The formula that shows the relationship between the surface area (S) and volume (V) for spheres is S = 4πr² and V = (4/3)πr³ where r is the radius of the sphere.
This formula shows that the surface area of a sphere is directly proportional to the radius squared, and the volume is directly proportional to the radius cubed. This means that as the radius of a sphere increases, the surface area and volume will increase at a much faster rate. For example, a sphere with a radius of 2 will have four times the surface area and eight times the volume of a sphere with a radius of 1.
The question is incomplete, hence the answer is general.
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1. A force of 60 Newtons is applied to the end of a wrench 0. 12 m long. How much torque is produced?
Answer: The amount of Torque produced is 7.2 Nm.
Explanation:
Given:
Force applied (F) to the end of a wrench = 60 Newton
Length of wrench = 0.12 meter
To find:
Quantity of Torque produced
Solution:
The quantity of Torque produced can be calculated from the following formula:
Ƭ = r F sin(θ)
Where,
Ƭ = Torque, r = radius, F = Force, (θ) = angle between F and the lever arm
In the given question,
r = 0.12,
F= 60,
(θ)= 900 {Since the force is applied at the end of a wrench, it must be perpendicular}
Torque (Ƭ) = 0.12* 60 * sin 900
= 7.2 m {sin 900 = 1}
Hence, in the given situation, 7.2 Nm Torque will be produced.
3. The rougher the surface the ____________ the friction. (Greater or lesser) The _____________ the surface the lesser the friction produced. (Rougher or smoother) 4. Which would b
The rougher the surface the _Greater_ the friction. The _Smooth_ the surface the lesser the friction produced.
The rougher surface has Greater friction, as rough surfaces have more irregularities which lead to interlocking of the surface as a result it increases the friction between two surfaces.
Similarly, in the case of a Smooth surface, there are no irregularities so two surfaces could easily slit without any friction.
Friction is necessary for a number of places so that contact between two surfaces could be improved for walking we need friction and in so many places we try to reduce the friction so that we can save energy.
And we can reduce the friction by applying lubricates between the surfaces, and increase the friction we make the surface rougher.
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The half life of a radioactive substance is the time taken for the activity to halve. Use the graph to calculate the half life of the radioactive isotope.
Radioactive element which keeps on decaying over the time. Decay of radioactive element always comes under first order kinetics. Therefore the half life time of radioactive substance is 2seconds.
What is half life?Half life tells about the time at which the radioactive material decays to half of its initial concentration.
Mathematically,
half life time=0.693/ rate constant of the decay
The half life of a radioactive substance is the time taken for the activity to halve. Using the graph to calculate the half life of the radioactive isotope, we find that activity that is 3500 so, half of this activity is 17500 which is corresponding to time 2 seconds.
Therefore the half life time of radioactive substance is 2seconds.
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In a transformer, energy is carried from the primary coil to the secondary coil by
A. The magnetic field in the iron core
B. The electrical heating of the primary coil
C. Electricity conducted through the iron core
D. The difference in voltage between the primary and secondary coils.
In a transformer, energy is carried from the primary coil to the secondary coil by The magnetic field in the iron core.
What is transformer?
A Transformer is an electrical device used to increase or decrease the voltage provided to an electrical circuit. It is made up of two or more coils of wire wound around a common core. The coils are typically referred to as the primary and secondary winding. Electricity flowing in the primary winding creates a magnetic field, which in turn induces a voltage in the secondary winding. The ratio of primary to secondary winding determines the output voltage. Transformers are used extensively in the electricity distribution network, enabling the safe and efficient transmission of electricity over long distances.
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The heat of fusion of a substance is 42. 5 J/g. How much energy is released when 40 g of this substance at its freezing point completely changes into a solid? Show your work.
A. ) 1. 700
B. ) 1. 06
C. ) 42. 5
D. ) 0 J
The heat energy of the substance option (A) -1700J is correct.
We are given that,
Heat of fusion of a substance = ΔHf = 42.5J/g
Mass of the substance = m= 40g
The latent heat of fusion is the quantity of heat required to transform one gramme of a substance from a solid to a liquid. But in this case, it's important to figure out how much heat is released as liquid copper solidifies. So, ΔHf = -42.5 J/g
Thus , we have to calculated here the heat energy of the substance by the formula,
q = m·ΔHf
Where, q is heat energy ,m is mass ΔHf is the heat of fusion of a substance,
q = m·ΔHf
q = -42.5 J/g× 40g
q = -1700J
Therefore , the heat energy of the substance would be option (A) -1700J
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How electrostatic induction differ from charging by friction
Explanation:
Electrostatic is a force between two non-conductors
while
Friction oppose the relative motion between two surface or object.
true or false Visual inspection of the brake drum friction surface is not required, only measure drum diameter.
