The parallel axis theorem relates Icm, the moment of inertia of an object about an axis passing through its center of mass, to Ip, the moment of inertia of the same object about a parallel axis passing through point p. The mathematical statement of the theorem is Ip=Icm+Md2, where d is the perpendicular distance from the center of mass to the axis that passes through point p, and M is the mass of the object. Part A Suppose a uniform slender rod has length L and mass m. The moment of inertia of the rod about about an axis that is perpendicular to the rod and that passes through its center of mass is given by Icm=112mL2.
Required:
Find Iend, the moment of inertia of the rod with respect to a parallel axis through one end of the rod.
Answer:
I = ⅓ m L²
Explanation:
They tell us to use the parallel axes theorem
I = [tex]I_{cm}[/tex] + M d²
The moment of inertia of a rod with respect to the center of mass is
I_{cm} = [tex]\frac{1}{12}[/tex] m L²
the distance from the center of mass that coincides with its geometric center to the ends of the rod is
d = L / 2
we substitute
I =[tex]\frac{1}{12}[/tex] m L² + m (L/2)²
I = m L² ( [tex]\frac{1}{12} + \frac{1}{4}[/tex] )
I = m L² ( [tex]\frac{1+3}{12}[/tex] )
I = ⅓ m L²
If the outermost electron in an atom is excited to a very high energy state, its orbit is far beyond that of the other electrons. To a good approximation, we can think of the electron as orbiting a compact core with a charge equal to the charge of a single proton. The outer electron in such a Rydberg atom thus has energy levels corresponding to those of hydrogen.
Sodium is a common element for such studies. How does the radius you calculated in part A compare to the approximately 0.20 nm radius of a typical sodium atom?
r100/rNa = _______.
Answer:
the calculated ratio to the radius of the sodium [tex]r_{100[/tex] / [tex]r_{Na[/tex] is 2645.0
Explanation:
Given the data in the question;
the calculated ratio to the radius of the sodium = [tex]r_{100[/tex] / [tex]r_{Na[/tex]
so from here we can write the number of energy states as 100
The number of energy states; n = 100
A;
We know that the radius of the sodium atom is;
[tex]r_n[/tex] = n²α₀
Now, the value of the Bohr radius; α₀ = 5.29 × 10⁻¹¹ m
so lets determine the radius of the sodium atom; by substituting in our values;
[tex]r_{100[/tex] = (100)² × (5.29 × 10⁻¹¹ m )
[tex]r_{100[/tex] = 5.29 × 10⁻⁷ m
B
given that, the theoretical value of the radius of the sodium is;
[tex]r_{Na[/tex] = 0.2 nm = 2 × 10⁻¹⁰ m
so we calculate the ratio of the radii of the sodium;
[tex]r_{100[/tex] / [tex]r_{Na[/tex] = ( 5.29 × 10⁻⁷ m ) / ( 2 × 10⁻¹⁰ m )
[tex]r_{100[/tex] / [tex]r_{Na[/tex] = 2645.0
Therefore, the calculated ratio to the radius of the sodium [tex]r_{100[/tex] / [tex]r_{Na[/tex] is 2645.0
A student at another university repeats the experiment you did in lab. Her target ball is 0.860 m above the floor when it is in the target holder and the steel ball she uses has a mass of 0.0120 kg. She finds that the target ball travels a distance of 1.50 m after it is struck. Assume g = 9.80 m/s2. What is the kinetic energy (in joules) of the target ball just after it is struck?
Answer:
K = 0.076 J
Explanation:
The height of the target, h = 0.860 m
The mass of the steel ball, m = 0.0120 kg
Distance moved, d = 1.50 m
We need to find the kinetic energy (in joules) of the target ball just after it is struck. Let t is the time taken by the ball to reach the ground.
[tex]h=ut+\dfrac{1}{2}at^2\\\\t=\sqrt{\dfrac{2h}{g}}[/tex]
Put all the values,
[tex]t=\sqrt{\dfrac{2\times 0.860 }{9.8}} \\\\=0.418\ s[/tex]
The velocity of the ball is :
[tex]v=\dfrac{1.5}{0.418}\\\\= $$3.58\ m/s[/tex]
The kinetic energy of the ball is :
[tex]K=\dfrac{1}{2}mv^2\\\\K=\dfrac{1}{2}\times 0.0120\times 3.58^2\\\\=0.076\ J[/tex]
So, the required kinetic energy is 0.076 J.
