The solid sphere goes the least distance up its incline.
How do you define the moment of inertia of a body?
In physics, the term "moment of inertia" refers to the quantitative measurement of a body's inertia with respect to rotation, or the resistance that a body shows when a torque is applied to change its speed of rotation around an axis (turning force). The axis may or may not be fixed, and it may or may not be internal or external.The formula for moment of inertia is =I = L/ω
I = inertia
L = angular momentim
ω = angular velocity
In the question it is given that a solid sphere, solid cylinder, a spherical shell and a hoop all having the same mass(m) , radius(r) and linear center of mass speed(v) roll up identical inclines
Since all the bodies have same mass, radius and linear speed as such according to conservation of energy for every object,
Rotational Energy + Kinetic Energy = Potential Energy
Iω^2/2 + mv^2/2 = mgh
where, the symbols represent-
I = moment of inertia
ω = angular speed
v= linear speed
m = mass
h = height
We know the
I for solid sphere = 2mr^2/5
I for solid cylinder = mr^2/2
I for spherical shell = 2mr^2/3
I for hoop = mr^2/2
As per the given informations kinetic energy of all bodies is same therefore, on the value of I or the moment of inertia depends which body will cover the highest or least distance up its incline
I for solid sphere is minimum among all the given bodies and thus it will attain the least distance.
Hence, the solid sphere goes the least distance up its incline.
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Why is gas production not recognized as nitrate reduction when the organism is a known fermenter.
There are other gases produced during fermentation such as carbon dioxide. There are other possible gases produced by the organism during fermentation.
There are different gases produced during fermentation such as carbon dioxide. Certainly the gasoline produced can not be considered from nitrate reduction. Seeing that, there are different viable gases produced via the organism at some stage in fermentation.
Fermentation is a metabolic method that produces chemical modifications in natural substrates via the motion of enzymes. In biochemistry, it's far narrowly defined as the extraction of strength from carbohydrates inside the absence of oxygen.
This is a -step method, the first step is the formation of ethyl alcohol from sugar anaerobically using yeast. Inside the second step, ethyl alcohol is similarly oxidized to shape acetic acid the use of acetobacter micro organism. Microbial oxidation of alcohol to acid is an aerobic manner.
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A block weighing 7.6 N requires a force of
3.1 N to push it along at constant velocity.
What is the coefficient of friction for the
surface?
The coefficeint of friction given that the object weighing 7.6 N requires a force of 3.1 N to push it along at constant velocity, is 0.41
How do I determine the coefficient of friction?We know already that coefficient of friction is related to frictional force and normal reaction according to the following formula:
Frictional force (N) = coefficient of friction (μ) × normal reaction (N)
F = μN
Using the above formula, we can obtain the coefficient of friction as illustrated below:
Weight of object = 7.6 NForce (F) = 3.1 NNormal reaction (N) = Weight of object = 7.6 NCoefficient of friction (μ) =?Frictional force (N) = coefficient of friction (μ) × normal reaction (N)
F = μN
3.1 = μ × 7.6
Divide both sides by 7.6
μ = 3.1 / 7.6
μ = 0.41
Thus, we can conclude that the coefficient of friction is 0.41
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if a beetle is travelling at a speed of 2 cm/sec how far will it go in 1 minute
Answer: 120cm
Explanation: It will go 120cm because theres 60 sec in one minute and each second the beetle is travelling 2cm.
A bar magnet with its north pole pointing downward is falling toward the center of a horizontal conducting ring. As viewed from above, is the direction of the induced current in the ring counterclockwise
explain why please
The magnet is moving down with the north pole downward, and during the transition, there will be an increase in magnetic flux through the ring, which will produce the induced current through the ring.
When the bar is moved toward loop the flux will increase and the induced current will counter this flux.
The induced current tries to oppose the change in magnetic flux and this is possible just if the current direction is counterclockwise.
Result: The current direction is counterclockwise
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(a) determine the ratio of the momentum immediately after the collision to the momentum immediately before the collision.
We know duat Momentum is conserved during Collision
P(i) = P(t) - part (a)
Part(b) Momentum = P
K(i) = 1/2 m₁ v₁ (1)²
K = p²/2m
K(1) = p2/2x mi
Solve for Vf.
m₁ x v₁ (i) = (m₁ +m₂) Vf.
