The volume of solid aluminum sphere is 0.00858 cubic meters and mass is 23.16 kg.
The atomic mass is the mass of an atom. The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The atomic mass is carried by the atomic nucleus, which occupies only about 10-12 of the total volume of the atom or less, but it contains all the positive charge and at least 99.95% of the total mass of the atom. Note that, each element may contain more isotopes, therefore this resulting atomic mass is calculated from naturally-occuring isotopes and their abundance.The volume of sphere is given by formula : [tex]\frac{4}{3} \pi r^{3}[/tex]
Where,
r = radius of sphere
Given, r = 5 inches = 0.127 meters
Putting this value in above equation we get, Volume= 0.00858 cubic meters.
Given density of aluminum is 2700 kg/m^3
We know that:
Density = Mass / Volume
i.e. Mass = Density * Volume
= 2700 kg/m^3 * 0.00858 m^3
= 23.16 kg
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A steel wire of length 1.93 m with circular cross section must stretch no more than 0.240 cm when a tensile (stretching) force of 450 N is applied to each end of the wire. What minimum diameter is required for the wire?
The minimum diameter required for the wire is 1.48 m when A steel wire of length 1.93 m with a circular cross-section must stretch no more than 0.240 cm when a tensile (stretching) force of 450 N is applied to each end of the wire.
Given,
wire length, l = 1.93 m
Δl = 0.240 cm = 0.24 x 10⁻² m
F = 450 N
we know that, young's modulus for steel
Y = 2.1 x 10¹¹ N/m²
let the radius of the wire is r
we know that,
Y = Fl/AΔl = (450 x 1.93)/(3.14 x r² x 0.24 x 10⁻²)
r² = 5.486 x 10⁻⁷ m²
or r = 7.4 x 10⁻⁴ m
so diameter of wire is d = 2r = 2 x 7.4 x 10⁻⁴ m
d = 1.48 x 10⁻³ m or d = 1.48 mm
Therefore, the minimum diameter required for the wire is 1.48 m when A steel wire of length 1.93 m with a circular cross-section must stretch no more than 0.240 cm when a tensile (stretching) force of 450 N is applied to each end of the wire.
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an air cannon fires a brick straight upward. the initial velocity of the brick and time required to reach its maximum height are recorded. which of the following statements describe the expected relationship between the time to maximum height and the initial velocity? assume that the effects of air resistance are negligible.
The greatest height is dictated by the starting vertical velocity. Because higher launch angles have a bigger vertical velocity component, increasing the launch angle increases the maximum height.
What is the relationship between maximum velocity and average velocity?The maximum velocity of a fully developed laminar viscous flow through a circular pipe is double the average velocity. The maximum velocity for fully developed laminar flow over parallel plates is equal to (3/2) times the average velocity.
The amount of distance an item travels in a given length of time is measured by its velocity. Here's a word equation that describes the link between distance, velocity, and time: Distance travelled divided by time equals velocity.
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An inclined track is secured to a table. The height of the highest point of the above the tabletop is h1. The height from the tabletop to the floor is h2. A block of as M is released from rest and slides down the track such that all the frictional forces are considered negligible. The block leaves the track horizontally and strikes the ground at a distance D. Which of the following statements is correct about the scenario? Select two answers.
answer choices
the total mechanical energy of the system containing only the block increases from the moment of release to the moment it hits the ground.
the total mechanical energy of the system containing only the black remains constant
the total mechanical energy of the block-earth system remains constant
the total mechanical energy of the block-earth system increases from the moment of release to the moment it hits the ground.
The total mechanical energy of the block-earth system remains constant, and the total mechanical energy of the system containing only the block increases from the moment of release to the moment it hits the ground.