Điện tích Q = 8. 10-6C đặt cố định trong
không khí , điện tích q = - 10. 10-6C di
chuyển trên đường thẳng xuyên qua Q,
từ M cách Q một khoảng 100cm, lại
gần Q thêm 50cm. Tính công của lực
điện trường trong dịch chuyển đó?
Answer:
0.72J
Explanation:
Hey, can a physics major help me?
I have been wondering about the exact difference between theories laws facts and hypothosis.
I know the general layout but I am still a bit confused.
100 points for answering and brainly if it is a good one.
Answer:
A hypothesis is a limited explanation of a phenomenon; a scientific theory is an in-depth explanation of the observed phenomenon. A law is a statement about an observed phenomenon or a unifying concept
Answer:
Explanation:
will try 2 explain fact, hypothesis, theory n law
fact is the starting pt: e.g. apple falls from tree
hypothesis tries 2 explain a fact: e.g. there is a force pulling down apple
theory is a complete explanation w/ equations n stuff: e.g. Newton came up w/ theory of gravitational attraction force
law is a theory dat has been proven right through tests n experiments: Newton's gravity theory had been proven right in many many tests.
Two astronauts, each having a mass of 88.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.40 m/s. Treating the astronauts as particles, calculate each of the following.
a. the magnitude of the angular momentum of the system
b. the rotational energy of the system
c. What is the new angular momentum of the system?
d. What are their new speeds?
e. What is the new rotational energy of the system
Answer:
a) L = 4.75 103 kg m² / s, b) K_total = 2.57 10³ J,
c) L₀ = L_f =4.75 103 kg m² / s, d) K = 1.03 10⁴ J, K = 1.03 10⁴ J
Explanation:
a) the angular momentum is the sum of the angular momentum of each astronaut
the distance is measured from the center of the circle r = 10/2 = 5.0 m
L = 2m v r
L = 2 88.0 5.40 5.0
L = 4.75 103 kg m² / s
b) rotational kinetic energy
K = ½ I w²
As there are two astronauts, the total energy is the sum of the energy of each no.
The moment of inertia of a point mass
I = m r²
I = 88 5²
I = 2.2 10³ kg m²
the angular velocity is given by
v = w r
w = v / r
w = 5.40 / 5
w = 1.08 rad / s
the kinetic energy of the system
K_total = 2 K
K_total = 2 (½ I w²)
K_total = 2.2 10³ 1.08²
K_total = 2.57 10³ J
c, d) as astronauts are isolated in space, these speeds do not change unless there is an interaction between them, for example they approach each other, suppose they reduce their distance by half
r = 2.5 m
I = 88 2.5²
I = 5.5 10² kg m²
for the change in angular velocity let us use the conservation of moment
L₀ = L_f
2Io wo = 2 I w
w = Io / I wo
w = 2.2 10³ / 5.5 10² 1.08
w = 4.32 rad / s
linear velocity is
v = w r
v = 4.32 2.5
K = 1.03 10⁴ J
the kinetic energy of the system is
K = 5.5 10² 4.32²
K = 1.03 10⁴ J
What is 1 second….???? Give a meaningful answer…..
Explanation:
.....................................
Answer:
1 second is defined as 1/86400th part of a mean solar day.
A 50-kg copper block initially at 140°C is dropped into an insulated tank that contains 90 L of water at 10°C. Determine the final equilibrium tempera
Answer:
16.33°C
Explanation:
Applying,
Heat lost by copper = heat gained by water
cm(t₁-t₃) = c'm'(t₃-t₂).............. Equation 1
Where c = specific heat capacity of copper, m = mass of copper, c' = specific heat capacity of water, m' = mass of water, t₁ = initial temperature of copper, t₂ = initial temperature of water, t₃ = final equilibrium temperature.
From the question,
Given: m = 50 kg, t₁ = 140°C, m' = 90 L = 90 kg, t₂ = 10°C
Constant: c = 385 J/kg°C, c' = 4200J/kg°C
Substitute these values into equation 1
50(385)(140-t₃) = 90(4200)(t₃-10)
(140-t₃) = 378000(t₃-10)/19250
(140-t₃) = 19.64(t₃-10)
140-t₃ = 19.64t₃-196.6
19.64t₃+t₃ = 196.4+140
20.64t₃ = 336,4
t₃ = 336.4/20.6
t₃ = 16.33°C
In a 2-dimensional Cartesian coordinate system the y-component of a given vector is equal to that vector's magnitude multiplied by which trigonometric function, with respect to the angle between vector and y-axis?
a. sine
b. cosine
c. tangent
d. cotangent
Answer:
Option b, cosine.