V+ M₁ x V₁ (1)/(m₁ +m2)
Kf = p2 / (2x (m, +m₂))/p2(2xm,)) P2
= m₁ /m1+m2 = K.E Ratio
When two objects collide their total momentum before the collision is equal to their total momentum after the collision. This is the law of conservation of momentum. where M is the mass of the pendulum, m is the mass of the sphere, and v is the velocity of the center of mass of the composite system after the collision. According to the law of conservation of momentum, the sum of the momentum of the two bodies before the collision equals the sum of the momentum after the collision.
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a block is attached to an oscillating spring. the expression below shows its position (cm) vs. time (s). what is the frequency of oscillation?
A 20 rad/s angular frequency is used. An object's rotation or oscillation with regard to time is measured by its angular frequency, a scalar physical quantity. Usually, it is indicated by the Greek letters or.
The SI unit of radians per second, or rpm, is used to measure it (revolutions per minute). It deviates by a factor of two from frequency.
A block is fastened to a spring that oscillates. The function that plots its position (in cm) against time (in s) is as follows:
x= 1.5 cos (20 t) (20 t)
x=A cos w t is the formula for the oscillating particle's general equation.
w= 20 rad/sec is obtained by comparing equations (1) and (2).
Therefore, the oscillation's angular frequency is 20 rad/s.
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A guitar string vibrates at a frequency of 440 Hz. A point at its center moves in SHM with an amplitude of 3.0 mm and a phase angle of zero. (a) Write an equation for the position of the center of the string as a function of time. (b) What are the maximum values of the magnitudes of the velocity and acceleration of the center of the string? (c) The derivative of the acceleration with respect to time is a quantity called the jek. Write an equation for the jek of the center of the string as a function of time, and find the maximum value of the magnitude of the jek.
The equation of the position of string from the center is 3.0 sin(2π × 440t), the maximum values of acceleration, velocity and jek are 1.29 × 10⁴ m/s², 8.26 m/s and 1.29 × 10⁴ m/s³.
(a) The following equation describes the position of the string's center as a function of time,
y(t) = A sin(2πft), where A is the amplitude (3.0 mm), f is the frequency (440 Hz), and t is time. Substituting the given values, we get,
y(t) = 3.0 sin(2π × 440t)
(b) The maximum value of the magnitude of the velocity of the center of the string occurs when the displacement is maximum, i.e., at t = 0. Therefore,
vmax = 2πfA
vmax = 2π × 440 × 3.0 × 10⁻³
vmax = 8.26 m/s
For acceleration,
amax = 4π²f²A
amax = 4π² × 440² × 3.0 × 10⁻³
amax = 1.29 × 10⁴ m/s²
(c) The jek of the center of the string as a function of time is given by:
j(t) = Aω²cos(2πft) where ω is the angular frequency, given by ω = 2πf.
The maximum value of the magnitude of the jek occurs when the displacement is zero, i.e., at t = T/4, where T is the period of the string. Substituting the given values, we get,
jmax = Aω²
jmax = 4π²f²A
jmax = 1.29 × 10⁴ m/s³.
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if an oncoming vehicle has started to turn left in front of you: choose one a. honk your horn to warn the driver and maintain your speed. b. maintain your speed and take your right-of-way c. slow or stop your car to prevent a collision
Option B is correct. Except where a sign expressly states that you may not turn left at a red light, we are permitted to do so.
Give way to oncoming traffic, including pedestrians, when making a turn. When the signal is switching from green to red, the amber light allows time for vehicles to clear the road. Make sure there is enough space for approaching cars to pass. Look both ways for oncoming traffic or pedestrians before making any turns. You should turn from the lane that is closest to the direction you want to go and into the lane that is closest to the one you came from if there are no signs or lane markings to control turning.
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What is brewster’s angle for light traveling in water that is reflected from crown glass?.
The correct answer to Brewster’s angle is 48.8 degrees.
What is Brewsters's law?
The Brewster's angle is the angle of incidence at which polarised light travels perfectly through a clear dielectric surface without being refracted. The light that is reflected from the surface when unpolarized light is incident at this angle is therefore perfectly polarised.