What is mechanical energy?Mechanical energy is energy associated with the motion and position of an object. It is the sum of both the kinetic energy, which is energy associated with the object's motion, and the potential energy, which is energy associated with the object's position. Mechanical energy is present in a variety of forms, including kinetic energy, potential energy, heat, and elastic energy. Mechanical energy is converted into other forms of energy, such as thermal energy, electrical energy, and chemical energy. Mechanical energy can be used to do work, such as turning a crank to lift a heavy object, and can be harnessed to power machines and devices. Mechanical energy is an important concept in physics and engineering, as it can be used to analyze the motion and behavior of objects, and to develop solutions to problems.
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given two strings s and t, both consisting of lowercase english letters and digits, your task is to calculate how many ways exactly one digit could be removed from one of the strings so that s is lexicographically smaller than t after the removal. note that we are removing only a single instance of a single digit, rather than all instances (eg: removing 1 from the string a11b1c could result in a1b1c or a11bc, but not abc).
I came up with this test case myself. If s = '3ab' and t = 'cd', return 1. If s = '123ab' and t = '423cd', return 6.
What are lexicograph?The study of lexicons is called lexicography, and it is separated into two distinct academic fields. It involves the creation of dictionaries. [1]
The process of compiling, writing, and editing dictionaries is known as practical lexicography.
Theoretical lexicography is the academic study of the semantic, orthographic, syntactic, and paradigmatic characteristics of the lexicon (vocabulary) of a language. It also develops theories of the elements and structures of dictionaries that connect the data in dictionaries, the information needs of users in various contexts, and the most effective ways for users to access the data included in printed and electronic dictionaries. This practise is sometimes known as "metalexicography."
On what defines lexicology as different from lexicography, there is some debate. Some people use the term "lexicology" to refer to theoretical lexicography, whereas others do not.
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how far must the stone fall so that the pulley has 4.30 j of kinetic energy? express your answer numerically in meters to three significant figures.
To calculate the distance first you have to find the angular velocity of the pulley with the formula K.E = 1/2 I ω² using the given value of kinetic energy. Then, also find the potential energy loss of the stone and then the distance.
Since the system here is released from rest, therefore there will be loss in potential energy of the system and gain in its kinetic energy.
Therefore,
Loss in potential energy = gain in (kinetic energy of the pulley + kinetic energy of the stone)
Using the given mass of the pulley disk, find its moment of Inertia.
Inertia (I) = 1/2 mass x radius²
Then, find the angular velocity of the pulley,
K.E = 1/2 I ω²
Finally, find the total kinetic energy of the system by dividing the two fractions of the pulley's kinetic energies .
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determine the work required to deflect a linear spring with a spring constant of 70 kn/m by 20 cm from its rest position. (5points)
The work required to deflect a linear spring by 20 cm from its rest position with a spring constant of 70 kn/m is 1.4 KJ.
What is spring constant?spring constants (physics) A spring property defined as the ratio of the force acting on the spring to the displacement induced by it. Hooke's Law states that as a spring is extended, the force exerted is proportional to the increase in length from the equilibrium length. F represents the force, while x represents the change in spring length. The spring constant is the proportional constant k. It is a measure of the stiffness of the spring. When a spring is stretched or compressed by an amount x from its equilibrium length, it produces a force F = -kx in the direction of its equilibrium position.
Here,
spring constant=70 KN/m
d=0.2 m
W=kx²/2
=70*10^3(0.2²)/2
=1.4 KJ
The work required to deflect a linear spring with a spring constant of 70 kn/m by 20 cm from its rest position is 1.4 KJ.
