The period of a pendulum with length l swinging with small oscillations is given by the formula T = 2π√(l/g), where g is the acceleration due to gravity (approximately 9.81 m/s^2 on Earth).
This formula is derived from the fact that the period of a pendulum is dependent only on the length of the pendulum and the acceleration due to gravity, and not on the mass or amplitude of the pendulum's swing.
In terms of the general form of a forcing function that would result in resonance, it would depend on the specific characteristics of the system and the nature of the forcing function. However, in general, a forcing function that matches the natural frequency of the system can result in resonance, where the amplitude of the oscillations increases dramatically. For a pendulum, the natural frequency is given by the formula ω = √(g/l), where ω is the angular frequency. So, a forcing function with a frequency close to this value could result in resonance.
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If we wanted to improve the efficiency of technology to reduce electrical power consumption. The sectors we would choose are?
If the efficiency of technology was to be improved in other to reduce electrical power consumption, the sectors which would be chosen is referred to as residential and commercial.
What is Technology?This is defined as the application of science to the practical aims and activities of human life. Power on the hand is defined as the amount of energy which is transferred per unit time and the S.I unit is referred to as Watts.
It can be inferred that electric power consumption is most abundant in residential and commercial sectors due to the number of appliances and hours which are present and used in this area.
It is therefore appropriate to focus on these two sectors so as to achieve the aim of an efficient technology in reduction of electrical power consumption.
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How much the aproximate number of atoms in bacteria.assume that average mass of an atom in bacteria is ten times the mass of hydrogen atom
Which type of galaxy is likely to contain only o-spectral type stars?
deidre walked her dog a distance of 95 meters to the north. the walk took 45 seconds. what was their velocity
Velocity of Deidre and her dog is 2.11m/s.
What is velocity?Velocity is the rate of change of position of an object in a particular frame of reference Mathematically, velocity of an object = Displacement of the object/time taken What is velocity of Deidre and her dog ?The distance covered by Deidre and her dog is 95 meter towards north.The time taken to cover the distance is 45 second.So velocity of Deidre and her dog =95/45=2.11m/s
Thus , we can conclude that the velocity of Deidre and her dog is 2.11 m/s towards north .
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Rank in order, from largest to smallest, the magnitudes of the momentum p1x through p5x of the objects presented in (Figure 1). Rank the magnitudes of the momentum from largest to smallest. To rank items as equivalent, overlap them.
The decreasing order of the momenta are b>a=d=e>c.
What is Momentum?Momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction.According to Isaac Newton's second equation of motion, the force acting on the particle equals the time rate of change of momentum.According to Newton's second law, if a particle is subjected to a constant force for a specific amount of time, the result of the force and time (referred to as the impulse) is equal to the change in momentum. On the other hand, a particle's momentum represents the length of time needed for a consistent force to bring it to rest.Solution: The momentum of all the options are mentioned below according to the formula:
a. p = 20 × 1 = 20gm/s
b. p = 20 × 2 = 40gm/s
c. p =10 × 1 = 10gm/s
d. p = 10 × 2 = 20 gm/s
e. p =200 × 0.1 = 20gm/s
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Question:
I hope you are trying to ask the question below:
Rank in order, from largest to smallest, the momenta a to e of the objects
a. 20 g & 1 m/s
b. 20 g & 2 m/s
c. 10 g & 1 m/s
d. 10 g & 2 m/s
e. 200 g & 0.1 m/s
A convex lens of focal length 25 cm is in contact with a concave lens of focal length 50 cm. The equivalent focal length of this combination-lenses should be Group of answer choices
The equivalent focal length of this combination-lenses should be +50 cm.
Given:
Focal length of convex lens, f₁ = +25 cm
Focal length of concave lens, f₂ = -50 cm
Calculation:
We know that the power of a lens is given as:
P = 1 / f
where, f is the focal length of lens
Now, the power of convex lens can be calculated as:
P₁ = 1/f₁
= 1/(25×10⁻² m)
= 100/25
= +4 D
Similarly, the power of concave lens can be calculated as:
P₂ = 1/f₂
= (1/-50×10⁻² m)
= -100/50
= -2 D
Thus, the power of the combined lenses can be calculated as:
P₍₁₊₂₎ = P₁ + P₂
= +4 D - 2 D
= +2 D
Now, the combined focal length of the lens can be calculated as:
f₍₁₊₂₎ = 1 / P₍₁₊₂₎
= 100 / 2 D
= +50 cm
Therefore, the equivalent focal length of this combination-lenses will be +50 cm.
