Answer:
b = 0.6487 kg / s
Explanation:
In an oscillatory motion, friction is proportional to speed,
fr = - b v
where b is the coefficient of friction
when solving the equation the angular velocity has the form
w² = k / m - (b / 2m)²
In this exercise we are given the angular velocity w = 1Hz, the mass of the body m = 0.1 kg, and the spring constant k = 5 N / m. Therefore we can disperse the coefficient of friction
let's call
w₀² = k / m
w² = w₀² - b² / 4m²
b² = (w₀² -w²) 4 m²
Let's find the angular velocities
w₀² = 5 / 0.1
w₀² = 50
w = 2π f
w = 2π 1
w = 6.2832 rad / s
we subtitute
b² = (50 - 6.2832²) 4 0.1²
b = √ 0.42086
b = 0.6487 kg / s
The coefficient friction of the mass during the measurement is 0.648 kg/s.
The given parameters;
mass, m = 0.1 kgspring constant, k = 5 N/mfrequency of the mass, F = 1 HzDuring oscillatory motion, friction is directly proportional to speed.
[tex]F_k = -vb[/tex]
where;
b is the coefficient of frictionThe angular velocity is given as;
[tex]\omega ^2 = \frac{k}{m} - \frac{b^2}{4m^2} \\\\\omega ^2 = \omega _0^2 - \frac{b^2}{4m^2}\ \ ---\ (1)[/tex]
From the equation above, we will have the following;
[tex]\omega_0^2 = \frac{k}{m} \\\\\omega_0^2 = \frac{5}{0.1} \\\\\omega_0^2 = 50[/tex]
Also, the instantaneous angular speed is calculated as;
[tex]\omega = 2\pi f\\\\\omega = 2\pi \times 1\\\\\omega = 2\pi\\\\\omega = 6.284 \ rad/s[/tex]
From equation (1), the coefficient of friction is calculated as follows;
[tex]\omega ^2 = \omega ^2_0 - \frac{b^2}{4m^2} \\\\ \frac{b^2}{4m^2} = \omega ^2_0 - \omega ^2 \\\\b^2 = 4m^2( \omega ^2_0 - \omega ^2)\\\\b= \sqrt{ 4m^2( \omega ^2_0 - \omega ^2)}\\\\b = \sqrt{ 4\times 0.1^2\times ( 50 - 6.284^2)}\\\\b = 0.648 \ \ kg/s[/tex]
Thus, the coefficient friction of the mass during the measurement is 0.648 kg/s.
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A very long straight current-carrying wire produces a magnetic field of 20 mT at a distance d from the wire. To measure a field of 5 mT due to this wire, you would have to go to a distance from the wire of
A- 4d.
B - 16d.
C - d sqrt2
D- 8d.
E- 2d.
Answer:
A. 4d
Explanation:
Magnetic field strength is inversely proportional to distance. So in order to have a smaller magnetic field, we need to move further out from the wire. How far we go exactly can be determined from the formula: B=(μ₀I)/(2πr)
(That is derived from Ampere's Law, which states ∫B•dl=μ₀I)
With that you can set up a ratio between the magnetic fields in both cases. Because the current is the same for both instances, everything reduces out on one side of the equation and leaves you with something that relates the two distances by a ratio of each magnetic field value.
My work is in the attachment, comment for questions.
how far must he mirror mz of the michelson interferometer be moved so that 1600 fringes of laser light move across a line int he field of view
Answer:
The question is not complete. Let me explain Michelson interferometer and how to calculate a question like this.
Answer 4.85 * [tex]10^{-4}[/tex]m
Explanation:
The Michelson Interferometer is an instrument which produces interference fringes by splitting a light beam into two parts, it then recombines them after they have travelled different optical paths.
The formula to measure the minute displacement is Δd=m * λ[tex]_{0}[/tex]/2
where m is the number of fringes passing a given point as the movable plane mirror is moved
and λ[tex]_{0}[/tex] is the monochromatic lamp of wavelength
In the question, m = 1600. Let us assume that the wavelength is 606 nm
Solution
Δd=m * λ[tex]_{0}[/tex]/2
Δd=1600 * 606nm/2 = 1600 * 303nm = 484800nm
We convert the nm to m (nm / [tex]10^{-9}[/tex])
4.85 * [tex]10^{-4}[/tex]m
Train A is moving at 100 kmh–1 through a station. Train B is also travelling at 100 kmh–1 through the station but in the opposite direction to train A. What is the speed of a seated passenger on? (a) train A relative to an observer on the station? (b) train A relative to another seated passenger on the same train? (c) train B relative to a passenger on train A?