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Classify each of the following failures by identifying its category in Fig. 1.1, and explain the reasons for each choice in one or two sentences: (a) The plastic frames on eyeglasses gradually spread and become loose. (b) A glass bowl with a small crack breaks into two pieces when it is immersed, while still hot, into cold water (c) Plastic scissors develop a small crack just in front of one of the finger rings (d) A copper water pipe freezes and develops a lengthwise split that causes a leak (e) The steel radiator fan blades in an automobile develop small cracks near the base of the blades
We classified each of the following failures by identifying its category in the Figure shown:
Plastic eyeglass frames gradually stretch and loosen. This is an example of creep failure.A glass bowl with a small crack breaks into two pieces when immersed, still hot, in cold water. This is an example of thermal shock failure.A plastic scissors has a small crack just in front of one of the finger rings. This is an example of fatigue failure.A copper water pipe freezes and develops a longitudinal crack that causes a leak. This is an example of brittle fracture.The steel fan blades on the radiator fan are leaking. This is an example of creep failure.Explanation of each of the failures of the mentioned materials:This is an example of creep failure, which occurs when a material is subjected to constant stress over time and causes it to deform. Plastic eyeglass frames stretch and loosen due to constant stress from wearing them. This is an example of thermal shock failure, which occurs when a material is subjected to a sudden change in temperature, causing it to crack or break. The glass bowl broke in two when immersed in cold water while it was still hot. This is an example of fatigue failure, which occurs when a material is subjected to repeated cycles of stress, causing it to eventually crack or break. The plastic scissors developed a small crack due to repeated stress from use. This is an example of brittle fracture, which occurs when a material is subjected to high stress and fractures without any significant deformation. The copper water pipe froze and split longitudinally due to the high stress from the freezing temperatures. This is an example of creep failure, which occurs when a material is subjected to constant stress over time and causes it to deform. Steel radiator fan blades developed small cracks due to the constant stress of being used while an automobile develops small cracks near the base of the blades.Learn more about material failures:
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each night different meteorologists give us the probability that it will rain the next day. to judge how well these people predict, we will score each of them as follows: if a meteorologist says that it will rain with probability p, then he or she will receive a score of
If a meteorologist says that it will rain with probability p, then he or she will receive a score of -10log(p) and a score of -10log(1-p) if it does not rain.
What will be the score if a meteorologist says that it will rain with probability p?The scoring system is called the Brier score, which is a commonly used method for evaluating accuracy of probabilistic forecasts. The Brier score ranges from 0 to 1, with score of 0 indicating perfect accuracy and score of 1 indicating total inaccuracy.
If a meteorologist says that it will rain with probability p, then he / she will receive a score of -10log(p) if it does rain. This is because log(p) is a measure of how uncertain the forecast is, and negative sign is used to penalize inaccurate forecasts.
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i.
An ant crawl around a circular track of are length 22cm. At an instant it makes an
angular displacement 45°, then the radius of that circular track iS
The correct answer is 2.77m.
a car burns fuel with a density of 700 kg/m3 under atmospheric conditions that produce an air density of 1.2 kg/m3. the car has a fuel rating of 36 mpg (miles per gallon) at a speed of 60 mph (miles per hour) and a frontal cross-section of 4.5 feet by 2.5 feet. 1. calculate
The drag coefficient of the car is calculated as equal to 0.0947.
What is drag coefficient ?A dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water is called drag coefficient.
60 mph = 26.8 m/s
1 mpg = 0.425144 liters/kilometer
36 mpg = 15.60512 liters/kilometer
4.5 ft * 2.5 ft = 11.25 ft^2 = 1.042 m^2
The drag force can be calculated as:
Fd = 0.5 * Cd * A * r * v^2
where, Cd = drag coefficient (unitless), A = frontal area of the car (m^2), r = air density (kg/m^3), v = velocity of the car (m/s)
So, Fd = (15.60512 liters/kilometer) * 4.5 kg/liter / (3600 sec/hour) = 0.0066 N
Cd = Fd / (0.5 * A * r * v^2)
Cd = 0.0066 N / (0.5 * 1.042 m^2 * 1.2 kg/m^3 * 26.8 m/s^2) = 0.0947
The drag coefficient of the car is 0.0947.
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Note: The question given on the portal is incomplete. here is the complete question.