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Two worlds in the outer solar system that seem remarkably similar to each other are:
Two worlds in the outer solar system that seem remarkably similar to each other are: Triton and Pluto
The outer solar system comprises the next four planets and everything beyond the planet Neptune but within the gravitational pull of the Sun. The Kuiper Belt and the Oort Cloud are also parts of the outer region.
Triton is only slightly larger than Pluto. Both worlds have similar surface materials, such as nitrogen, methane and carbon monoxide. Their diameters, masses and densities are also similar. Both Triton and Pluto may also have originated within the Kuiper Belt. Triton is thought to be originally a Kuiper Belt Object that was captured by Neptune's gravity.
Because Triton and Charon-Pluto are both from the Kuiper belt they are both made of similar materials such as nitrogen, methane, carbon dioxide and water ice. Both have large cores that are made primarily of rock with mantles of water ice and crusts made of frozen nitrogen. Neither of them have a magnetic field.
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A 10 kg box initially at rest is pulled with a 50 N horizontal force for 4 m across a level surface. The force of friction acting on the box is a constant 20 N. How much work is done by the 50 N force?
The work is done by the 50 N force is 200 J.
Work done by the 50 N forceWork done = Fd
where;
F is Force applied d is the displacement of the objectWork done = 50 N x 4 m = 200 J
Thus, the work is done by the 50 N force is 200 J.
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question is down below
The vertical components of velocity is 10.35 m/s and the horizontal component of velocity is 38.6 m/s
What are the components of velocity?We know that velocity is a vector quantity, a vector often can be resolved into its components. The vertical components is V sinθ while the horizontal component is vcosθ.
Hence;
Vertical component = 40 m/s sin 15 degrees = 10.35 m/s
Horizontal component = 40 cos 15 degrees = 38.6 m/s
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A mountain skier has begun descending the 30o slope. if the coefficient of kinetic friction is 0.10, what is her acceleration?
The acceleration of the body is found to be -4.05 m/s^2
What is the acceleration?We define the acceleration as the rate of change of the velocity with time. Hence, we can write that;
a = (μcosθ - sinθ)g
a = acceleration
μ = coefficient of kinetic friction
θ = angle of inclination
g = acceleration due to gravity
Thus;
a = (0.10cos 30 - sin 30) 9.8
a = -4.05 m/s^2
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A see-saw is balanced on its
midpoint. A 22.4 kg kid sits on the left, 1.75 m from the axis. A second kid sits on the other side, 1.22 m from the axis. What is the mass of the second kid?
Answer:
W1 L1 = W2 L2 equation for balancing torques
M1 g L1 = M2 L2 g
Or M2 = M1 * 1.75 / 1.22 = 1.43 M1 = 32.1 kg
in the photoelectric effect a photon with an energy of 5.3 * 10^-19 J strikes an electron in a metal
The velocity of the photo electron is 6.11 × 105 ms
Given :
Supplied energy, Es = 5.3 x 10-19 J
Minimum energy of the electron to escape from the metal, E. = 3.6 x 10-19 J
To Find :
Velocity of photoelectron
Solution : The energy supplied by the photon is equal to the sum of minimum escape energy and the kinetic energy of the escaping electron. So
5.3 × 10^-19 J = 3.6 × 10^-19 J + K
K = 5.3 x 10^-19 - 3.6 x 10^-19
K = 1.7 × 10^-19 J
The formula of kinetic energy is given by:
K = 1/2 mv^2
v = √2K/m
= √2 x 1.7 x 10^-19
√ 9.1 x 10^-31
v = 6.11 x 10^5 m/s
So, the velocity of the photo electron is 6.11 x 10^5 m/s
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Which element of a valid contract is established by getting the signatures of all parties?
The element of a valid contract which is established by getting the signatures of all parties is mutual agreement
What is an element of a valid contract?An element of a valid contract simply refers to that promise made between two or more parties that which allow the courts to make judgement.
Some elements of valid contract are:
OfferAcceptanceConsiderationIntention to create legal relationCertainty and capacity.So therefore, the element of a valid contract which is established by getting the signatures of all parties is mutual agreement
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Based on illustrations of magnetic field lines, where could an object be placed so it would not experience a magnetic force
Halfway between the like poles of two magnets, because the field lines bend away and do not enter this area.
