(a) Equation for the radius of the ball, r, treating it as a sphere, in terms of its surface area will be [tex]r & =\sqrt{\frac{A}{4 \pi}}[/tex]
(b) The density of the ball is 4.9307 g/cm^3.
(c) The density of the ball is 4903.7 Kg/m^3 or 4904 Kg/m^3
Surface area of a spherical ball, A=45 cm^2
Part a
The surface area of a spherical ball is given as
[tex]$$\begin{aligned}A & =4 \pi r^2 \\\therefore r & =\sqrt{\frac{A}{4 \pi}}\end{aligned}$$[/tex]
So, this is the expression for the radius of the ball in terms of surface area.
Part b
Mass of the ball, M=140 grams
The density of the ball is given as [tex]$$\rho=\frac{M}{V}$$[/tex]
Where, V is the volume of the spherical ball.
And [tex]$V=\frac{4}{3} \pi r^3$[/tex]
So, the value of the density will be
[tex]$$\begin{gathered}\rho=\frac{M}{\frac{4}{3} \pi r^3} \\\rho=\frac{3 M}{4 \pi r^3}\end{gathered}$$[/tex]
Now, putting the value of "r" in the above expression,
We will get
[tex]$$\begin{aligned}& \rho=\frac{3 M}{4 \pi\left(\sqrt{\frac{A}{4 \pi}}\right)^3} \\& \therefore \rho=\frac{3 M}{4 \pi\left(\frac{A}{4 \pi}\right)^{\frac{3}{2}}}\end{aligned}$$[/tex]
Now putting the value of M and A in above,
We will get,
[tex]$$\begin{gathered}\therefore \rho=\frac{3 \times 140}{4 \pi\left(\frac{45}{4 \pi}\right)^{\frac{3}{2}}} \\\therefore \rho=\frac{420}{4 \times 3.14(3.583)^{\frac{3}{2}}} \\\therefore \rho=\frac{420}{4 \times 3.14 \times 6.782} \\\therefore \rho=\frac{420}{85.18} \mathrm{~g} / \mathrm{cm}^3 \\\therefore \rho=4.9307 \mathrm{~g} / \mathrm{cm}^3\end{gathered}$$[/tex]
Part c
The density in Kg/m^3 is to be calculated.
[tex]$1 \mathrm{~g} / \mathrm{cm}^3=1000 \mathrm{~kg} / \mathrm{m}^3$[/tex]
So,
[tex]$$\begin{gathered}\therefore 4.9307 \mathrm{~g} / \mathrm{cm}^3=1000 \times 4.9307 \mathrm{~kg} / \mathrm{m}^3 \\\therefore \rho=4903.7 \mathrm{~kg} / \mathrm{m}^3\end{gathered}$$[/tex]
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A rightward force is applied to a 6-kg object to move it across a rough surface at constant
velocity. The object encounters 15 N of frictional force. Use the diagram to determine the
gravitational force, normal force, net force, and applied force.
Fnorm = 58.8 N; Fnorm = 58.8 N; Fapp = 15 N; Fnet = 0 N. In the case of constant velocity, a = 0 m/s/s and Fnet = 0 N, Fgrav = m • g • 9.8 m/s/s • 6 kg • 58.8 N Ffrict = Fapp = 15 N since there is no horizontal acceleration.
A rightward force is what?A book is moved across a desk with a rightward acceleration by applying a rightward push to it. Consider the effects of friction. Pass over air resistance. Static Friction = Normal Force x Static Friction Coefficient is the formula for calculating static friction.
How can I determine force?Newton's second law of motion provides the definition of the force formula: An object's force is equal to its mass times its acceleration. F = m ⨉ a. To apply this formula, you must use SI units for force (newtons), mass (kilograms), and acceleration (meters per second squared).
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A simple harmonic wave of wavelength 18.7 cm and amplitude 2.34 cm is propagating in the negative x-direction at 38.0 cm/s.
Part A. Find its angular frequency.
Part B. Find its wave number.