Explanation:
Below you can see an image that illustrates this situation.
Remember that for a triangle rectangle with a given angle θ, we have:
Cos(θ) = (adjacent cathetus)/(hypotenuse)
In the image, you can see a vector of magnitude M, and the angle θ defined between the vector and the positive y-axis.
In this case, the y-component is the adjacent cathetus and the hypotenuse is the magnitude of the vector.
Then we will have:
Cos(θ) = (adjacent cathetus)/(hypotenuse) = y/M
solving that for y, we get:
y = Cos(θ)*M
Then the y-component is the vector's magnitude multiplied by the cosine of the angle between the vector and the y-axis.
The correct option is b.
Answer:
(b) cosine
Explanation:
In a 2-dimensional Cartesian coordinate system, a vector has a x-component and/or a y-component. To get these components, the magnitude of the vector is resolved with respect to the x-axis and the y-axis by multiplying it (the magnitude) by some trigonometric function with respect to the angle between the vector and the x or y axis.
For example, given a vector A of magnitude A which makes an angle α with the x-axis and an angle β with the y-axis, the x and y components of the vector A can be found as follows;
i. x-component is given by [tex]A_{x}[/tex]
[tex]A_{x}[/tex] = A cos α (with respect to the angle between A and the x-axis) or
[tex]A_{x}[/tex] = A sin β (with respect to the angle between A and the y-axis)
ii. y-component is given by [tex]A_{y}[/tex]
[tex]A_{y}[/tex] = A sin α (with respect to the angle between A and the x-axis) or
[tex]A_{y}[/tex] = A cos β (with respect to the angle between A and the y-axis)
Therefore, the y-component of a vector in a 2-dimensional Cartesian coordinate is given by the product of the magnitude of the vector and the cosine of the angle between the vector and the y-axis.
6)An electric field of 6 N/C points in the positive X direction. What is the electric flux through a surface that is 4 m2, if its surface normal isin the XY plane and along a line that isinclined at 60 degrees to the positive Y axisand 30 degrees to the positive X axis
Answer:
Flux is 21 Nm^2/C.
Explanation:
Electric field, E = 6 N/C along X axis
Electric filed vector, E = 6 i N/C
Area, A = 4 square meter
Area vector
[tex]\overrightarrow{A} = 4 (cos30 \widehat{i} + sin 30 \widehat{j})\\\\\overrightarrow{A} = 3.5 \widehat{i} + 2 \widehat{j}\\[/tex]
The flux is given by
[tex]\phi= \overrightarrow{E}.\overrightarrow{A}\\\\\phi = 6 \widehat{i} . \left (3.5 \widehat{i} + 2 \widehat{j} \right )\\\\\phi = 21 Nm^2/C[/tex]
Calculate the forces that the supports \rm A and \rm B exert on the diving board shown in when a 58-\rm kg person stands at its tip.
To understand the nature of electric current and the conditions under which it exists.Electric current is defined as the motion of electric charge through a conductor. Conductors are materials that contain movable charged particles. In metals, the most commonly used conductors, such charged particles are electrons. The more electrons that pass through a cross section of a conductor per second, the greater the current. The conventional definition of current isI=Qtotal/Δtwhere I is the current in a conductor and Qtotalis the total charge passing through a cross section of the conductor during the time interval Δt.The motion of free electrons in metals not subjected to an electric field is random: Even though the electrons move fairly rapidly, the net result of such motion is that Qtotal=0 (i.e., equal numbers of electrons pass through the cross section in opposite directions). However, when an electric field is imposed, the electrons continue in their random motion, but in addition, they tend to move in the direction of the force applied by the electric field.In summary, the two conditions for electric current in a material are the presence of movable charged particles in the material and the presence of an electric field.Quantitatively, the motion of electrons under the influence of an electric field is described by the drift speed, which tends to be much smaller than the speed of the random motion of the electrons. The number of electrons passing through a cross section of a conductor depends on the drift speed (which, in turn, is determined by both the microscopic structure of the material and the electric field) and the cross-sectional area of the conductor.In this problem, you will be offered several conceptual questions that will help you gain an understanding of electric current in metals.You are presented with several long cylinders made of different materials. Which of them are likely to be good conductors of electric current?
Answer:
The metallic conductors
Explanation:
The metallic conductors has more free electrons that are movable, thus they conduct electricity better.
can someone help plz
Answer:
29.15 N
Explanation:
Applying,
Pythagoras theorem,
a² = b²+c²................ Equation 1
Where a = resultant of the two forces, b = first force, c = second force.