Explanation:
(a) An observer on the station has a speed of 0 km/h. The speed of a passenger on Train A is 100 km/h. The relative speed is 100 km/h − 0 km/h = 100 km/h.
(b) The speed of both passengers is 100 km/h, in the same direction. The relative speed is 100 km/h − 100 km/h = 0 km/h.
(c) The speed of both passengers is 100 km/h, in opposite directions. The relative speed is 100 km/h − (-100 km/h) = 200 km/h.
A cruise started its trip 8:00. Its average speed was 100 km/h.
When it travelled 2/5 of its journey by 12:00, the boat changed
its speed. If the boat was required to arrive at the destination at
17:00, what average speed must the boat travel at for the
remaining journey?
Answer:
120 k/m
Explanation:
Answer: 120
Explanation:
A diffraction-limited lens can focus light to a 10-μ m-diameter spot on a screen. Do the following actions make the spot diameter larger, smaller, or leave it unchanged? a. Decreasing the wavelength of light: b. Decreasing the lens diameter c. Decreasing the focal length: d. Decreasing the lens-to-screen distance:
Answer:
a) the size of the sport DECREASES , b)the spot size is increased
c) it has no effect and d) spot size DECREASES
Explanation:
The expression for constructive interference in diffraction is
a sin θ = m λ
the chaff of the spot is given by the minimum interference m = 1
a sin θ = λ
let's use trigonometry to find the angle
tan λ= y / L
tan θ = sin θ / cos t = sin θ
sin θ = y / L
a y / L = lam
in the case of materials with circular dome, the problem must result in polar coordinates, with which a numerical constant is introduced
y = 1.22 L / a lam
let's analyze each electrode action in this equation
a) Decrease lam
y ’= 1.22 L / a lm2
lam2 <lamo
y '<y
therefore the size of the sport DECREASES
b) decreases the lens diameter
a '<a
y ’= 1.22 L / a’ lam
y '> y
the spot size is increased
c) Decrease the focal length
The expression does not depend on the focal length, so it has no effect
d) decrease in L
y ’= 1.22 L’ / a lam
spot size DECREASES
When landing after a spectacular somersault, a 41 kg gymnast decelerates by pushing straight down on the mat. Calculate the force she must exert if her deceleration is 7.00 times the acceleration due to gravity. Explicitly show how you follow the steps in the Problem-Solving Strategy for Newton's laws of motion.
Answer:
The force the gymnast must exert is 2812.6 N.
Explanation:
Given;
mass of the gymnast, m = 41 kg
her deceleration, -a = 7g = 7 x 9.8m/s² = 68.6 m/s²
Apply Newton's second law of motion;
F = ma
where;
F is the magnitude of the force exerted
m is the mass of the gymnast
a is the deceleration
Substitute in the given values of m and a into the force equation;
F = ma
F = 41 x 68.6
F = 2812.6 N
Therefore, the force the gymnast must exert is 2812.6 N.
What magnetic field strength will allow the electrons to pass through without being deflected?
Answer:
Explanation:
If magnetic field exists parallel to the direction of motion of electron , no force will act on the electrons and hence there will be no deflection in them .
In such cases , the magnitude of magnetic field is immaterial . No matter how high or low magnitude of magnetic field be , if it is parallel to the velocity of electron , it will not be deflected as the force created on them will be zero.
Only in case magnetic field makes some angle with the direction of velocity , force will be created and electron will be deflected .
plz solve this. plz plz plz plz simple machine
Answer:
Explanation:
i. CW moment = 10 N (10 cm) + 30 N (30 cm) - 60 N (40 cm) = - 1400 N-cm
ii. ACW momenet = 60 N (40 cm) - 10 N (10 cm) + 30 N (30 cm) = 1400 N-cm
iii. No. The lever is not balanced in the situation. Because the moment is ± 1400 N-cm. if balance, the moment must be Zero.
iv. the location of 10N by keeping the other loads unchanged to balance the lever is 150 cm
take moment from Δ (support)
60(40) = 10(x) + 30(30)
2400 = 10x + 900
10x = 2400 - 900
10x = 1500
x = 1500/10
x = 150 cm
therefore, the location of 10N by keeping the other loads unchanged to balance the lever is 150 cm
When asked how to create an electromagnet, the best answer would be:
"You can create an electromagnet by applying a direct current to a non–magnetic material in order to create an electromagnetic field."