Part C. Write a mathematical expression describing the displacement y of this wave (in centimeters) as a function of position x and time t measured in cantimeters and seconds, respectively. Assume the maximum displacement occurs at x = 0 when t = 0 .
a) Angular frequency is 12.75 rad/s b) The wave number is 33.59m c)
y ( x ,t) = 2.34 x sin(33.59 x - 12.75t)
Given,
wavelength = λ = 18.7 cm
= 0.187 m
amplitude , A = 2.34 cm
v = 0.38 m/s
A) angular frequency = ?
f = v/λ
f = 0.38/1.87 = 2.03
angular frequency ,
ω = 2π f
ω = 2π x 2.03
ω = 12.75 rad/s
B) the wave number,
K = 2π/λ = 33.59m
c) as the wave is propagating in -x direction, the sign is positive between x and t
y ( x ,t) = A sin(k x - ω t)
y ( x ,t) = 2.34 x sin(33.59 x - 12.75t)
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what is the resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts?
The resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts = 2 Ω
Electrical resistanceElectrical resistance is the force that opposes the flow of current, it's a component that can reduce the speed and quantity of the flow of electrons in an electric circuit.
The formula for electrical resistance can be seen to have several components, namely R is the resistance (Ω), V is the voltage (V), and I is the current strength (A).
The equation:
R = V/I
We have,
Current strength = 120 A
The potential difference between its ends = 240 V
So, the resistance of a conductor that carries a current of 120 amperes when the potential difference between its ends is 240 volts:
R = 240 V / 120 A
= 2 Ω
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what is the maximum speed of a 2.0 g particle that oscillates between x =2.0 mm and x =8.0 mm in
The period of motion is simple hormonic motion and the maximum speed of the particle is 0.0031s
(a) Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".
(b) The equation that describes the simple harmonic motion is given by =
= X = Acos(ωt + θ) [1]
And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.
For the velocity:
= V = dx/dt = -Aωsin(ωt + θ) [2]
For the acceleration:
= A = dv/dt = -Aω²cos(ωt + θ) [3]
As we can see in equation [3] the acceleration would be maximum when the cosine term would be -1 and on this case:
= Aω² = 8x10³ m/s²
Since we know the amplitude A=0.002m we can solve for ω like this:
= ω = √ (8000/0.002)
= ω = 2000 rad
And we with this value we can find the period with the following formula;
= T = 2π/ω = 0.0031s
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The complete question:
A 10 g particle undergoes SHM with an amplitude of 2.0 mm and a maximum acceleration of magnitude 8.0 multiplied by 103 m/s2, and an unknown phase constant ?.(a) What is the period of the motion?1 s(b) What is the maximum speed of the particle?
consider the situation in the figure below, where two charged rods are placed a distance d on either side of an aluminum can. what does the can do?
The left side of the can receives a negative charge from the positively charged rod, which creates a force of attraction between both the rod and the can.
How does science define force?In science, the term "force" has a particular definition. At this point, describing a force as pushing or pulling is quite acceptable. A force does not "exist in an object" or "contain an object." One object experiences a force from another. Living organisms and inanimate objects are both included in the concept of a force.
Why is force so crucial?A force is either a push or a pull, and it has an impact on our everyday lives because without it, we couldn't open and close things, lift our arms and legs, or do much of anything else.
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A 150-kg object takes 1.5 minutes to travel a 2,500-meter straight path. It begins the trip traveling 120 meters per second and decelerates to a velocity of 20 meters per second.
What was its acceleration?
Responses
(A) −1.11 m/s2
(B) −0.3 m/s2
(C) +1.11 m/s2
(D) +80 m/s2
Answer: So the answer is (A) -1.11 m/s^2.
Explanation: To solve this problem, we need to use the formula for average acceleration, which is given by:
a = (vf - vi) / t
Where a is the acceleration, vf is the final velocity, vi is the initial velocity, and t is the time.
Plugging in the values given in the problem, we get:
a = (20 m/s - 120 m/s) / (1.5 minutes * 60 seconds/minute) = -100 m/s / 90 seconds = -1.11 m/s^2
So the answer is (A) -1.11 m/s^2.
A monochromatic beam of light is absorbed by a collection ofground-state hydrogen atoms in such a way that six differentwavelengths are observed when the hydrogen relaxes back to theground state.
(a) What is the wavelength of the incident beam? Explain the stepsin your solution.