Question: A car burns fuel with a density of 700 kg/m3 under atmospheric conditions that produce an air density of 1.2 kg/m3. the car has a fuel rating of 36 mpg (miles per gallon) at a speed of 60 mph (miles per hour) and a frontal cross-section of 4.5 feet by 2.5 feet. 1. calculate the drag coefficient of the car.
the froude number, fr, is a dimensionless value that describes different flow regimes of open channel flow. if it depends on velocity v , gravitational constant g, and length l, use buckingham pi theorem to show.T/F
False. Buckingham Pi theorem states that if a physical relationship involves a certain number of independent variables, then the relationship can be written as a product of powers of a certain number of dimensionless groups.
What is Buckingham Pi theorem?Buckingham Pi theorem is a mathematical theorem that states that any physical system can be expressed as a combination of an appropriate number of variables, together with the appropriate number of independent dimensionless parameters. The theorem was developed by Edward Buckingham in 1914 and is considered to be the most general form of dimensional analysis.
The Froude number does not depend on the independent variables mentioned (velocity, gravitational constant, and length) so Buckingham Pi theorem is not applicable.
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Can anyone help me answer this question?
Find the mass of an object whose density is 250 kg / cm^3 and volume is 2000 mm^3.
The Mass of the object is 500kg have a density of 250 kg/cm³.
What is Density?Mass per unit of volume is referred to as density, volumetric mass density, or specific mass. The Latin sign D may also be used, however, the Greek letter rho is more frequently employed to represent density. Mass divided by volume is the mathematical formula for density.
Although this is technically incorrect, density is generally described as a substance's weight divided by its volume. The term "specific weight" is more accurate.
The density and mass concentration of a pure substance is numerically equivalent. Density can affect buoyancy, purity, and packing. Varied materials typically have different densities. At normal temperatures and pressures, osmium and iridium have the highest densities of any known elements.
Volume = 2000mm³ = 2cm³
Density = Mass / Volume
250 = Mass/ 2
mass = 500kg
Hence, the mass will be 500kg.
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two charged particles, one q and the other q, are held fixed a certain distance, 2d, apart. find the electric field at point p. for the coordinate system, take x to be to the right and y to be up
The vector sum of the electric fields resulting from each of the two charges at point P is the electric field. The field owing to q will point to the right, whereas the field due to -q will point to the left. As a result, the net electric field at point P is zero.
An electric field is a physical field that surrounds electrically charged particles and acts as an attractor or repellent to all other charged particles in the vicinity. It can also refer to a system of charged particles' physical field. The force per unit charge exerted on a positive test charge that is at rest at a given position is the force per unit charge that is used to define the electric field analytically. Electric charge or magnetic fields with variable amplitudes can produce an electric field. The area of space surrounding an electrically charged particle or object in which the charge body perceives force is known as the electric field.
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A student must conduct an experiment to verify the conservation of momentum for a closed two-cart system. Cart X and cart Y travel toward each other and eventually collide. The student has determined the following procedure.
Step 1: Measure the mass of cart X and cart Y with a balance.
Step 2: Use a motion sensor to record data of the velocity of each cart before, during, and after the collision.
Step 3: Use the data and ∑pf = ∑p0 to determine if the right-hand side of the equation is equal to the left-hand side of the equation.
Which of the following steps should the student add to the procedure so that the conservation of momentum can be experimentally verified?
answer choices
Conduct the experiment on a smooth, level surface.
Attach adhesive strips to each cart so that they stick together after they collide.
Ensure that the mass of each cart is the same.
Ensure that the initial speed of each cart is the same.
The surfaces should be frictionless . The vector sum of the momenta should be compared, because momentum is a vector quantity.
Define conservation of momentum ?
The law of conservation of momentum states that in an isolated system the total momentum of two or more bodies acting upon each other remains constant unless an external force is applied. Therefore, momentum can neither be created nor destroyed.The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.Every moving object has momentum, and momentum is defined as the product of an object's mass and its velocity. As an equation, this can be written as p=mv p = m v , where p represents the momentum.To learn more about momentum refers to:
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A fish in a lake looks up at the
surface of the water. At what
distance d along the surface,
measured from the normal, is
a water-skimming insect safe
from the roving eye of the
fish?
the distance traveld by a body fallling freely from rest in one,two and three seconds are in the range of the object is equal
which of the following diagrams represents the equipotential curves in the region between a positive point charge and a negatively charged metal plate?