From the diagram,
Given: b = 15 N, c = 25 N
Substitute these values into equation 1
a² = 15²+25²
a² = 225+625
a² = 850
a = √850
a = 29.15 N
Hence the resultant of the two forces is 29.15 N
Which of these statements is true?
a) Neither (a) nor (b) is true.
b) Both (a) and (b) are true.
c) Electric current is stored in the battery of a circuit.
d) Electric current is the flow of electrons in a circuit.
Answer:
d electric current is the flow of electrons in a circuit
When a single high-resistance (long) bulb is connected to a 1.5 V battery, the current through the battery is about 80 mA. If you add another high-resistance (long) bulb in parallel, the battery current of course increases to 160 mA. Select all of the true statements given this situation.
a. The battery is ohmic.
b. The battery is not ohmic.
c. Current through the battery is proportional to ΔV across the battery.
d. Current through the battery is not proportional to ΔV across the battery.
e. The battery always puts out the same current.
Answer:
a) True. The battery obeys ohm's law, it is formed by an ideal source with a fixed internal resistance
c) True. Ohm's law is V = iR therefore voltage and current are proportional
Explanation:
In this problem let's analyze the load of the system, when a resistance is placed the current is 80 mA, if we place two resistors in parallel the voltage remains the same, but the current is divided between each resistance (bulb), therefore the current in the battery it must be 160 mA
Let's analyze the answers
a) True. The battery obeys ohm's law, it is formed by an ideal source with a fixed internal resistance
b) false
c) True. Ohm's law is V = iR therefore voltage and current are proportional
d) False
e) False. The current coming out of the battery is proportional to the load placed
Convert Rev/min to rad/s x 2pie/60?
Anyone knows this please?
Answer:
Thus, [tex]\frac{1 rev}{min} =\frac{2\pi}{60} rad/s[/tex]
Explanation:
The angular speed is defined as the rate of change of angular velocity.
Its SI unit is rad/s and other units are rev/min or rev/s.
[tex]\frac{1 rev}{min } = \frac{1 rev}{60 sec}\\\\1 rev = 2\pi rad\\\\So\\\\\frac{1 rev}{min} = \frac{2\pi}{60} rad/s[/tex]
A certain electric stove has a 16 Ω heating element. The current going through the element is 15 A. Calculate the voltage across the element.
Answer:
V = 240V
Explanation:
V = I*R
V = 15A*16ohms
V = 240V
A crucible (container) of molten metal has an open top with an area of 5.000 m^2. The molten metal acts as a blackbody radiator. The intensity spectrum of its radiation peaks at a wavelength of 320 nm. What is the temperature of that blackbody?
Answer:
T = 9056 K
Explanation:
In the exercise they indicate that the body can be approximated by a black body, for which we can use the Wien displacement relation
λ T = 2,898 10⁻³
where lam is the wavelength of the maximum emission
T = 2,898 10⁻³ /λ
let's calculate
T = 2,898 10⁻³ / 320 10⁻⁹
T = 9.056 10³ K
T = 9056 K
A car of mass M traveling with velocity v strikes a car of mass M that is at rest. The two cars’ bodies mesh in the collision. The loss of the kinetic energy the moving car undergo in the collision is
a) a quarter of the initial kinetic energy.
b) half of the initial kinetic energy.
c) all the initial kinetic energy.
d) zero.
Answer:
the correct answer is B
Explanation:
Let's propose the solution of the problem, for this we form a system formed by the two cars, so that the forces during the collision are internal, the momentum is conserved
instantly starts. Before the crash
p₀ = M v +0
final instant. After the crash
m_f = (M + M) v_f
the moment is preserved
p₀ = p_f
M v = 2 M v_f
v_f = v / 2
let's look for kinetic energy
before the crash
K₀ = ½ M v²
after the crash
K_f = ½ 2M (v_f)²
K_f = ½ 2M (v/2)²
K_f = (½ M v²) ½
K_f = K₀ / 2
therefore the correct answer is B
6. Which of these contain muscles that are not under the mind's control? (Select all that apply.)
Answer:
a c
Explanation:
edu 2021
The magnetic force exerted on a 1.2-m segment of straight wire is 1.6 N. The wire carries a current of 3.0 A in a region with a constant magnetic field of 0.50 T. What is the angle between the wire and the magnetic field
Answer:
The angle between the wire and the magnetic field is 62.74⁰
Explanation:
Given;
length of the wire, L = 1.2 m
force exerted on the wire, F = 1.6 N
current carried by the wire, I = 3.0 A
magnetic field strength, B = 0.5 T
The magnitude of a magnetic force on a current-carrying conductor is given as;
F = BIL(sinθ)
[tex]sin(\theta) = \frac{F}{BIL} = \frac{1.6}{0.5 \times 3 \times 1.2} = 0.8889 \\\\sin(\theta) =0.8889\\\\\theta = sin^{-1} (0.8889)\\\\\theta = 62.74^0[/tex]
Therefore, the angle between the wire and the magnetic field is 62.74⁰
An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Can you determine from this information if F is a conservative or nonconservative force?