(b) What is the longest wavelength in the emission spectrum ofthese atoms? To what portion of the electromagnetic spectrum and towhat series does it belong?
(c) What is the shortest wavelength? To what series does itbelong?
Answer Key:
(A) The atoms must be excited to energy level n = 4, to emit sixdifferent photon
energies in the downward transitions 4→3, 4→2,4→1, 3→2, 3→1, and 2→1. The
photon energy absorbed in the 1→4 transition is 12.8 eV,making the wavelength 97.4
nm.
(B) 1.88 μm, infrared, Paschen
(C) 97.4 nm, ultraviolet, Lyman
The incident beam of light has a single, monochromatic wavelength. When this beam is absorbed by the hydrogen atoms, the atoms become excited and eventually relax back to the ground state, emitting light at several different wavelengths.
(a) It is not possible to determine the wavelength of the incident beam based on the information provided.
(b) The longest wavelength in the emission spectrum of the hydrogen atoms corresponds to the transition between the lowest energy levels in the atom. In the case of hydrogen, the ground state is the lowest energy level, so the longest wavelength would correspond to a transition from an excited state to the ground state.
(c) The portion of the electromagnetic spectrum to which the longest wavelength belongs depends on the specific value of the wavelength. The electromagnetic spectrum includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays.
(d) The series to which the longest wavelength belongs can be determined by the values of the energy levels involved in the transition. In the case of hydrogen, there are three series: the Lyman series, the Balmer series, and the Paschen series. The Lyman series corresponds to transitions from higher energy levels to the ground state, the Balmer series corresponds to transitions from intermediate energy levels to the ground state, and the Paschen series corresponds to transitions from lower energy levels to the ground state.
(e) The shortest wavelength in the emission spectrum corresponds to the transition between the highest energy levels in the atom. In the case of hydrogen, the shortest wavelength would correspond to a transition from an excited state to a higher energy level.
(f) The portion of the electromagnetic spectrum to which the shortest wavelength belongs depends on the specific value of the wavelength.
(g) The series to which the shortest wavelength belongs can be determined by the values of the energy levels involved in the transition. In the case of hydrogen, the shortest wavelength would belong to the Lyman series, since it corresponds to a transition from an excited state to a higher energy level
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A 3000kg helicopter, tilted as shown, is flying horizontally (neither gaining nor losing altitude). The helicopter is experiencing a 1200N drag.
How many forces are acting on the helicopter?
Are all the forces on the helicopter balanced?
What is the magnitude of the thrust?
What is the magnitude of the net force on the helicopter?
What is the magnitude of the helicopter's acceleration?
Describe the helicopter's speed. (increasing/decreasing/constant)
The number of forces acting on the helicopter is 3.
The forces on the system are not balanced
The magnitude of the thrust is 7,112,5 N.
The net force of the helicopter is 5,912.5 N
The magnitude of the helicopter's acceleration is 1.97 m/s².
The speed of the helicopter is increasing towards to the right.
How many forces are acting on the trailer?The number of forces acting on the helicopter is calculated as follows;
the weight of the helicopter acting downwardsthe thrust of the helicopterdrag force of the helicopterThe magnitude of the thrust is calculated as;
F = W sinθ
F = (3000 x 9.8 x sin14)
F = 7,112.5 N
The net force of the helicopter is calculated as follows;
F (net) = drag force + thrust force
F (net) = - 1200 N + 7,112.5 N
F (net) = 5,912.5 N
The acceleration of the helicopter is calculated as follows;
F (net) = ma
where;
m is the mass of the helicoptera is the accelerationa = F (net) / m
a = 5,912.5 / 3000
a = 1.97 m/s²
Thus, since the acceleration of the helicopter is positive, the speed of the system is increasing towards to the right
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what is the current i(t) in the circuit at time t after the switch is closed? express your answer in terms of q0 , l , c , and other variables given in the introduction.