These lines, which are also known as electric field lines, point in the direction that a positive test charge would accelerate if it were placed along the line.
Is there a positive to negative transition in the electric field lines?The direction of an electric field line is always away from a positive charge and in the direction of a negative charge. In actuality, positive and negative charges are where electric fields begin and end.These lines, which are also known as electric field lines, point in the direction that a positive test charge would accelerate if it were placed along the line. As a result, the lines are pointed in the opposite direction of positively charged source charges—that is, toward negatively charged source charges.These lines, which are also known as electric field lines, point in the direction that a positive test charge would accelerate if it were placed along the line.To learn more about electric field refer to:
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A helium balloon has a volume of 2.00 L at 101 kPa. As the balloon rises the pressure drops to 97.0 kPa. What is the new volume?
Answer:
The volume of a gas is inversely proportional to the pressure at constant temperature, according to Boyle's law. Mathematically, it can be expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
As the temperature is constant, we can use the following formula to calculate the new volume of the balloon:
V1 / P1 = V2 / P2
where V1 = 2.00 L, P1 = 101 kPa, P2 = 97.0 kPa.
V2 = (V1 * P2) / P1
V2 = (2.00 L * 97.0 kPa) / 101 kPa = 1.9608 L
So, the new volume of the helium balloon is 1.9608 L.
two hypothetical metals are created with different elements that have the same atomic mass (g/mole) and the same atomic radius. metal a has a density of 9.50 g / cm 3 and metal b has a density of 8.73 g / cm 3 . if one of these metals has a bcc lattice structure and the other has an fcc lattice structure, identify the structure that corresponds to each of one of them. justify your answer.
Metal A has a more density(9.50 g/cm³) for the same atomic mass, so it is more likely to have an FCC lattice structure, whereas metal B has a comparatively less density(8.73 g/cm³), so it is more likely to have BCC lattice structure.
A body-centered cubic (bcc) lattice structure has 8 atoms at the corners of a cube and one atom in the center of the cube. This structure has a lower density compared to face-centered cubic (fcc) lattice structure, which has atoms at the corners and the centers of each face of a cube.
According to the given densities, metal A with a density of 9.50 g/cm³ is likely to have an FCC lattice structure, while metal B with a density of 8.73 g/cm³ is likely to have a BCC lattice structure. This is because the FCC structure has a higher density due to the more close-packed arrangement of atoms compared to the bcc structure.
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a black mamba snake has a length of 2.60 m and a top speed of 4.50 m/s. suppose a mongoose and a black mamba find themselves nose to nose. in an effort to escape, the snake accelerates past the mongoose at 8.37 m/s2 from rest.
The snake takes 0.53 seconds to reach its top speed.
Speed is defined as: The rate of change of the object's position in any direction. Speed is measured as the ratio of distance traveled and time traveled. In physics, an equation of motion is an equation that describes the behavior of a physical system related to motion as a function of time..
We know the snake's initial speed (zero) and its final speed (4.50 m/s). Also, its acceleration is 8.37 m/s2
The relevant equation is:
v = v0 + at
4.50 = 0 + 8.37t
0.53 s = t
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positive charge is distributed uniformly on a plastic rod bent to form a quarter-circular arc (figure 1). figure1 of 1 a positively charged rod is bent so that it forms a concave rightward arc symmetrical about a horizontal dashed line going through the center of the rod. the center of curvature of the bent rod is marked with a black dot. part a what is the direction of the electric field at the center of the circle?
Radial direction of the electric field at the center of the circle.
What are Electric field?Take into consideration the little equivalent arc elements on either side of the horizontal first. Now determine the electric field they caused, how to fix it, and how to eliminate the ones that were directed in the other direction. Now, swap out the common expression for the electric field caused by charge density, integrate over the arc's length, and you'll get the necessary electric field.