It is False that Visual inspection of the brake drum friction surface is not required, only measure drum diameter.
What serves as a brake drum?No matter whether the vehicle is moving forward or backward, drum brakes produce uniform braking force. Drum brakes produce the same amount of braking force in both directions, which explains this. This kind is typically utilized for the passenger car's rear brakes.
Unusual brake pedal sensation is one of the first indications when drum brakes are damaged or failing. Excessive brake drum wear might result in vibrations that can be felt in the pedal. When you press the pedal, any trembling or pulsating brought on by worn drums will be audible.
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It has been suggested that rotating cylinders about 10 mi long and 5.0 mi in diameter be placed in space and used as colonies. What
The proposed size of 10 miles long and 5 miles in diameter for such a colony is quite large and would require significant technological advancements in terms of materials, and construction to be feasible.
What causes lift from a rotating cylinder?In general, a spinning cylinder produces lift when its top and bottom are subjected to higher pressure and quicker velocities, respectively. The lifting force, it was said, is pointed perpendicular to the cylinder velocity.
How do you calculate angular speed using radius and linear velocity?If r is an object's radius, v is its linear speed and is its angular velocity in radians per unit of time, then v = r. This formula connects these three values so that we can always determine the third if we know the first two.
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The populations of the great apes in Africa are recovering and on the rise.
Please select the best answer from the choices provided
T
F
Answer:
False
Explanation
Poaching, habitat loss and diseases are contributing to the death of animals there, example: Gorilla
Answer:
false
Explanation:
Suppose two dinosaurs with masses of 80. 0 kg and 120. 0 kg sat on the middle and the far end, respectively, of a tree branch. The dinosaurs produced a net counterclockwise torque of 9,400N•m about the end of the branch that was attached to the tree. What was the length of the branch?
The dinosaurs produced a net counterclockwise torque of 9,400Nm about the end of the branch that was attached to the tree. The length of the branch is 4.7m.
τ = Σr × F = rmg
where g is the acceleration caused by gravity, m is the mass, and r is the distance.
Torque has a direct relationship with -
1.the object's mass, in m
2. The mass's separation, r, from the location where the torque is being calculated.
Therefore, the torque will change whether we increase or reduce them.
Therefore, increasing mass will result in an increase in torque, but since we must retain the same torque, we must reduce mass's distance from the location of the torque.
As a result, the mass should be moved closer to the location of the torque.
Total Mass = (80 + 120)kg
= 200kg
Torque = 9400N
τ = Σr × F = rmg
τ = 200 × r × 10
9400 = 200 × r × 10
r = 9400 / 2000
r = 4.7m
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A car goes into a skid and comes to a gradual stop, accelerating at a constant rate to do so. At the midpoint of the skid, how much of its kinetic energy has the car lost (as a percentage, give % as the units)?
The percentage of the lost kinetic energy of the car, at the midpoint of the skid, is 50%.
In physics, work is the measurement of the energy used to move objects. When you are walking, you're using energy to move your body so the work done would be greater than zero.
According to work-energy theorem, work is equal to force times displacement (W = F · x).
A type of energy is kinetic energy, which is the energy of a moving object. If an object is at rest, its kinetic energy is zero. Kinetic energy is equal to one half of a mass times velocity squared (KE = 0.5 · m · v²).
When a car goes into a skid and comes to a gradual stop, at the midpoint of the skid the car has spend 50% its kinetic energy. This is simply because the velocity of the car at the midpoint of the skid is half the velocity of the car when the car starts going into a skid, assuming constant acceleration.
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if 15.0 g of water vapour at 135°C cools to 100°C, condenses to liquid water, and then cools to 90°, how much energy is released to the environment?
The heat that is evolved by the environment is 36.42 kJ.
What is the heat that is involved?We know that heat is a form of energy that can be known for the fact that it could lead to a change in the temperature of the object. We have to note that the energy that is released is a sum total of all the process that are involved here.
We know that;
H = (15 * 4.18 * (135 - 100)) + (15 * 2240) + (15 * 4.18 * (100 - 90))
H = 2194.5 + 33600 + 627
H = 36.42 kJ
The total heat that has been evolved would now be 36.42 kJ.