"You can create an electromagnet by covering a wire with insulation and applying a direct electrical current to the magnet."
"You can create an electromagnet by coiling a ferromagnetic material, wrapping in an insulator, and applying a current to the coil."
"You can create an electromagnet by wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current."
Answer:
"You can create an electromagnet by wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current."
Explanation:
An electromagnet is created by coiling a ferromagnetic material with the help of an insulated wire around it and applying a current . Insulated wire carrying current produces magnetic field around it . This field produces magnetic flux in the magnetic material and makes it magnet . When we switch of current , magnetic field ceases to exist and therefore , magnetic material ceases to be a magnet .
Explanation:
Suppose that you measure the length of a spaceship, at rest relative to you, to be 400 m. How long will you measure it to be if it flies past you at a speed of v
Answer:
264 m
Explanation:
The complete question is
Suppose that you measure the length of a spaceship, at rest relative to you, to be 400 m. How long will you measure it to be if it flies past you at a speed of v = 0.75c
using the length contraction relationship,
[tex]l = l_{0} \sqrt{1 - \beta ^{2} }[/tex]
where [tex]\beta = \frac{v}{c}[/tex]
[tex]l[/tex] is the relativistic length
[tex]l_{0}[/tex] is the actual length = 400 m
v is the velocity of the spaceship
c is the speed of light
since v = 0.75c
v/c = 0.75
substituting, we have
[tex]l = 400 * \sqrt{1 - 0.75 ^{2} }[/tex] = 400 x 0.66 = 264 m
Two resistors connected in parallel, with R1 = 150 ohms and R2 = 75 ohms, are connected to a battery that experiences a current of 0.18 A. The current through R1 is _____ A.
Answer:
Explanation:
Given:
Two resistors (Parallel)
R1 = 150 ohms
R2 = 75 ohm
Current (I) = 0.18 A
Find:
Current through R1
Computation:
Common resistance
1/R = 1/R1 + 1/R2
1/R = 1/150 + 1/ 75
R = 50 ohms
V = IR
V = 0.18 x 50
V = 9v
So,
V = IR1
9 = I (150)
Current through R1 = 9 / 150
Current through R1 = 0.06 A
Given 1ft = 12in, how many feet are in 36 inches?
Answer:
Hey there!
1 ft= 12 inches
3 ft= 36 inches.
Let me know if this helps :)
Answer: 3
The formula is to divide by 12
36÷12=3
1ft = 12in
When a p-n-p transistor is operated in saturation region, then its ___________
Answer:
Base-emitter and Base-collector junctions are forward biased
what is the percent uncertainty in the volume of a spherical beach ball whose radius is r = .84 plus or minus .04 m?
Answer:
The percent uncertainty in the volume [tex]\frac{\delta V}{V} * 100 = 14.286\%[/tex]
Explanation:
From the question we are told that
The radius is [tex]r = 0.84 \pm 0.04 \ m[/tex]
From the given value
The uncertainty of radius is [tex]\delta r = 0.04[/tex]
Generally the volume of a spherical beach ball is mathematically represented as
[tex]V = \frac{4\pi }{3}* r^3[/tex]
Now taking the log of both sides
[tex]log V = log [\frac{4\pi}{3} ] * r^3[/tex]
=> [tex]log V = log [\frac{4\pi}{3} ] + log( r^3)[/tex]
=> [tex]log V = log [\frac{4\pi}{3} ] + 3log( r)[/tex]
Differentiating both sides
[tex]\frac{1}{V} \delta V = 0 + 3 [\frac{1}{r} ] \ \delta r[/tex]
Now converting them to percentage by multiplying by 100
[tex]\frac{\delta V}{V} * 100 = [\frac{ 3 \delta r }{r} ] \ * 100[/tex]
=> [tex]\frac{\delta V}{V} * 100 = [\frac{ 3 * 0.04 }{ 0.84} ] \ * 100[/tex]
=> [tex]\frac{\delta V}{V} * 100 = 14.286\%[/tex]
A uniform disk a uniform hoop and a uniform sphere are released at the same time at the top of an inclined ramp. They all roll without slipping in what order do they reach the bottom of the ramp?
a. disk hoop, sphere
b. sphere, hoop, disk
c. hoop, sphere, disk
d. sphere, disk, hoop
e. hoop, disk, sphere
What is a property of “normal force”? a. It always points perpendicular to the contact surface. b. It always points parallel to the contact surface. c. It always points up. d. It always completely counters gravity.