The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them, is known as an electric field (also known as an E-field.
It can also refer to a system of charged particles' physical field. Electric charges and time-varying electric currents are the building blocks of electric fields.
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Which statements about rainbows are true? Choose more than one answer.
The true options about a rainbow are, sunlight slows down as it enters water droplets in the sky. Rainbows are a type of interference pattern. Refracted Sunlight makes the arc in the rainbow.
Are rainbows caused by refraction or diffraction?The result of light striking water droplets is a multicolored arc. A rainbow is a meteorological phenomenon that appears in the sky as a spectrum of light due to light reflection, refraction, and dispersion in water droplets. It appears as a circular arc with various colors. The part of the sky right across from the Sun is where rainbows brought on by sunlight always occur.
When light encounters a water droplet, it is bent at the air-water interface and penetrates the droplet, where it is divided into seven hues. The light then reflects inside the droplet before being refracted out into the atmosphere once more, creating a rainbow appearance.
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If a laborer weighing 895N and carrying bricks weighing 575N to scaffold up a ladder 3.1 m above the ground how much work has he done? If he climbed the ladder in 12.0 seconds what was his power output?show your work
If he climbed the ladder in 12.0 seconds, the laborer's power output is 394.875 watts.
What is work?Work is the product of force and distance and is measured in Joules (J). In physics, work is the energy transferred to or from object via application of force along a displacement.
As, work = force x distance x cos(theta)
So, the work done by the laborer would be:
work = (895 N + 575 N) x 3.1 m x 1 = 4738.5 J
As, power = work / time
where time is measured in seconds.
power = 4738.5 J / 12.0 s = 394.875 W
So, the laborer's power output is 394.875 watts.
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figure q21.7 shows some of the electric field lines due to three point charges arranged along the vertical axis. all three charges have the same magni- tude. (a) what are the signs of the three charges? explain your reasoning. (b) at what point(s) is the magnitude of the elec- tric field the smallest? explain your rea- soning. explain how the fields produced by each individual point charge combine to give a small net field at this point or points.
The charges q1 and q3 are positive while charge q2 is negative.
The fundamental quantity in electrostatics is electric charge. There are two kinds of charge, positive and negative. Charges of the same sign repel each other; charges of opposite sign attract. Charge is conserved; the total charge in an isolated system is constant.Electric field is a vector quantity, is the force per unit charge exerted on a test charge at any point. The electric field produced by a point charge is directed radially away from or toward the charge.Field lines provide a graphical representation of electric fields. At any point on afield line, the tangent to the line is in the direction of E and at that point. The number of lines per unit area (perpendicular to their direction) is proportional to the magnitude of E and at the point.Electric field lines go away from charge q1 and q3, therefore these charges are positive.
Field line come towards the charge q 2, therefore this charge is negative.
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1. How much force is required to
accelerate a 795 kg car by 15 m/s2?
Answer: 11925 N
Explanation: It's a very simple question.
According to Newton's 2nd law,
The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
F=ma
where m = mass of an object
a= acceleration
F = 795*15
=11925 N
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If a laborer weighing 895N and carrying bricks weighing 575N to scaffold up a ladder 3.1 m above the ground how much work has he done?
Answer:
Explanation:
W=Fd
a brick 20cm long 10cm wide and 2cm thick has a mass of 5kg . determine the . Maximum pressure that can be exerted by the brick on a flat surface
Hence the maximum pressure exerted by the brick is 2450 dyne/cm²
Given the mass of the brick=5kg
Dimension of the brick=20cm*10cm*2cm.
So weight of the brick= F= mg
Where f= force on the body due to gravity
where m= mass, g= gravity.
