will be : (c)
Answer: c I think
Explanation I think its c
QUESTION 3 Consider a block of mass 6 kg on a rough plane inclined at 25° to the horizontall A force, F of magnitude 37,173 N is applied to this block to keep it moving at a constant velocity 6 kg 25 what is the normal force
The normal force is 53.3 N.
What is the normal force on an object?We have to note that the force that is acting on the object may be a single force or a system of forces. In this case, the force that is acting on the object would have many components including the normal force.
You must note that the normal force is the force that in a direction that is opposite to the weight of the object but does have the same magnitude as the weight of the object.
Thus we can see that the normal force is obtained from;
R = mgcosθ
m = mass
g = acceleration due to gravity
θ = angle
R = 6 * 9.8 * cos 25
R = 53.3 N
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Sr spontaneously undergoes beta-minus decay. Write an equation for its decay reaction, including the symbol for the element into which Sr converts.
The equation for the beta-minus decay reaction of Sr-90 is:
90Sr --> 90Y + β⁻ + ν
In this reaction, Sr-90 (Strontium-90) undergoes beta-minus decay, emitting a beta particle (β⁻) and a neutrino (ν). As a result of this reaction, Sr-90 is converted into Y-90 (Yttrium-90). Beta-minus decay is a type of radioactive decay in which an electron is emitted from the nucleus, converting a neutron into a proton and thus changing the element's atomic number by one. This type of decay is common in isotopes of elements in the middle of the periodic table, such as carbon-14 and strontium-90. The result of this decay process is that the strontium-90 atom is converted into a yttrium-90 atom, which is one proton heavier than the strontium-90 atom. Energy is released as this process progresses.
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What are the magnitude Δ and angle of the change in velocity if the initial velocity is 65.0 m/s south and the final velocity is 20.0 m/s west? Let the angle be measured relative to the east direction (e.g., =90∘ means Δ⃗ points north, =180∘ means Δ⃗ points west, etc.).
Answer:
∆ = 68.0∠ = 107.1°Explanation:
You want the magnitude and direction of the change in velocity from 65.0 m/s south to 20.0 m/s west.
ChangeThe change in velocity can be represented by a vector from the initial velocity to the final velocity as shown in the attachment. The magnitude and direction of it can be found using the usual tools for solving triangles.
MagnitudeThe magnitude of the change is the hypotenuse of a right triangle with legs 20 and 65. Its value is ...
∆ = √(20² +65²) = √4625 ≈ 68.007 . . . . m/s
The magnitude of the velocity change is ∆ = 68.0 m/s.
DirectionAs the diagram shows, the direction of the change is west of north by an angle θ that satisfies ...
tan(θ) = 20/65
θ = arctan(20/65) ≈ 17.1027°
The direction of the change measured from east is 90° +17.1° = 107.1°.
The angle of the velocity change is about 107.1°.
__
Additional comment
These calculations are handled neatly by a vector calculator, as shown in the second attachment.
A glider of length 12.4 cm moves on an air track with
constant acceleration (Fig P2.31). A time interval of 0.628 s
elapses between the moment when its front end passes a
fixed point A along the track and the moment when its
back end passes this point. Next, a time interval of 1.39 s
elapses between the moment when the back end of the
glider passes the point A and the moment when the front
end of the glider passes a second point B farther down the
track. After that, an additional 0.431 s elapses until the
back end of the glider passes point B. (a) Find the average
speed of the glider as it passes point A. (b) Find the acceleration
of the glider. (c) Explain how you can compute the
acceleration without knowing
the distance between points A
and B.
[tex]19.7cm/s and 4.70 cm/s^2[/tex] are the average speed and acceleration of the glider.
(a) As the glider's front end crosses point A, start a timer at t=0. The instantaneous speed at t=0.314s, halfway through the time interval, is [tex]12.4cm/(0.628s)=19.7cm/s[/tex], which equals the glider's average speed for the interval between t=0 and t=0.628s.
(b) The instantaneous speed at the point [tex]t=(2.02+2.45)/2=2.23s[/tex]. is equal to [tex]12.4cm/(0.431s)=28.8cm/s[/tex], which is the average speed of the glider for the time span between [tex]0.628+1.39=2.02s[/tex] and [tex]0.628+1.39+0.431=2.45s[/tex].
Now that we are aware of the velocities at two points, we can calculate the acceleration using the formula [tex][(28.8-19.7)cm/s]/[(2.23-0.314)s]=4.70cm/s2[/tex].
(c) The average velocity over a predetermined period of time is determined using the glider's length rather than the distance between points A and B.
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Class work 6 1. A 1 kg wooden block is stationary on a desk tip. The coefficient of static friction for the two surfaces is 0.2. a) b) Find the normal force experienced by the block. Determine the maximum static frictional force for this situation c) What force will get the block to move? d) Calculate the kinetic frictional for if the coefficient of kinetic friction is 0.19
(a) The normal force experienced by the block is 9.8 N.
(b) The maximum static frictional force is 1.96 N.
(c) The minimum force required to move the block is 1.96 N.
(d) The kinetic friction force is 1.862 N.
What is the normal force?
The normal force experienced by the block is equal to the weight of the block and is given by:
F_normal = mg
where;
m is the mass of the block (1 kg) and g is the acceleration due to gravity (9.8 m/s^2).F_normal = 1 kg x 9.8 m/s^2 = 9.8 N
The maximum static frictional force is given by:
F_friction_max = μ_s x F_normal
where;
μ_s is the coefficient of static friction (0.2).F_friction_max = 0.2 x 9.8 N = 1.96 N
To get the block to move, a horizohntal force greater than the maximum static frictional force must be applied. The minimum force required to move the block is given by:
F_min = F_friction_max + ε
where;
ε is a small positive value to account for any slight inaccuracies.The kinetic friction force is given by:
F_friction_kinetic = μ_k x F_normal
where;
μ_k is the coefficient of kinetic friction (0.19).F_friction_kinetic = 0.19 x 9.8 N = 1.862 N
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