This equation's name is Brewster's law, and the angle it specifies is Brewster's angle. For a glass medium in air, Brewster's angle for visible light is around 56° (n2 = 1.5), while it is roughly 53° for an air-water interface (n2 = 1.33)
Brewster's Angle is defined as the inverse tan of n 2 over n 1. The inverse tan of 1.52 divided by 1.33 is thus 48.8 degrees.
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A paint brush is dropped from the top of a tall ladder and free falls to the ground. What changes, if any, would be observed of the velocity of the brush as it falls?.
When the paint brush is dropped from the top the acceleration increases.
Gravity is a force that pulls objects down toward the ground. When objects fall to the ground, gravity causes them to accelerate.
An object in free fall experiences an acceleration of -9.8 m/s². Whether explicitly stated or not, the value of the acceleration in the kinematic equations is -9.8 m/s² for any freely falling object.
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a ball is shot at an angle of 45 degrees into the air with initial velocity of 45 ft/sec. assuming no air resistance, how high does it go? how far away does it land? hint: the acceleration due to gravity is 32 ft per second squared.
Answer:
Explanation: GIVEN :
∅ = 45°
INITIAL VELOCITY (V·) = 45 FT/SEC
ACC DUE TO GRAVITY = 32 FT/SEC²
REQUIRED :
MAXIMUM HEIGHT (HMAX) = ? OR how high does it go 2.MAXIMUM RANGE (RMAX) = ? OR how far away does it land?BY APPLYING FORMULA OF MAXIMUM HEIGHT OF PROJECTILE
HMAX = V·²SIN²∅/2G
HMAX = 45²SIN45²/2X32
HMAX = 1012.5/64
HMAX = 15.82FT
FOR MAX RANGE
BY APPLYING FORMULA OF MAX RANGE
R = V·²SIN2∅/G
R = 45²SIN2X45/32
R = 2025 X 1/32
R = 63.28FT
Sand falls from a conveyor belt at a rate of onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the height and the radius changing when the pile is m high?.
The radius changing when the pile is 0.031 m^3/min high
What is a conical pile?
Bulk material that has been discharged from the end of a static conveyor falls freely, forming conical stockpiles. The descent of material through the gusty air produces blinding plumes of dust in open-air conical stacks. Geometrical domes assist your plant to achieve its environmental objectives by obstructing the wind and containing this dust.
h=3d/8 = 3r/4
dh/dt = 3/4dr/dt
dV/dt = 11 m^3/min
V=1/3pi*r^2*h
dV/dt = pi/3 [2rhdr/dt + r^2 dh/dt]
In an instant, h is given
h=8m
r=32/3 m
dV/dt = pi/3 [2rhdr/dt + r^2 dh/dt]
11 = pi/3 [2*32/3*8dr/dt + 32*32/9* 3/4 dr/dt]
dr/dt = 0.041 m^3/min
dh/dt = 0.031 m^3/min
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what best describes the part of the graph where the classical kbos are found? eccentric (out-of-round) orbits that stay farthest from the sun eccentric (out-of-round) orbits that get closest to the sun nearly circular orbits that stay farthest from the sun nearly circular orbits that get closest to the sun
The statement that best describes the part of the graph where the classical (Kuiper Belt Objects)kbos are found is "nearly circular orbits that stay farthest from the sun".
What are Kuiper Belt Objects?
The Kuiper belt object is described as a circumstellar disc in the outer Solar System, extending from the orbit of Neptune at 30 astronomical units (AU) to approximately 50 AU from the Sun.
The Kuiper belt object like the asteroid belt, consists mainly of small bodies or remnants from when the Solar System formed. While many asteroids are composed primarily of rock and metal, most Kuiper belt objects are composed largely of frozen volatiles (termed "ices"), such as
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consider the jet engine and mount indicated in fig.3 and model it as a mass on the end of a beam. the mass of the engine is usually fixed. find an expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement that the engine is allowed to vibrate.
The expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement is k = 1 / m ( m[tex]_{b}[/tex] v / I x I )²
m x ( t ) + k x ( t ) = F δ ( t )
I x I = F / m ω[tex]_{n}[/tex]
m = Mass of engine
k = Stiffness of transverse mount
F = Magnitude of impulse
ω[tex]_{n}[/tex] = Natural frequency
ω[tex]_{n}[/tex] = √ k / m
I x I = F / m ( √ k / m )
I x I = F / √ k m → ( 1 )
For bird,
F = m[tex]_{b}[/tex] v
Substitute this momentum value in ( 1 ),
I x I = m[tex]_{b}[/tex] v / √ k m
√ k = m[tex]_{b}[/tex] v / I x I √ m
k = 1 / m ( m[tex]_{b}[/tex] v / I x I )²
Therefore, the expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement that the engine is allowed to vibrate is k = 1 / m ( m[tex]_{b}[/tex] v / I x I )²
The question is incomplete. The complete question is :
Consider the jet engine and mount indicated in fig.3 and model it as a mass on the end of a beam. the mass of the engine is usually fixed. find an expression for the value of the transverse mount stiffness, k, as a function of the relative speed of the bird, v, the bird mass, the mass of the engine and the maximum displacement that the engine is allowed to vibrate. Fig 3. is shown in the image attached below.
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Where do rock formations go when they are subducted?
Group of answer choices below
A. Above the surface
B. Into the ocean
C. Into the mantle
D. To the core
Rock formations go Into the mantle when they are subducted.
What is Subducted rock?Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, the heavier plate dives beneath the second plate and sinks into the mantle.
Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries.
Rock formations go Into the mantle when they are subducted.
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what best describes SONAR waves
Answer:Sonar, short for Sound Navigation and Ranging, is helpful for exploring and mapping the ocean because sound waves travel farther in the water than do radar and light waves.
a weightlifter lifts a set of weights a vertical distance of 2.00 m. if a constant net force of 350 n is exerted on the weights, what is the net work done on the weights?
The net work done on the weights is 700 joules.
What is net force?
The total of all forces acting on the object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the term "net force" is used. The total of all forces acting on an object is known as the net force. A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion. When there are a lot of forces acting on a system, the term "net force" is used. When a force is applied to a body, numerous additional forces, such as gravitational force Fg, frictional force Ff, and the normal force, also work to balance the applied force.
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at a particular instant a proton is traveling in the x direction, with speed 5105 m/s. at the location of the proton there is a magnetic field of magnitude 0.33 t in the y direction, due to current running in a nearby coil.what is the directio
The proton would move in x direction with a force of 2.64 x 10 power minus 4
Force = q ( v x b)
q = 1.6 x 10 -19 C
v = 5 x 10 power 5
b = 0.33 t
F = 1.6 x 10 -19 x 5 x 10 power 15 x 0.33
F =2.64 x 10 power minus 4
What is a magnetic field?
The magnetic field can be defined as an area around a magnet which exerts magnetic force and is caused by moving electric charge. Field lines are a visual tool used to represent magnetic fields.
Properties of Magnetic field are;
Magnetic field lines never intersect each other.It takes the least resistant path between the opposite magnetic poles. Path of magnetic lines of force of a bar magnet is closed loops from one pole to the other.The length of magnetic field lines will be the same.Hence in the given question proton would move in x direction with a force of 2.64 x 10 power minus 4
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why can the sunlight that illuminates the earth be approximated by plane waves, whereas the light from a nearby lamp cannot?
The wavefront is parallel to the motion's direction. The spherical wavefront still maintains its shape with a "nearby" lamp, therefore we cannot ignore the wavefront's shape.
In contrast to the shorter waves of blue light, the rings would be more widely separated for the longer wavelength red light. Since the wavefront from the Sun is coming from a point source, it is actually spherical. However, because of how tiny the Earth is in relation to the Sun and how far away the Sun is from the Earth. Since the pattern is made up of parallel straight-line-shaped fringes rather than the fringes of overlapping circles, Young's interference experiment with slits results in a crisper fringe pattern than with pinholes.
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what is the most common injury related to electrical hazards?
The most common injury related to electrical hazards are Electrical burns.
What are electrical hazards?
The term "electrical hazard" refers to a major workplace risk that puts employees in danger of suffering burns, electrocution, shock, arc flash or arc blast, fire, or explosions.Electrical shock and burns are risks when contacting energized sources.The body enters the electric circuit, resulting in an electrical shock (when an individual comes in contact with both wires of an electrical circuit, one wire of an energized circuit and the ground, or a metallic part has been energized by contact with an electrical conductor).An electrical burn is a type of skin burn that develops when your body comes into contact with electricity. It is possible for electricity to pass through your body when it comes into contact with it. When this occurs, the voltage has the potential to harm tissues and organs.