How does a magnetic field diagram show where the field is strongest?
The magnetic field lines do not ever cross. The lines include arrowheads to indicate the direction of the force exerted by a magnetic north pole. The closer the lines are to the poles, the stronger the magnetic field (thus the magnetic field from a bar magnet is highest closest to the poles).Where is magnetic field the strongest and weakest on a magnet?
The bar magnet's magnetic field is strongest at its core and weakest between its two poles. The magnetic field lines are densest immediately outside the bar magnet and least dense in the core.Which two locations on the magnet would have the greatest attractive forces?
Inside the magnet itself, the field lines run from the south pole to the north pole. The magnetic field is strongest in areas of greatest density of magnetic field lines, or areas of the greatest magnetic flux density.Learn more about magnetic field
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As the electric potential near the ground increases during a thunderstorm, a positive charge current can move up pointed objects, such as masts of ships, producing a luminous halo or glow known as ____.
Answer:
St. Elmo's Fire - well known to old time sailors
The ___________ is a plane perpendicular to the optic axis through the focal point.
The focal plane is a plane perpendicular to the optic axis through the focal point.
What is focal plane?
The focal plane is the distance between your camera lens and the perfect point of focus in an image. This area is located a certain distance in front of your camera lens, and spans horizontally, left to right across your frame.What is focal plane and lens?
The focal plane is the one in which each focus is most likely to be located. The focal plane houses the lens' focus. The primary axis of the lens and the focus plane are perpendicular. The focal length of the lens determines how far the focal plane is from the lens.Learn more about focal plane
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A person stands on the ground with a slingshot and tries to hit a high limb on a nearby tree. The limb is 18.3 feet above the ground. What is the minimum initial velocity in meters/second of a rock leaving the slingshot at 6 feet above the ground that would be able to reach the limb
The minimum initial velocity of the rock is V = 8.56 m/sec.
What is Conservation of Energy?According to the rule of conservation of energy, energy can only be transformed from one form of energy to another and cannot be created or destroyed. This indicates that unless energy is added from the outside, a system always has the same quantity of energy.
Calculate the rock's minimal initial velocity in meters/second as it exits the slingshot at a distance of 6 feet [tex]$\left(h_{2}=6\right.ft.)[/tex] above the ground.
Using the provided information, the net height of the limb is calculated as shown below.
[tex]$$h &=h_{1}-h_{2}$$[/tex]
h = 18.3 - 6
h = 12.3
Now, using the conservation of energy the minimum initial velocity of the rock is computed as shown below,
Kinetic energy of the rock = Potential energy the rock
[tex]$$\begin{aligned}\frac{1}{2} m V^{2} &=m g h \\\frac{1}{2} V^{2} &=g h \\\frac{1}{2} V^{2} &=\left(32.1 \mathrm{ft} / \mathrm{s}^{2}\right)(12.3 \text { feet }) \\V &=\sqrt{2\left(32.1 \mathrm{ft} / \mathrm{s}^{2}\right)(12.3 \mathrm{feet})}\end{aligned}$$[/tex]
V = 28.10 [tex]\frac{ft}{s}[/tex].
The minimal initial velocity in meter/second is 8.56.
Therefore, the minimum initial velocity of the rock is 8.56 m/sec
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A crate with a mass of 44.0 kg is pushed with a horizontal force of 150 N. The crate moves at a constant speed across a level, rough floor a distance of 5.50 m.
Work done will be 825 N*m
Given:
mass of crate = 44.0 kg
horizontal force = 150 N
distance moved by crate = 5.50 m
To Find:
Work done
Solution: Work is done whenever a force moves something over a distance. You can calculate the energy transferred, or work done, by multiplying the force by the distance moved in the direction of the force.
First we want to find the work, it is given by the force applied times the distance moved, so the work is just:
W = Force x displacement
W = 150N*5.50m
W = 825 N*m
So, work done will be 825 N*m
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John is talking to his friend about painting a fence. He states that if he uses a roller brush he will cover the fence faster than if he uses a bristle brush. This is an example of a a. Law b. Belief c. Theory d. Hypothesis
Answer:
b
Explanation:
Four identical lab carts each have a mass of 200 kg. different masses are added to the carts and the velocities are measured. all carts move to the right. an illustration with four carts labeled cart a, cart b, cart c, and cart d. cart b has a 20 kilogram mass in it, cart c has a 40 kilogram mass in it, and cart d has a 60 kilogram mass in it. there are labels under each cart. under cart a is v = 4.8 meters per second, under cart b is v = 4.0meters per second, under cart c is v = 3.8 meters per second, and under cart d is v = 3.5 meters per second. which cart has the greatest momentum? cart a cart b cart c cart d
Cart A has the greatest momentum.