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which effect proves more conclusively that an object is charged, attraction to or rep;usion from antoher object
According to Coulomb's Law the observation of repulsion between two objects provides more conclusive evidence that an object is charged, as opposed to attraction.
What is Coulomb's Law?
Coulomb's Law is a fundamental principle in physics that describes the interaction between electrically charged objects. It states that the force of attraction or repulsion between two charged objects is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Attraction or repulsion between two objects is one way to determine if an object is charged. The presence of an electric charge on an object can be determined by observing whether it experiences a force of attraction or repulsion when brought near another charged object.
Attraction or repulsion between two charged objects is a fundamental effect of electric charges. Opposite charges will experience a force of attraction towards each other, while like charges will experience a force of repulsion away from each other. This is known as Coulomb's Law.
Therefore, as per Coulomb's Law the observation of repulsion between two objects provides more conclusive evidence that an object is charged, as opposed to attraction.
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If an electric heater is rated at 15,000 W, and the voltage used is 240 V, what size breaker in amps would be required
The current required by the electric heater which has the power of 15,000 W is 62.5 A
The power of the heater = 15,000 W
The voltage used by the heater = 240 V
The current required by the electric heater can be found using the formula,
P = VI
where P is the power of the electric heater
V is the voltage used by the electric heater
I is the current required by the electric heater
Let us rearrange the above equation in order to get the current required by the heater is
I = P/V
Let us substitute the known values in the above equation, we get
I = 15,000 / 240
= 62.5 A
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The doctor lands his tardis on a planet whose radius is 1. 2x10^7m the acceleration due to gravity is 18m/s^2. What is the mass of the planet
The mass of planet is 3.886×10^25 kg. The radius of planet is 1. 2x10^7m.
What is a planet with half the mass's acceleration caused by gravity?Complete Resolution. If the acceleration caused by gravity on the surface of the earth is given by the formula g, then the acceleration caused by gravity on a planet with a mass half that of the earth and a radius equal to that of the earth is given by the formula g/2. Where G = 6.67 ×10^-11 N m2/kg2 (Newton's gravitational constant).
Is the explanation for the gravitational acceleration independent of mass?As a result, acceleration due to gravity (a) depends on the gravitational constant (G), the mass of the Earth (M), and the radius of the Earth (R), but not on the mass of the body (m).
Given:
Radius of planet (r) = 1. 2x10^7m
Acceleration due to gravity (g) = 18 m/s^2
The acceleration due to gravity at the surface of the planet is,
[tex]g=G\frac{M}{r^2}[/tex]
Where, G = Universal gravitational constant
[tex]G= 6.67*10^-11N.m^2/kg^2[/tex]
[tex]M=\frac{g*r^2}{G}[/tex]
[tex]M=\frac{18*(1.2*10^7)^2}{6.67*10^-11}[/tex]
M =3.886×10^25 kg
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What is the SI unit of momentum?
Answer:
kgm/s(-1)
Explanation:
the units of momentum will be the product of the units of mass and velocity. Mass is measured in kg and velocity in ms-1, therefore, the SI unit of momentum will be kgm/s(-1).
A 16-cm-long nichrome wire is connected across the terminals of a 1.5 V battery.
What is the electric field inside the wire?
What is the current density inside the wire?
If the current in the wire is 2.0 A , what is the wire's diameter?
The electric field inside the wire is equal to 1.5 V/16 cm, or 0.09375 V/cm.
What is battery?
Battery is a device that stores energy and is capable of providing a current of electricity when connected to an electrical device. It typically consists of one or more electrochemical cells, which convert stored chemical energy into electrical energy.
The current density inside the wire is equal to 2.0 A/16 cm, or 0.125 A/cm.
The wire's diameter can be calculated using the formula I = πρd2/4,
where I is the current in the wire,
ρ is the resistivity of nichrome,
and d is the diameter of the wire.
Plugging in the values given,
we get 2.0 = π(1.1×10-6 Ω•m)d2/4, or d2 = 8.18×10-5 m.
Taking the square root of both sides, we get d = 0.028 m, or 2.8 mm.
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Nan suitcase has a mass of 14 kg how much potential energy does it gain when she lifts it onto a bench that is 40 cm tall
The potential energy of Nan suitcase of mass 14 kg is 54.88 J.
What is Potential energy?Potential energy is the energy of a body due to its position in the gravitational field.
To calculate the potential energy, we use the formula below
Formula:
P.E = mgh............... Equation 1Where:
P.E = Potential energym = Massg = Acceleration due to gravityh = HeightFrom the question,
Given:
m = 14 kgg = 9.8 m/s²h 40 cm = 0.4 mSubstitute these values into equation 1
P.E = 14×9.8×0.4P.E = 54.88 JHence, the potential energy is 54.88 J.