Hence, The most common injury related to electrical hazards are Electrical burns.
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the two charges are brought together until they touch for enough time for the charge to equalize between the two spheres. the charges are then returned to their original places. what is the repulsive force on each charge with their new charges?
Coulomb force, also known as electrostatic force or Coulomb interaction, is the electric charge of a particle or object's ability to attract or repel other particles or things.
What exactly is a Coulomb force?The force of force of attraction between two like it or unlike charges is known as the Coulombic force or an electrostatic force. The two charges are spaced apart and have opposite charges with equal magnitude.
What example of coulomb's law is there?Comb and paper scraps When a comb is scraped against hair, charges are transferred to the teeth of the comb. Paper scraps with opposite charges or those with neutral charges are drawn to the charged comb. Coulomb's law is well shown by the electrical interaction between both the paper fragments and the comb.
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a radio can be tuned into a particular station frequency by adjusting the capacitance in an l-c circuit. suppose that the minimum capacitance of a variable capacitor in a radio is 4.14 pfpf . part a what is the inductance lll of a coil connected to this capacitor if the oscillation frequency of the l-c circuit is 1.67 mhzmhz , corresponding to one end of the am radio broadcast band, when the capacitor is set to its minimum capacitance? express your answer in henrys to three significant figures.
1.08* is the inductance L of a coil connected to this capacitor if the oscillation frequency of the l-c circuit is 1.67 mhz.
What is a Capacitor?A capacitor is a device that uses the accumulation of electric charges on two nearby surfaces that are electrically isolated from one another to store electrical energy in an electric field. It has two terminals and is a passive electrical component. Capacitance refers to a capacitor's effect.
What is a I-c circuit?An L-C circuit is a type of electric circuit that consists of a capacitor and an inductor coupled together. It is also known as a tuned circuit, tank circuit, or resonant circuit.
The inductance is found from the resonant frequency formula :
ω2= (2πf)2 =1/LC=L=1/(2πf)2C
So, L=1/(2π1.67*106hz)(4.14*10-12F)
L=1.08*[tex]10^{-5}[/tex]
Hence, 1.08*[tex]10^{-5}[/tex] is the inductance L of a coil connected to this capacitor if the oscillation frequency of the l-c circuit is 1.67 mhz.
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moment of inertia is moment of inertia is the rotational equivalent of mass. the point at which all forces appear to act. the time at which inertia occurs. an alternative term for moment arm.
Moment of inertia is moment of inertia is the rotational equivalent of mass because the rotational equivalent of mass
The torque of a rigid body is governed by a property called the moment of inertia, also referred to as the mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia. In physics, the term "moment of inertia" refers to the quantitative measurement of a body's inertia with respect to rotation, or the resistance that a body shows when a torque is used to modify the rotational speed of an object around an axis. The axis may or may not be fixed, and it may or may not be internal or external. A property of matter known as inertia is the tendency for it to remain at rest or to move uniformly in a straight line without being affected by outside forces.
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13. What is the weight of a 2.5 kg watermelon?
Answer:
w=mg
Explanation:
w=2.5(10)
= 25N
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a rod-shaped magnet is suspended from its midpoint so that it is parallel to the ground and so that it can freely rotate. what will happen when two such magnets are placed in close proximity (but not close enough that they can touch)? will they align in a parallel or anti-parallel configuration?
Both rod-shaped magnets will align in a parallel configuration as similar poles and the magnetic field will repel each other.
What are Magnets?Anything that creates a magnetic field is considered to be a magnet. The most noteworthy characteristic of a magnet—a force that pulls on other ferromagnetic elements like iron, steel, nickel, cobalt, etc.—is caused by this invisible magnetic field, which also attracts or repels other magnets.
A piece of equipment built from a substance that has been magnetized and produces a consistent magnetic field is called a permanent magnet. A typical illustration is a fridge magnet used to keep notes on the door of the refrigerator. The term "ferromagnetic" refers to materials that can be magnetized and are also strongly attracted to a magnet. These comprise several naturally occurring minerals, some alloys of rare-earth metals, and the elements iron, nickel, and cobalt and their alloys.