What is momentum?The definition of momentum is "mass in motion." Since every item has mass, if it is moving, it must have momentum because its mass is in motion. Mass and velocity are two factors that affect momentum. According to an equation, an object's momentum is determined by multiplying its mass by its velocity.
p = mv
p = momentum
m = mass
v = velocity
Calculation:Cart A
m₁ = 200 kg
v₁ = 4.8 m/s
p₁ = 200 × 4.8
p₁ = 960 kg-m/s
Cart B
m₂ = 200 + 20 = 220 kg
v₂ = 4 m/s
p₂ = 220 × 4
p₂ = 880 kg-m/s
Cart C
m₃ = 200 + 40 = 240 kg
v₃ = 3.8 m/s
p₃ = 240 × 3.8
p₃ = 912 m/s
Cart D
m₄ = 200 + 60 = 260 kg
v₄ = 3.5 m/s
p₄ = 260 × 3.5
p₄ = 910 kg-m/s
Hence concluded, cart A has the greatest momentum.
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________ occurs when a person is holding an object that is directly hit or splashed by lightning.
Contact injury happens when a person is holding an object that is directly hit or splashed by lightning.
To find answer, we need to know more about the lightning and injuries.
What are the injuries caused by lightning?The phenomenon of natural electrical discharge happens in a short time with a bright flash is called lightning.It carries a huge amount of energy.The injuries caused by lightning can be classified as Direct strikes, Side splash and the Contact injury.Direct injuries happens when a person directly hit by lightning.Side splash occurs when a current splashes from a nearby object.Contact injury happens when a person touching an object that is hit by lightning.Thus, we can conclude that, contact injury occurs when a person is holding an object that is directly hit or splashed by lightning.
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When someone is holding something that has been struck or splashed by lightning, contact damage occurs.
We need additional information concerning lightning and injuries in order to identify the solution.
What types of injuries are brought on by lightning?Lightning is the name for a natural electrical discharge that occurs quickly and with a dazzling flash.It has a tremendous amount of energy.Lightning-related injuries can be divided into three categories: direct strikes, side splashes, and contact injuries.When someone is struck by lightning directly, they can get direct injury.When a current splashes from a neighboring object, it is called a side splash.When someone touches a lightning-hit object, contact harm results.In light of this, we can say that contact injuries happen when a person is holding an object that has been struck by lightning or splashed by it.
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A proud deep-sea fisherman hangs a 69.5-kg fish from an ideal spring having negligible mass. The fish stretches the spring 0.130 m. (a) Find the force constant of the spring.
Force constant = k = 6811 N/m
Given:
mass = m = 69.5 kg
L(initial) = ideal spring length = 12 cm= 0.120 m
L(final) = final spring length = 13 cm= 0.130 m
Two forces acting on the object is k*x and mg
so,
kx-mg=0
kx = mg
k = mg/x
We know that x= displacement = L(final)- L(initial)
0.130-0.120=0.10
k= 69.5×9.8/0.10
k =6811 N/m
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A certain frictionless simple pendulum having a length l and mass m swings with period t. If both l and m are doubled, what is the new period?.
If l and m both are doubled then the period becomes √2*T
what is a simple pendulum?
It is the one which can be considered to be a point mass suspended from a string or rod of negligible mass.
A pendulum is a weight suspended from a pivot so that it can swing freely.
Here,
A certain frictionless simple pendulum having a length l and mass m
mass of pendulum = m
length of the pendulum = l
The period of simple pendulum is:
[tex]T = 2\pi \sqrt{\frac{l}{g} }[/tex]
Where k is the constant.
Now the length and mass are doubled,
m' = 2m
l' = 2l
[tex]T' = 2\pi \sqrt{\frac{2l}{g} }[/tex]
[tex]T' = \sqrt{2}* 2\pi \sqrt{\frac{l}{g} }[/tex]
[tex]T' = \sqrt{2} * T[/tex]
Hence,
If l and m both are doubled then the period becomes √2*T
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A fireworks shell is accelerated from rest to a velocity of 60.0 m/s over a distance of 0.200 m. How long did the acceleration last
The acceleration lasted for 0.007s.