If the current i(t) in the circuit at time t after the switch is closed in terms of q0 , l , c the differential equation will be V(t) = (q0/C) × e^(−t/RC )
The equation for V(t) would be V(t)=E(RC)(dV(t)/dt) if a battery with EMF E was present in the circuit. With respect to V(t), this differential equation is no longer homogenous. But it can be resolved by simply substituting Vb(t)=V(t)E. This substitution has the effect of removing the E term and producing an equation for Vb(t) that is the same as the equation you solved for V(t). When a battery is supplied, the capacitor's initial condition is typically that it is completely discharged at time t=0.
In these circumstances, the solution will appear as V(t)=E(1et/(RC)) Since the voltage across the capacitor is zero at time t=0 according to this solution, is 0 at time t=0 since the capacitor wasn't charged at that point, and it climbs asymptotically to E.
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coherent red light illuminates two narrow slits that are 25 cm apart. will a two-slit interference pattern be observed when the light from the slits falls on a screen? explain.
No two-slit interference pattern be observed when the light from the slits will not falls on a screen.
Because the condition of the interference is the distance between the slits equals or close to the wavelength of the red light. For distance of 25 cm, it is a very large distance that prevents the interference of the red light to occur. So, the answer is no.
Interference is the phenomenon where two waves combine by applying a displacement at any one point in space and time to form waves of greater, lesser or equal amplitude. Constructive and destructive interference arise from correlated or coherent wave interactions. This is because they originate from the same source or have the same or nearly the same frequency. Interference effects can be observed in all kinds of waves: light, radio waves, sound, surface water, gravity, matter waves.
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does initial velocity equal final velocity when doing a one dimenstion free fall problem if you throw a ball up
If we assume at time instance t= 0, then the same thing happens. initial velocity is equal to final velocity
During a free fall, only the gravitational force acts on a body. The initial velocity of the body is zero during free fall.
Vertical motion is symmetrical - the distance and time are the same in the rise as in the fall; the final velocity will have the same magnitude as the initial velocity but in the opposite direction. Horizontal components will never be effected by gravity; it is constant velocity motion
The average velocity is the ratio of the total distance traveled to the total time taken. This can happen in two cases, first if the initial velocity and the final velocity are equal to the average velocity and there is no change in the velocity for the entire trip
Velocity is the measure of the amount of distance an object covers in a given amount of time. Here's a word equation that expresses the relationship between distance, velocity and time: Velocity equals distance travelled divided by the time it takes to get there.
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A box is released from rest and slides down a ramp in a closed system. Even though the box speeds up, its kinetic energy at the bottom of the ramp is less than the potential energy that it had at the top of the ramp.
What best explains why the box’s final kinetic energy is less than its initial potential energy?
In a closed system, kinetic energy is always less than potential energy.
Some potential energy was converted into thermal energy due to friction.
The acceleration due to gravity became smaller as the box slid down the ramp.
In a closed system, total energy is constantly being lost to outside objects.
The best explanation why the box’s final kinetic energy is less than its initial potential energy is that some potential energy was converted into thermal energy due to friction.
option B is the correct answer.
What is the law of conservation of energy?
The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.
According to law of conservation of energy, we have the following energy conversion process.
potential energy to kinetic energykinetic energy to potential energychemical energy to electrical energypotential energy to heat and kinetic energy, etcIn absence of friction, the potential energy of the box at the top of the ramp is equal to the kinetic energy of the box at the bottom of the ramp.
In the presence of friction, some potential energy will be converted into thermal energy due to friction and the final kinetic energy will be smaller than the initial potential energy.
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Answer:
The answer above is correct (I just did it on Edge.) - It's option B!
Explanation:
Hope this helped - brainliest would be greatly appreciated!
Have a great day :D
A boat travels 12.0 m while it reduces its velocity from 9.5 m/s to 5.5 m/s. What is the magnitude of the boat’s acceleration while it travels the 12.0 m?
a. 1.3 m/s2
b. 2.5 m/s2
c. 3.0 m/s2
d. 7.5 m/s2
The magnitude of the boat’s acceleration while it travels 12.0 m is b. 2.5 [tex]ms^{-2}[/tex]
u= 9.5 [tex]ms^{-1}[/tex]
v= 5.5 [tex]ms^{-1}[/tex]
s= 12 m
From the given data we can use,
[tex]v^{2} -u^{2} =2as[/tex]
to calculate acceleration.