Answer:
a. It always points perpendicular to the contact surface.
Explanation:
"Normal" means perpendicular. Normal forces are always perpendicular to the contact surface.
Which of these particles are equal in number when an atom is neutral?
A. protons, neutrons
B. protons, electrons
C. neutrons, electrons
D. protons, neutrons, electrons
A tank 20 m deep and 7m wide is layered with 8m of oil,6m of water and 5m of mercury.complete total hydroatatic force.(density of oil and mercury is 800 and 13600kg/m respectively ).
Answer:
F = 3.03 10⁷ N
Explanation:
We will eat by calculating the pressure in the tank
P = ρ g h
the pressure totals the sum of the pressure of each liquid
P_total = P_oil + P_water + P_Hg
P_total = ρ_oil g h_oil + ρ_water g h_water + ρ_Hg g h_Hg
P_total = g (ρ_oil h_oil + ρ_water h_water + ρ_Hg h_Hg)
P_total = 9.8 (800 8 + 1000 6 + 13 600 5)
P_total = 7,879 10⁵ Pa
The definition of Pressure is
P = F / A
F = P A
The area of a tank is the area of a circle
A = π r² = π d² / 4
F = P π d² / 4
let's calculate
F = 7,879 10⁵ π 7²/4
F = 3.03 10⁷ N
In this calculation the atmospheric pressure was not taken into account because they ask the hydrostatic pressure
If a ball is accelerating down through the air with no horizontal motion, what must be true about the net forces acting on the ball? (a) The net force on the ball is directed upward. (b) The net force on the ball is zero. (c) The gravitational force is greater than the drag. (d) The drag is greater than the gravitational force.
Answer:
The net force on the ball is zero.
Explanation:
The net force and the acceleration on the falling skydiver is upward. An upward net force on a downward falling object would cause that object to slow down. The skydiver thus slows down. As the speed decreases, the amount of air resistance also decreases until once more the skydiver reaches a terminal velocity.A force can cause a resting object, or it can accelerate a moving object by changing the object's speed or direction. When the forces on an object are balanced, the net force is zero and there is no change in the object's motion. When an unbalanced force acts on an object, the object accelerates.
Two cars collide head on while each is traveling at 60km/h .Suppose all their kinetic energy is transformed into the thermal energy of the wrecks. What is the temperature increase of each car?You can assume that each car's specific heat is that of iron.
Answer:
The temperature rise [tex]\Delta T = 0.3088 \ ^oC[/tex]
Explanation:
From the question we are told that
The speed is [tex]v = 60 \ km /h = 16.67 \ m/s[/tex]
Generally according to the law of energy conservation we have that
The kinetic energy = increase in the internal energy of the car
i,e [tex]\frac{1}{2} * m * v^2 = m * c_p * \Delta T[/tex]
Here [tex]c_p[/tex] of iron is [tex]c_p = 450 \ J/kg K[/tex]
So
[tex]0.5 * 16.67^2 = 450 * \Delta T[/tex]
=> [tex]\Delta T = 0.3088 \ ^oC[/tex]
The temperature increase of each car will be 0.3088 °C.
What is temperature?Temperature directs to the hotness or coldness of a body. In clear terms, it is the method of finding the kinetic energy of particles within an entity. Faster the motion of particles more the temperature.
The given data in the problem is;
v is the velocity= 60 km/h=16.67 m/sec
ΔT is the temperature difference=?
[tex]\rm c_P[/tex] is the specific heat of iron=450 J/KgK
From the law of energy conservation of the energy, the kinetic energy is equal to the increase in the internal energy of the car.
[tex]\rm KE=\triangle E \\\\\ \frac{1}{2} mv^2=mc_p \triangle T \\\\ \triangle T=\frac{v^2}{2C_p} \\\\\ \triangle T=\frac{(16.67)^2}{2\times 450} \\\\ \triangle T=0.3088 ^0\C[/tex]
Hence the temperature increase of each car will be 0.3088 °C.
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An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?