To find the answer, we need to know about the Newton's equation of motion.
What's the Newton's equation of motion that relates initial velocity, final velocity, acceleration, time and distance?Newton's equations are
V²-U²= 2aSV²-U²= 2aSV= U+atV= final velocity, U= initial velocity, a= acceleration, t= time and S = distance
What's the acceleration, if the fireshell is accelerated from rest to a velocity of 60.0 m/s over a distance of 0.200 m?Here, U= 0m/s, V= 60.0 m/s, S= 0.200 m60²-0= 2a×0.2= 0.4a
a= 3600/0.4= 9000m/s²What's the time taken by the fireshell to achieve 60m/s with 9000m/s² acceleration from rest?Here, U= 0m/s, V = 60.0 m/s, a= 9000m/s²60= 0+9000tt= 60/9000= 0.007 sThus, we can conclude that the acceleration of the fireshell lasted for 0.007s.
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Which starting material is the limiting reagent in this procedure? which reagent is used in excess? how great is the molar excess (how many times greater)?
The limiting reagent in this procedure is the substance that is completely used in the reaction. The substance which is not completely used is called excess.
The beginning cloth in a chemical reaction is known as the reactant. each chemical response could have one or more reactants.
In a chemical response limiting reagent is the reactant this is fed on first and prevents any similar reaction from happening. the quantity of product shaped during the response is decided by means of the limiting reagent. as an example, allow us to recall the response of solution and chlorine
Materials used during the manufacture of the lively substance (e.g., tradition media, growth factors, and so on) and that are not meant to form a part of the active substance shall be taken into consideration as raw substances. cloth forming a critical part of the lively materials element shall be considered as the beginning substance.
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When operating an aircraft at cabin pressure altitudes above 12,500 feet msl up to and including 14,000 feet msl, supplemental oxygen shall be used during?
Supplemental oxygen shall be used in that flight time in excess of 30 minutes at those altitudes.
Most plane cabins are pressurized to 8,000 feet above sea level, an altitude that lowers the amount of oxygen inside the blood by approximately 4 percentage points, researchers say.
The higher the altitude, the less oxygen there is in the air and the lower the overall air pressure is. If flights were not pressurized, passengers could be prone to various physiological illnesses. Because of this, federal policies require that all commercial flights over 8,000 feet be pressurized.
The flight crew must use supplemental oxygen for the entire duration of flight operations above a cabin pressure altitude of 14,000 feet MSL.
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Although centuries ago, astronomers thought that a nova was a new star, appearing for the first time in the heavens, today we know that it is:
Astronomers thought that a nova was a new star, appearing for the first time in the heavens, today we know that it is as a binary star system.
What is the binary star system about?A binary star system is known to be one where one star is known to be called a white dwarf and there is a mass that is said to be transferred to it
A binary star is known to be a kind of a system that is composed of two stars that are known to be gravitationally held together to and in orbit near each other.
Note that Binary stars in the night sky are ones that are often seen as a single object and thus Astronomers thought that a nova was a new star, appearing for the first time in the heavens, today we know that it is as a binary star system.
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Two 5000-kg passenger cars roll without friction (one at 1 m/s, the other at 2 m/s) toward one another on a level track. They collide, couple, and roll away together with a combined momentum of
The combined momentum of the passengers is 5000 kgm/s.
Combined momentum of the passengerThe combined momentum of the passengers is calculated as follows;
P = mv1 + mv2
where;
m is mass of the passengersv1 is velocity of the first passengerv2 is velocity of the second passengerP = m(v1 + v2)
P = 5000(-1 + 2)
P = 5000 kgm/s
Thus, the combined momentum of the passengers is 5000 kgm/s.
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What is the strength of the electric field between two parallel conducting plates separated by 1.00 cm and having a potential difference (voltage) between them of 1.50×10^4v ?
Which type of fire suppression system is designed to work in areas where electrical equipment is used and contains pressurized air?
In a dry pipe sprinkler system, pressurized air or nitrogen, rather than water, is used to fill the pipes. This air maintains the closed position of a remote valve, also referred to as a dry pipe valve.
The dry-pipe valve, which is situated in a hot area, keeps water from flowing into the pipe until a fire triggers the operation of one or more sprayer. When this occurs, the dry pipe valve releases and the air leaves. After that, water enters the pipe and pours onto the flames through open sprinklers.
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