So F= 5000*9.8
by doing the multiplication we get the result as
F= 49000 dyne where dyne is unit of force
Where surface area is 10cm*2cm is in contact with the ground then
Area= (10*2)= 20cm²
Applying pressure formula = F/Area= 49000/20
By dividing we get the answer as= 2450 dyne/cm²
When surface area is 20cm*2cm is in contact then
Area= 20cm*2cm= 40cm²
Applying pressure formula = F/Area= 49000/40 dyne/cm²= 1225 dyne/cm²
When the surface area is 20cm*10cm in contact then
Area= 20cm*10cm= 200cm²
By applying the pressure formula= F/Area= 49000/200=245 dyne/cm²
Hence the maximum pressure exerted by the brick is 2450 dyne/cm²
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a wire loop is in a uniform magnetic field. current flows in the wire loop, as shown. what does the loop do?
The ring has a magnetic field travelling across it because of current I. The magnetic field as the paper goes through the ring is perpendicular to the internal plane, according to the right-hand thumb rule.
In proportion to a drop in the current I flowing from B to A, the magnetic field across the ring and magnetic flux both decrease. According to Lenz's law, the magnetic flux fluctuation is opposed by the current that is induced in the rings. This shows that the magnetic field produced by the induced current and the current I both point in the same general direction. The induced current in the ring is therefore flowing clockwise.
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what two quantities could be graphed to yield a straight line whose slope could be used to calculate a numerical value for the mass of the cart?
Railway tracks or the freeway quantities could be graphed to yield a straight line whose slope could be used to calculate a numerical value for the mass of the cart.
What is Slope ?A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula. According to linguists, the Middle English adverb aslope, which meaning "at an angle," is where the term slope is said to have originated. You can use the word's noun form to describe things that are sloped or at an angle, such as a steep hill or a ramp.
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A hockey player is standing on his skates on a frozen pond when an opposing player, moving with a uniform speed of 4.0 m/s, skates by with the puck. After 2.80 s, the first player makes up his mind to chase his opponent. If he accelerates uniformly at 0.46 m/s2, determine each of the following.
(a) How long does it take him to catch his opponent? (Assume the player with the puck remains in motion at constant speed.)
1 s
(b) How far has he traveled in that time?
2 m
The time it takes the hockey player to catch his opponent is 8.2s and he has he traveled 130m in that time.
A defenseman's main goal is to keep the team with the puck from scoring into their net. Therefore, the defensemen will frequently step up and stop the puck-bearing team from moving it into their defensive zone when they are skating through the neutral zone. The dump and chase tactic is used in this situation.
a) The given data is:
v = 4 m/s
t = 2.8 s
d=?
Use the formula:
v = d/t....(i)
Put the value of given data in equation (i)
d = v × t
d = 4 m/s × 2.8 s
d = 130 m
Thus, distance will be 8.2 s
Ice hockey skates are typically used for leisure ice skating by themselves, but they can also be used for the sports of ice hockey and ringette. The components of each individual skate are the boot, laces, blade, and blade holder.
b)
d = 8.2 s
t = 2.80 s
Use the formula:
v = d/t....(i)
Put the value of given data in equation (i)
d = v × t
d = 4 m/s × 8.2 s
d = 8.2 s
Thus, distance will be 8.2 s
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determine the moment of the couple formed by the two forces by resolving each force into horizontal and vertical components and adding the moments of the two resulting couples
The required moments of the resulting two couples is calculated to be 16.39 Nm.
Forces acting are two 60N forces
A and C are the corners of a 200-mm square plate
The equation for AC is given as(AC forms a hypotenuse, with two similar sides),
AC = √0.2²+0.2² = 0.2√2 m
sin75° = d/AC
d = 0.2√2 sin75° = 0.2732 m
m Fm = Fm × 0.2
m Fm = -30 V₃ 0.2
m Fm = -6 V₃
m Fv = -6 Nm
So, m = 16.39 Nm (clockwise)
Thus, the required moments of the resulting two couples is calculated to be 16.39 Nm.
The given question is incomplete. The complete question is 'Two parallel 60-N forces are applied as shown to the corners A and C of a 200-mm square plate.'
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