[tex]v^{2} -u^{2} =2as[/tex],
Where,
v is the final velocity,
u is the initial velocity,
a is the acceleration and
s is the distance covered.
Substituting the values we have,
[tex]v^{2} -u^{2}[/tex]= 2×a×s
[tex](5.5)^{2}[/tex] - [tex](9.5)^{2}[/tex]= 2 ×a×12
a= [tex]\frac{(5.5)^{2} -(9.5)^{2}}{(2)(12)}[/tex]
a= [tex]\frac{(30.25)^{2} -(90.25)^{2}}{(24)}[/tex]
a=[tex]\frac{-60}{2000}[/tex]
a=-2.5 [tex]ms^{-1}[/tex]
(The negative sign says that it is a negative acceleration )
Therefore the magnitude of the boat's acceleration is -2.5 [tex]ms^{-1}[/tex]
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find the turning-point angles if the child has a speed of 0.80 m/s when the ropes are vertical.
The turning-point angles is θ = 9.666 degrees if the child has a speed of 0.80 m/s when the ropes are vertical.
As per the details provided in the above question are as bellow,
The speed at bottom = v = 0.8 m/s
The length of the rope = l = 2.3 meter
The Work Energy Theorem provides us with,
The energy an item has as a result of motion is known as kinetic energy. A force must be applied to an item in order to accelerate it. We must put forth effort in order to apply a force. After the job is finished, energy is transferred to the item, which then moves at a new, constant speed.
Change in kinetic energy = net work done
[tex]0 - 0.5mv^2 =[/tex]- mgl (1-cosθ)
[tex]0.5 \times 0.8^2[/tex] = 9.8 x 2.3 (1-cosθ)
angle θ = 9.666 degrees
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Note:- The correct question would be as bellow,
A child swings back and forth on a swing suspended by 2.3m -long ropes.
Find the turning-point angles if the child has a speed of 0.80 m/s when the ropes are vertical.
a boy rides his bicycle which has wheels of radius 27.0 cm. if the boy accelerates from rest to a speed of 11.2 m/s in 24.0 s, what is the angular acceleration (in rad/s2) of the tires? (enter the magnitude.)
The angular acceleration is 0.01533rad/s.
We are given that,
Radius = r = 27.0cm
Speed = v = 11.2 m/s
Time = t = 24.0 s
Therefore , We shall first find the linear acceleration before calculating the angular acceleration from one of the linear motion kinematics equations and the initial velocity u will be 0.
v = u + at
a = v/t
a = (11.2m/s)/(27.0×10⁻²m)
a = 0.414 ×10⁻²m/s²
Now , calculating the angular acceleration,
a = α × r
α = a/r
α = (0.414 ×10⁻²m/s²)/(27.0×10⁻²m)
α = 0.01533rad/s
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an under-excited generator a. absorbs reactive power from the system. b. neither absorbs nor delivers reactive power. c. delivers reactive power to system.
An under-excited generator a. absorbs reactive power from the system
In an electrical power system, generators are used to produce electrical energy by converting mechanical energy into electrical energy. Under-excited generators are generators that are operating at a voltage below their rated value. These generators are used where it is necessary to maintain a specific voltage in the electrical system. For example, in some power systems, load on the generator may vary, and generator may need to adjust its output to match the changing load.
When a generator is under-excited, it absorbs reactive power from the system, which is a type of electrical power that is not used to do work. Reactive power is required to create and maintain the alternating current in an electrical system, but it does not perform any useful work. Absorbing reactive power helps to maintain the proper voltage and frequency in the system.
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under the influence of its drive force, a snowmobile is moving at a constant velocity along a horizontal patch of snow. when the drive force is shut off, the snowmobile coasts to a halt. the snowmobile and its rider have a mass of 136 kg. under the influence of a drive force of 205 n, it is moving at a constant velocity whose magnitude is 5.50 m/s. the drive force is then shut off. (a) calculate the distance in which the snowmobile coasts to a halt. (b) calculate the time required for the snowmobile to stop.
A) 13.2 m, The snowmobile moves at a constant speed when the drive force is engaged; as the acceleration is zero, there is no net force. On the other hand, the net force is the product of two forces acting on the snowmobile: the driving force, F, and the frictional force, Ff: F-Ff=0, Ff=F.