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which of the two stationary charges q1=2 c and q2=10 c will create stronger magnetic field?
Because the charges at rest are unable to produce a magnetic field, neither of the two stationary charges will do so.
There is no magnetic field created when a charge is stationary since there is no motion inside the charge. Thus, nothing except an electric field is created.
Charges that are at rest can also feel the electric force. Charges in motion can experience magnetic force. Therefore, the electric field must not be zero and the magnetic field may or may not be zero if a charged particle at rest experiences an electromagnetic force.
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a potential difference of 12 volts causes 2.0 x 10^ 20 electrons to pass a point in a wire in 1 minute calculate
1) the amount of the charge that passes the point in 1 minute ,given that the charge of each electron is 1.6 x10^-19
coulomb
2)electric current in the wire
3)resistance of the wire
Answer:
Q = N e total charge passing point
Q = 2.0E20 * 1.6E-19 coul = 32 coulombs
2) I = Q / t = 32 C / 60 s = .53 amps
3) R = V / i = 12 volts / .53 amps = 23 ohms
The centers of two 15.0 kilogram spheres are separated by 3000 millimeters. The magnitude of the gravitational force between the spheres is approximately:
The gravitational force here between spheres has an estimated magnitude of 1.67 10-9 N.
What is the gravity force?Any two bodies' gravitational attraction is exactly equal to the sum of their masses and divided by the square of their distance from one another.
Gravity, often known as the gravity force will bring any two bodies together. Although everything in the cosmos is attracted to one another, this attraction is usually too weak to just be felt since the things are so far apart. Gravity's attraction lessens as things are moved farther apart, but its influence sphere is boundless.
F=GMm/r^2
G=6.67 x 10^-11N kg^2/m^2
M=(15kg)
m=15 kg
r=(3.0m)^2
putting values we have
(6.67 x 10^-11N kg^2/m^2)(15kg)(15kg)/(3.0m)^2
1.67 x 10^-9N
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The 6 kg block is then released and accelerates to the right, toward the 5 kg block. The surface is rough and the coefficient of friction between each block and the surface is 0.3 . The two blocks collide, stick together, and move to the right. Remember that the spring is not attached to the 6 kg block. Find the speed of the 6 kg block just before it collides with the 5 kg
Assuming a 6 kg block is coupled to a spring with a 350 N/m spring constant, and that there is 0.5 m between the two blocks.
Solution:Use the formula
U=1/2kx2
U=1/23500.52
U=43.75 J
Utilizing the law of conservation of energy, KE = U - f.d, where f is the frictional force acting on
1/2 mv2 = 43.75 - mgd
1/2 ×6×v²= 43.75-0.3×6×9.8×0.5\s
v= √11.643
The spring constant is k, what is it?The "spring constant," denoted by the letter "k," is a figure that effectively indicates how "stiff" a spring is. A significant value of k indicates that more power is needed to extend it a given distance than would be necessary to stretch a less stiff spring the same distance.
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A car moves at 45 kilometers per hour.
Which option describes if the given value is speed or velocity?
speed, because there is a mention of time speed, because there is a mention of time
velocity, because there is a mention of time velocity, because there is a mention of time
velocity, because there is no specific directionvelocity, because there is no specific direction
speed, because there is no specific direction
Since this car moves at 45 kilometers per hour, an option which describes if the given value is speed or velocity include the following: D. speed, because there is no specific direction.
What is speed?In Science, speed can be defined as the distance covered by a physical object per unit of time. This ultimately implies that, speed is a scalar quantity because it has magnitude but no direction.
What is velocity?In Science, velocity can be defined as the distance covered by an object per unit of time in a specific direction. This ultimately implies that, velocity is a vector quantity because it has both magnitude and direction.
In this context, we can reasonably infer and logically deduce that a car that moves at 45 kilometers per hour describes speed rather than velocity, because there is no specific direction mentioned.
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Since no direction is specified, the correct answer is the last option which is speed, because there is no specific direction
Difference Between Speed and VelocitySpeed is a scalar quantity. That is, it has only magnitude but no direction. While velocity is a vector quantity. That is, it has both magnitude and direction.
If a car moves at 45 kilometers per hour, only the car magnitude is given but no direction.
The option that describes if the given value is speed or velocity is speed, because there is no specific direction
Therefore, the correct option is speed, because there is no specific direction.