Answer:
1.4E-3J
Explanation:
Given that
Time = 8hrs = 28.8E3 seconds
Intensity= 90dB
D= 0.008m
Radius= 0.004m
So intensity is sound level Bis
10dBlog(I/Io)
I= 10 (B/10dB)Io
= 10( 90/10) x 10^-12
=0.001W/m²
But we know that
I = P/A
P= I πr²
= 5.02 x10^-8W
But energy is power x time
So E= 5.02E-8 x 28.8E3
= 1.4E-3J
Answer:
1.44x10⁻³J
Explanation:
Given :
Time = 8hrs *(3600secs/1hr)= 28.8*10³seconds
Intensity= 90dB
D= 0.008m
Radius=0.008m/2
=0.004m
the sound level in decibel can be expressed below as
I=10dBlog[I/I₀]
where I₀=10⁻¹²/m² which is the refrence intensity
90=10log[I/10⁻¹²]
I=0.001W/m²
we know that intensity of the wave which id the average rate per unit area which energy is transfered can be calculated using below formular
I = P/A
where P= powerr which is renergy transfer at a time
A= area= πr²
making P subject of formular we have
P= I πr²
= 5.02 x10⁻⁸W
Energy =power x time
E=28800*5*10⁻⁸
=0.001443J
therefore,the energy in joules is 1.44x10⁻³J
Jane is sliding down a slide. What kind of motion is she demonstrating? A. translational motion B. rotational motion C. vibrational motion D. transverse motion
Answer:
Transational Motion
Explanation:
Mass on a Spring: A 0.150-kg air track cart is attached to an ideal spring with a force constant (spring constant) of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations
Answer:
The period is [tex]T = 1.286 \ s[/tex]
Explanation:
From the question we are told that
The mass of the spring is [tex]m = 0.150 \ kg[/tex]
The spring constant is [tex]k = 3.58 \ N/m[/tex]
Generally the period is mathematically represented as
[tex]T = 2 \pi \sqrt{ \frac{m}{k} }[/tex]
substituting values
[tex]T = 2 \pi \sqrt{ \frac{ 0.150}{3.58} }[/tex]
[tex]T = 1.286 \ s[/tex]
An electon in a box absorbs light. The longest wavelength in the absorbtion spectrum is 400 nm . How long is the box
Answer:
6.03x 10^-10 m
Explanation:
Given that
E= hc/ wavelength
And also
E= h²n2/8mL²
Equating the two and if we say the transition was from energy level 1 to 2 then
E2 - E1 = h²2/(8mL²) x ( 2² - 1²) = 3h²2/(8mL²)
So
L² = 3 h lambda / (8mc)
= 3 x6.626 10^-34 kg m^2/s x 400 10^-9 m /( 8 x 9.11 x10^-31 kg x3.00 10^8 m/s)
= 36.4 x 10^-20 m^2
L = 6.03 x 10^-10 m
The length of the box that absorbs the light is;
L = 6.03 × 10^(-10) m
We are given;
Longest wavelength of spectrum; λ = 400 nm = 400 × 10^(-9) m
Now, the formula for energy of quantization is;
E = h²n²/8mL²
Also, Energy of a photon is;
E = hc/λ
Thus;
hc/λ = h²n²/8mL²
h will cancel out to give;
c/λ = hn²/8mL²
Where;
h is Planck's constant = 6.626 × 10^(-34) m².kg/s
c is speed of light = 3 × 10^(8) m/s
λ is wavelength = 400 × 10^(-9) m
L is length of box
m is mass of electron = 9.11 × 10^(-31) kg
n² is difference in energy levels = (2² - 1²) = 3
Making L the subject gives;
L = √(hn²λ/8mc)
Thus;
L = √((6.626 × 10^(-34) × 3 × 400 × 10^(-9))/(8 × 9.11 × 10^(-31) × 3 × 10^(8))
L = √(3.636663007683 × 10^(-19))
L = 6.03 × 10^(-10) m
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You throw a balloon that floats in the air with a velocity of 2 m / s south . If the wind speed is 5 m / s west , how far south will the balloon travel after 2 seconds ?
Answer:
The distance traveled by the balloon is 10.77 m
Explanation:
velocity of the ball, [tex]v_b[/tex] = 2 m/s south
velocity of the air, [tex]v_a[/tex] = 5 m/s west
To determine the distance the balloon will travel after 2 seconds, first determine the resultant velocity of the balloon.
| 2m/s
|
|
↓
5m/s ←------------------
the two velocities forms a right angled triangle and the resultant will be the hypotenuses side of the triangle.
R² = 5² + 2²
R² = 29
R = √29
R = 5.385 m/s
The distance traveled by the balloon is calculated as;
d = R x t
where;
t is time of the motion = 2 seconds
d = 5.385 x 2
d = 10.77 m
Therefore, the distance traveled by the balloon is 10.77 m.
A paper pinwheel is spinning in the wind. Which statement is correct about the forces responsible for the rotation?