(b) 4.2 s, The relationship between the snowmobile's acceleration and time t is given by: a=v-u/t, The time it takes the snowmobile to stop is 4.2 seconds after rearranging for t and entering numbers.
How do you define magnitude?The simplest definition of magnitude in physics is "distance or quantity." In either an absolute or relative meaning, it displays the size or motion of an object.
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a 25-kg crate is pushed across a frictionless horizontal floor with a force of 20 n, directed 20o below the horizontal. the acceleration of the crate is:
1.75 m/s2 is the crate's acceleration.
mass=25kg, f=20n.
In terms of physics, what is frictionless?A surface is said to be frictionless if it has a force acting on any thing that is practically zero or insignificant, meaning that there is no resistance between the surface and the material, allowing the object to slide and move freely without any friction.
Can one walk on a frictionless surface?Every every activity that requires the interaction of two surfaces and motion involves friction, with the exception of space walks, which you may conduct without any resistance. Because there won't be any contact force to propel the individual forward, one cannot walk in the absence of friction.
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the electric potential in a region of space is v=200v⋅mx2+y2√, where x and y are in meters.
Electric field strength at (2.1m,3.0m) = 14.914 V/m
So in order to find electric field strength at a point whose cordinate is (x,y) is given by the term E(x,y)
Given:
V=200 (V⋅m) /√(x2+y2),
E = ∂V/∂x i + ∂V/∂y j
where i is vector along x axis whose magnitude is 1 and hence it is unit vector and j is vector along y axis whose magnitude is 1 and hence it is unit vector.
∂V/∂x = [tex]\frac{-200x}{(x^2+y^2)^3^/^2}[/tex]
=> (-200*2.1)/49.11
=> 8.55
∂V/∂x = [tex]\frac{-200y}{(x^2+y^2)^3^/^2}[/tex]
=> (-200*3)/49.11
=> 12.22
so E(2.1,3) = -8.55 i -12.22 j
so E = [tex]\sqrt{-8.55*-8.55 + -12.22*-12.22}[/tex]
=> [tex]\sqrt{222.43}[/tex]
=> 14.914 V/m
so the magnitude of Electric field at (2.1m,3.0m) = 14.914 V/m
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Complete question:
The electric potential in a region of space is V= 200 (V⋅m) /√(x2+y2), where x and y are in meters. Find the strength of the electric field at (x,y)=(2.1m,3.0m) ?
if you placed 1.00 c of positive charge on the earth and 1 c of negative charge 384,500 km away on the moon, how much force would the positive charge on the earth experience
If you placed 1.00 coulomb (C) of positive charge on the Earth and 1 C of negative charge 384,500 km away on the Moon, the positive charge on the Earth would experience a gravitational force of attraction towards the negative charge on the Moon.
The gravitational force of attraction between two charged particles is given by the formula:
F = (k * q1 * q2) / r^2where F is the gravitational force, k is the Coulomb constant, q1 and q2 are the charges of the two particles, and r is the distance between them.
Plugging in the values provided, we get:
F = (8.99 x 10^9 N*m^2/C^2) * (1 C) * (1 C) / (384,500 km)^2
= 2.34 x 10^-9 N.
This is a very small force due to the large distance between the two charges and the relatively small magnitude of their charges.
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you are holding short for an intersection departure on runway 8 with the sign in front of you. which way should you turn when taxiing onto the runway to depart runway 8?
With the sign in front of you, you are waiting in short formation for an intersection taxiing on runway 8. In order to depart from runway 8, you should turn left as you enter the runway.
In contrast to towing or pushback, where the aircraft is moved by a tug, taxing (sometimes written taxying) is the movement of an aircraft on the ground under its own power. Although the name refers to vehicles with wheels most often, it also covers vehicles with skis or floats.
Taxiways are used by airplanes to go between locations on an airport, such as from a hangar to the runway. The takeoff roll and landing rollout, which are the accelerating run and descending run along a runway, respectively, before takeoff and landing, respectively, are not referred to as "taxiing."
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A wire of cross sectional area of 6 * 10 ^ - 5 * m ^ 2 length 50cm stretches by 0.4mm under a load of 3000N. What is the Young's Modulus of the wire?