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Which of the statements about the protonephridia of freshwater flatworms is accurate?
a. Muscular contractions drive fluid movement through the excretory tubules.
b. The fluid passing through the tubules is not modified before excretion.
c. Protonephridia are surrounded by a capillary network to allow for selective reabsorption and secretion.
d. The urine leaving the body of a freshwater flatworm is more concentrated than its body fluids.
e. Fluid from the body enters the protonephridia without first being filtered.
Using the theories of protonephridia, we got that the statements about the protonephridia of freshwater flatworms which is accurate is e)Fluid from the body enters the protonephridia without first being filtered.
The flame cell is a specialized excretory cell found in the simplest freshwater invertebrates, including flatworms, rotifers, and the nemerteans. Bundles of the flame cells are called Protonephridia. Protonephridia helps in the osmoregulation or ion-regulation. They are also helpful in the excretion.
Protonephridium is the network of dead-end tubules lacking internal openings found in the phyla Platyhelminthes, Nemertea
Hence, the the statements about the protonephridia of freshwater flatworms is accurate is option e) Fluid from the body enters the protonephridia without first being filtered.
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The gravitational field of the Moon is weaker than that of the Earth. It
pulls on each kilogram of mass with a force of 1.6N. What will be the
weight of a 50kg mass on the Moon? [4]
On the Moon, a 50 kg mass weighs 80 N.
What is moon?
The only natural satellite of Earth is the Moon. With a diameter that is roughly one-fourth that of the Earth, it is the fifth largest satellite inside the Solar System and the largest and also most massive when compared to its parent planet. According to the geophysical definitions of a term, the Moon qualifies as a satellite planet because it is a planetary-mass object with such a differentiated rocky body. There isn't much of an atmosphere, hydrosphere, as well as magnetic field there. With a surface gravity of 0.1654 g, it has a gravity that is roughly one-sixth that of Earth. Jupiter's moon Io is the only satellite inside the Solar System that is known to have a higher gravity and density. The main cause of Earth's tides, with an average orbital distance of 384,400 km (238,900 mi) or about 30 times the diameter of the planet, is the gravitational influence of the moon.
>Weight of 1 kilogram= 1.6 N
>Weight of 50 kilograms= 1.6 x 50
= 80
∴ On the Moon, a 50 kg mass weighs 80 N.
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During glucose catabolism, 686 kcal of energy are made available to do work. A minimum of 686 kcal are required for the anabolism of the same molecule. In practice, more energy is required. Why is this the case?.
More energy is needed because not all energy transduction processes are 100 percent effective. More cellular energy is needed since there are inefficiencies.
Mechanism of production of cellular energyCellular energy is mostly produced by the breakdown of carbohydrates, especially glucose. the total oxidative decomposition of glucose into CO2 and water
G°′= -686 kcal/mol is the amount of free energy produced by the process. Glucose is oxidized within cells in a sequence of stages associated with the creation of ATP to capture this free energy in usable form.
Almost all cells go through the process of glycolysis, which is the first step in the breakdown of glucose. Without oxygen, glycolysis takes place and can supply all of the anaerobic organisms' metabolic energy. Glycolysis, however, is only the first step in the degradation of glucose in aerobic cells.
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Describe what is occurring in the following image
this question has several parts that must be completed sequentially. if you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. tutorial exercise a boat leaves a dock at 6:00 pm and travels due south at a speed of 20 km/h. another boat has been heading due east at 15 km/h and reaches the same dock at 7:00 pm. how many minutes after 6:00 pm were the two boats closest together?
The boats were closest together for approximately ; 22 minutes
What is velocity?
Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, "5 meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.
Time After 6 pm = t
Speed of boat 1 travelling south wards after 6 pm ( t ) = 20 t
Speed of boat 2 traveling east after 6 pm = 15 t
Distance of Boat 2 from Dock = 15 - 15 t
Distance of Boat 1 = 20t
∴ The distance between the boats
= ( 15 - 15 t )² + ( 20t )² = D * 2 ----- ( 1 )
Differentiating equation ( 1 ) ( note : make dD/dt = 0 )
2( 15 - 15 t )* (-15) + 2 (20t)*(20)
make t subject of the expression
t = 9 /25
= 0.36 h ≈ 22 minutes
Hence we can conclude that The boats were closest together for approximately ; 22 minutes
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