A paper pinwheel is spinning in the wind.
Which statement is correct about the forces responsible for the rotation?
The components of gravity and the force of wind that point through the pivot are responsible for the rotation.
Only the perpendicular component of wind is responsible for the rotation, because gravity points downward.
Only the perpendicular component of gravity is responsible for the rotation, because wind points toward the pivot.
The perpendicular components of gravity and the force of wind are responsible for the rotation.
Answer:
Only the perpendicular component of gravity is responsible for the rotation because wind points toward the pivot.
Explanation:
A pinwheel is a plaything that is made up of paper that is designed to spin when the wind comes in contact with it. The paper is held fast to its axle by a pin which enables it to spin.
Therefore, if the pinwheel is spun anti-clockwise, it brings electrical energy, converting the wind energy and only the perpendicular component of gravity is responsible for the rotation because wind points toward the pivot.
What is the power in a circuit that has a current of 12 amps and a resistance of 100 ohms? a. 14,400 watts b. 8.3 watts c. 144 watts d. 1200 watts
Answer:
a. 14,400 Watts
Explanation:
Power is current times voltage.
P = IV
Voltage is current times resistance.
V = IR
Substitute:
P = I²R
P = (12 A)² (100 Ω)
P = 14,400 W
A bar of silicon is 4 cm long with a circular cross section. If the resistance of the bar is 280 Ω at room temperature, what is the cross-sectional radius of the bar?
Answer:
r = 17.05 cm
Explanation:
Given that,
Length of silicon bar is 4 cm or 0.04 m
Resistance of the bar is 280 ohms
We know that the resistivity of the silicon is 640 Ωm
We need to find the cross-sectional radius of the bar. Let it is r.
Using definition of resistance of an object. It is given by :
[tex]R=\rho\dfrac{l}{A}[/tex]
A is area of bar, A = πr²
So,
[tex]R=\rho\dfrac{l}{\pi r^2}\\\\r^2=\dfrac{\rho l}{R\pi}\\\\r^2=\dfrac{640\times 0.04}{280\pi}\\\\r=0.1705\ m\\\\r=17.05\ cm[/tex]
So, the cross-sectional radius of the bar is 17.05 cm.
Two identical balls are thrown directly upward, ball A at speed v and ball B at speed 2v, and they feel no air resistance. Which statement about these balls is correct
Answer:
B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy.
Explanation:
The complete question is
Two identical balls are thrown directly upward, ball A at speed v and boll B at speed 2v. and they feel no air resistance. Which statement about these balls is correct? A) Ball B will go twice as high as ball A because it had twice the initial speed. B) Ball B will go four times as high as ball A because it had four times the initial kinetic energy. C) The balls will reach the same height because they have the same mass and the same acceleration. D) At its highest point, ball B will have twice as much gravitational potential energy as ball A because it started out moving twice as fast. E) At their highest point, the acceleration of each ball is instantaneously equal to zero because they stop for an instant.
According to conservation of energy, the mechanical energy of a ball thrown up is equal to the sum of the potential energy and the kinetic energy. At its highest point, all the mechanical energy will be equal to the potential energy. At the instant when it was thrown, all the mechanical energy is proportional to its kinetic energy, which will be proportional to the potential energy at the highest point. Also, potential energy is proportional to the maximum height reached.
We know that the kinetic energy is given as [tex]\frac{1}{2}mv^{2}[/tex]
where
m is the mass of the balls, which is the same for both ball,
and v is the velocity.
We can see that the kinetic energy is proportional to the square of the initial velocity with which the ball is thrown.
For the ball A thrown with velocity v, the kinetic energy is proportional to [tex]v^{2}[/tex],
and for the ball B with velocity 2v, kinetic energy is proportional to [tex]4v^{2}[/tex]
comparing the two, we'll see that the ball B will had 4 times the energy of ball A. Therefore ball B will go four times as high as ball A because it had four times the initial kinetic energy
The wave function for a particle must be normalizable because:________ a. the particle's angular momentum must be conserved. b. the particle cannot be in two places at the same time. c. the particle must be somewhere. d. the particle's momentum must be conserved. e. the particle's charge must be conserved
Answer:
C the particle must be somewhere.
Explanation:
This is because normalization of wave function means the maximum probability of finding a particle in a region is 1. And a Wave function describes the probability of finding a particle in region. Also Since it is a probability distribution, its integral over all space must be 1, explaining that the probability that the particle is somewhere and thus it must integrate to 1, meaning it must be it must be normalizable