The Young's Modulus of the wire of length 50 cm is 4.0×10⁵ N/m.
What is young's modulus?Young's modulus is a measure of the ability of a material to withstand changes in length when under lengthwise tension or compression.
To calculate the young's modulus of the wire, we use the formula below.
Formula:
γ = (F/A)/(L/e).................. Equation 1Where:
γ = Young's modulusF = ForceA = AreaL = Length of the wiree = ExtensionFrom the question,
Given:
F = 3000 NA = 6×10⁻⁵ m²L = 50 cm = 0.05e = 0.4 mm = 4×10⁻⁴ mSubstitute these values into equation 1
γ = (3000/6×10⁻⁵)/(0.05/4×10⁻⁴)γ = 4.0×10⁵ N/mHence, the Young's Modulus is 4.0×10⁵ N/m.
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if the amplitude increases to 0.20 mm , by what factor does the bug's maximum kinetic energy change?
The bug's maximal kinetic energy changes as 16 times of Kinetic energy before amplitude increases when the amplitude approaches 0.20 mm.
The amplitude of a wave is its largest displacement. The wave's greatest velocity is now expressed as its amplitude, which is: v =Aw= K/M.
Now, the square of the wave is directly proportional to the kinetic energy of a system. As a result, the wave's maximum kinetic energy is given by KE = k/2A^2, which means that
KE1/KE2 = A1^2/A2^2 where KE1 is the kinetic energy prior to the amplitude (A1) increasing and KE2 is the kinetic energy following the amplitude increasing (A2)
Due to that,
The bug's entire vertical journey was S = 0.10m
The wave's amplitude is equal to half of the whole distance from the top to the bottom, hence its value is (A) = S/2 = 0.1/2 = 0.05m.
Now that the wave's amplitude has increased to 0.20 m, KEA = KE1/KE2 = A1^2/A2^2
KE1/KE2 = (0.05)^2/(0.20)^2, which equals 0.0025/0.04 = 0.0625.
KE2 then equals 16KE1
Therefore, the largest change in kinetic energy is (KE2) = 16KE1.
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Find complete question: A bug on the surface of a pond is observed to move up and down a total vertical distance of 0.10 m, lowest to the highest point, as a wave passes. What is the amplitude of the wave? If the amplitude increases to 0.20 m, by what factor does the bug's maximum kinetic energy change?
find the weight of a car on a 12 degree slope if the force required to push the car up the hill is 650 lbs g
The weight of the car on the 12 degree slope is 546.72 lbs. This weight is important to know for various reasons, such as calculating the amount of force and energy required to move the car up the hill.
The weight of a car on a 12 degree slope can be calculated using the formula:
Weight = Force * sin(Slope Angle)
Therefore, the weight of the car on the 12 degree slope can be calculated as follows:
Weight = 650 lbs * sin(12°)
Weight = 546.72 lbs
The weight of a car on a 12 degree slope is important to know for various reasons. For example, if the car is being driven up the slope, it is important to know the weight of the vehicle to ensure that it will be able to make it up the hill. Additionally, knowing the weight of the car on the slope can help engineers and designers to calculate the amount of force and energy required to move the car up the hill.
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five hockey pucks are sliding across frictionless ice. the drawing shows a top view of the pucks and the three forces that act on each one. the forces can have different magnitudes (f, 2f, or 3f), and can be applied at different points on the puck. only one of the five pucks could be in equilibrium. which one?
When a hockey puck with a momentum of 5 kg-m/s is struck by a hockey stick, it receives an impulse of 100 N.
The force of friction is the imbalanced force in the situation of an already moving object (such as a puck sliding on an ice surface). In this situation, the puck's acceleration (slowing) is proportional to the amount of friction. More friction causes the puck to slow down faster. According to Newton's third law of motion, every action has an equal and opposite response. When a player is skating, for example, his skates push off the ice, causing an opposing reaction that propels the player ahead and increases his speed.
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Question 19(Multiple Choice Worth 2 points) Which statement best describes scientific theories? Scientific theories are based on facts that describe natural events. Scientific theories describe natural events but do not explain them. Scientific theories are facts based on observations of events in the natural world. Scientific theories attempt to explain how events occur in the natural world.