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What are the main mechanisms that affect the gene pool?
Answer: Natural selection, Genetic drift , Mutations and Gene flow
Explanation:
Describe what you could do to make the magnetic disk rotate faster
You could do to make the magnetic disk rotate faster: regular usage of a disc defragmentation program.
What is magnetic disk?A magnetic disk is a storage device that writes, rewrites, and accesses data using the magnetization process. It has a magnetic layer that retains data as tracks, spots, and sectors.
You could do to make the magnetic disk rotate faster:
Plan regular usage of a disc defragmentation program.Try to keep at least 20% of your disc space free, if you can. Defragmentation is facilitated and fragmentation is reduced as a result. Utilize a program like Crystal DiskInfo to regularly check the condition of your drive.Learn more about magnetic disk here:
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a force of 15 N is used to push a box along the floor a distance of 3 meters. find the amount of work done
Answer:
The amount of work done is 45 J.
Explanation:
We know that the force applied is 15N. The amount of displacement experienced by the box is 3 metres along the floor.
Thus, F= 15N
D= 3 metres
The formula for calculating work done is W= F×D
Thus, W=15×3
W=45J
Thus, the amount of work done is 45J.
What is the function of the countercurrent system of flow?
In the renal medulla, a countercurrent mechanism keeps things in balance. The solution flows concurrently in the same direction. The solution flows in the opposite direction of the countercurrent flow.
Cross-current flow here, the liquids move in the opposing directions through the two tubes. One end of a tube in a single tube starts to flow a solution with a concentration of 0%, while the other end in the same tube starts to flow a solution with a concentration of 100%.
The kidneys have two countercurrent processes. They are the vasa recta and the Henle loop. The nephron's Henle's loop is a U-shaped structure. The two limbs of the vessel's two blood streams move in the opposing directions, creating countercurrents.
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The Cessna Cardinal, a single-engine light plane, has a wing with an area of 16. 2 m^2, and an aspect ratio of 7. 31. Assume the span efficiency factor is 0. 62. A. If the airplane is flying at standard sea-level conditions with velocity of 251 km/h, what is the induced drag when the total weight is 9800N b. Calculate the induced drag when the
The Cessna Cardinal, a single-engine light plane, has a wing area of 16.2 m² and an aspect ratio of 7.31 with span efficiency factor of 0.62 then the induced drag when the total weight is 9800 N is 18.8 N.
Given that,
Wing area (A) = 16.2m²
Aspect ratio (r) = 7.31
Efficiency factor (e) = 0.62
Weight of plane (W) = 9800 N
Velocity of airplane (v) = 251 km/h = 251× 5/18 = 69.72 m/s
We know,
Dynamic pressure (p) = 1/2ρv²
where ρ is density of plane = 1.225
p = 1/2 × 1.225 × 69.72 × 69.72 = 2977.29 pa
Lift coefficient Cl = W/p × A = W/(1/2ρv²) A
where, A is the area of wing
Cl = 9800/2977.29 × 16.2 = 0.203
Induced drag coefficient (Cd) = Cl²/πer² = (0.203 × 0.203)/(π × 0.62 × 7.31 × 7.31) = 0.041/(104.08) = 0.39×10⁻³
Induced drag (d) = p × A × Cd = 2977.29 × 16.2 × 0.39 × 10⁻³ = 18.8 N.
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An athlete runs 140 m across a level field at an angle of 45.0° north of east. What is the north component of this displacement?
Displacement is a vector quantity thus, having different directional component. The component of the given displacement to the north is 98.99 m.
What is displacement ?The displacement is the measure of how long and in which direction an object is moved from the starting position. Displacement is a vector quantity thus, characterized by a magnitude and direction.
In physics, displacement is the product of velocity and time. The vertical component of the displacement = d sin θ
horizontal component = d cos θ.
The component to the north for a displacement of 140m with the angle of 45° is = 140 × sin 45 = 98.99 m.
Therefore, the north component of the displacement is about 99 m.
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Is there ever a case where one of the two charges in Coulomb's Law experiences a different force magnitude than the other charge? Why or why not?
Answer:
Yes, there is a case where one of the two charges in Coulomb's Law experiences a different force magnitude than the other charge. Coulomb's Law states that the electric force between two charged particles is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. If the magnitudes of the charges or the distance between them changes, the force experienced by one of the charges will also change. For example, if one of the charges is doubled in magnitude while the other charge and the distance between them remain the same, the force experienced by the charge with the increased magnitude will also double.