Answer:
Scientific theories are attempts to explain how events occur in the natural world.
Explanation:
A scientific theory is an explanation for a wide range of observations and phenomena that have been tested and supported by multiple lines of evidence. A theory is not based on a single piece of evidence, but rather on a collection of evidence that has been accumulated over time through careful observation and experimentation.
Scientific theories are based on facts, which are observations of events in the natural world. However, a theory goes beyond simply describing these events; it seeks to explain why and how they occur. For example, the theory of evolution explains how organisms have evolved over time through natural selection. It is based on a wide range of evidence, including observations of the fossil record, comparative anatomy, and molecular biology, among others.
Overall, scientific theories are important tools for understanding and explaining the natural world, and they are constantly being revised and updated as new evidence becomes available.
Hi, Guy I need help with thi quetion:
Find the angle of refraction of a ray of light that enter diamond from water at an angle of 21. 2 degree to the normal. Can omeone help me fatttt!
The angle of refraction of the ray of light entering the Diamond is 16.8°.
The diamond from the water at an angle of 21.2 degrees to the normal.
According to the law of refraction, the ratio of the sign of the angle of incidence and the angle of refraction of the ray of light is constant.
Sin i/Sin r = n
n is the refractive index of the material in which the light is entering.
The refractive index of the Diamond is 2.42.
Putting all the values,
Sin(21.2°)/Sin(r) = 2.42
0.71/Sin(r) = 2.42
Sin(r) = 0.71/2.42
Sin(r) = 0.29
r = Sin inverse (0.29)
r = 16.86°
So, the angle of refraction is found to be 16.86°.
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2. what property of tissue does a proton density image show? what tr and te times do we need to achieve proton density imaging?
In a proton density image the tissue magnetization, RF signal intensity, and image brightness are.
Proton Mail is the world's largest cozy e-mail provider. It gives end-to-cease encryption and plenty of different splendid safety capabilities to maintain your communications non-public. Even the company hosting your emails has no manner of reading them, so you can rest confident that they cannot be studied via third events either.
It has a completely, very wealthy internal shape. you could have heard that protons are made up of 3 smaller basic particles known as quarks, two united states, and one down quark to be particular, but it is only the top of the particle iceberg, as proton researcher Paul Reimer explains.
One or extra protons are present in the nucleus of every atom. They provide the attractive electrostatic crucial force which binds the atomic electrons. The quantity of protons in the nucleus is the defining belongings of an element and is referred to as the atomic quantity.
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How does changing the mass or speed of a moving object before it collides with
another object affect the forces on those objects during the collision?
PLEASE HURRY
Answer:
When two objects collide, the forces that are exerted on each other are determined by their masses and speeds. If the mass of one of the objects is increased, the force that it exerts on the other object during the collision will also increase. Similarly, if the speed of one of the objects is increased, the force that it exerts on the other object during the collision will also increase. In general, the greater the mass and speed of an object, the greater the force that it will exert on another object during a collision. However, it is important to note that the direction of the forces will remain the same, regardless of the masses or speeds of the objects involved.
a block of mass 0.482 kg is hung from a vertical spring and allowed to reach equilibrium at rest. as a result, the spring is stretched by 0.630 m. find the spring constant.
The spring constant of the spring is 7.497 N/m.
The given parameters;
mass of the block, m = 0.482 kg
extension of the spring, x = 0.630 m
additional extension, = 0.338 m
The spring constant of the spring is calculated as follow
F = mg
Kx = mg
K = mg/x
K = 0.482 × 9.8 / 0.630 = 7.497N/m
F = -kx.
The spring constant, or k, is the proportional constant. It is a gauge of the spring's rigidity. A spring exerts a force F = -kx in the direction of its equilibrium position when it is stretched or compressed to a length that deviates by an amount x from its equilibrium length. The spring constant is calculated by dividing the force required to extend or compress a spring by the length it goes up or down. It is used to assess the stability or instability of a spring, The spring's stiffness is quantified by the spring constant, or k. For various springs and materials, it differs. The stiffer the spring is and the harder it is to stretch, the greater the spring constant.
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