Answer:
F is non-conservative.
If F were conservative no work would be done in moving back to the original point. F dot S = W if the net distance is zero the work done is zero for a conservative force
An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Force, F is non-conservative.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Moving back to the initial point wouldn't need any labor if F were a conservative function. Given that F.S = W, a conservative force does not exert any effort if the net distance is zero.
An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Force, F is non-conservative.
To learn more about force refer to the link:
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Henry, whose mass is 95 kg, stands on a bathroom scale in an elevator. The scale reads 830 N for the first 3.6 s after the elevator starts moving, then 930 N for the next 3.6 s.
What is the elevator's velocity 4.0 s after starting?
Answer: [tex]3.816\ m/s[/tex]
Explanation:
Given
Mass of Henry is 95 kg
Normal weight of Henry is [tex]mg=95\times 9.8=931\ N[/tex]
The scale reads the weight as 830 N for first 3.6 s i.e. less than the normal weight i.e. Elevator is moving downwards
Apparent weight is given by
[tex]\Rightarrow 830=m(g-a)\quad [a=\text{acceleration of elevator}]\\\Rightarrow 830=95(9.8-a)\\\Rightarrow 8.736=9.8-a\\\Rightarrow a=1.06\ m/s^2[/tex]
After 3.6 s weight becomes 930 N which is approximately equal to normal weight. It implies elevator starts moving with constant velocity i.e. no acceleration.
If elevator starts from rest, it velocity after 3.6 s is
[tex]v=u+at\\\Rightarrow v=0+1.06(3.6)\\\Rightarrow v=3.816\ m/s[/tex]
This velocity will remain continues as after 3.6 s, elevator starts moving with constant velocity.
what is the escape velocity of earth
Answer:
The Escape Velocity Of Earth is
11.19 km/s
Explanation:
Hope it Helps!
A particle moves along a straight line with equation of motion s = f(t), where s is measured in meters and t in seconds. Find the velocity and speed (in m/s) when t = 5. f(t) = 18 + 48/t + 1
Answer:
The velocity of the particle = -1.92 m/s
The speed of the particle = 5.72 m/s
Explanation:
Given equation of motion;
[tex]f(t) = 18 \ + \ \frac{48}{t} \ + \ 1[/tex]
Velocity is defined as the change in displacement with time.
[tex]V = \frac{df(t)}{dt} = -\frac{48}{t^2} \\\\at \ t = 5 \ s\\\\V = -\frac{48}{5^2} = \frac{-48}{25} = - 1.92 \ m/s[/tex]
The distance traveled by the particle in 5 s:
[tex]s = f(5) = 18 + \frac{48}{5} + 1\\\\s= 28.6 \ m[/tex]
The speed of the particle when t = 5s
[tex]Speed = \frac{28.6}{5} = 5.72 \ m/s[/tex]
A 1000-kg car rolling on a smooth horizontal surface ( no friction) has speed of 20 m/s when it strikes a horizontal spring and is brought to rest in a distance of 2 m What is the spring’s stiffness constant?
Explanation:
kinetic energy was converted to potential energy in the spring.
the answer is in the above image
For an object with a given mass on Earth, calculate the weight of the object with the mass equal in magnitude to the number representing the day given in part 3 in kilograms using the formula F=W=mg. On the surface of the Earth g=9.8m/s^2
Answer: The weight of the object is 29.4 N
Explanation:
To calculate the weight of the object, we use the equation:
[tex]W=m\times g[/tex]
where,
m = mass of the object = 3 kg
g = acceleration due to gravity = [tex]9.8m/s^2[/tex]
Putting values in above equation, we get:
[tex]W=3kg\times 9.8m/s^2\\\\W=29.4N[/tex]
Hence, the weight of the object is 29.4 N
Two parallel circular plates with radius carrying equal-magnitude surface charge densities of are separated by a distance of How much stored energy do the plates have? A. 120 B. 360 C. 12 D. 37
Answer:
I guess it is A. I am not sure
A puck moves 2.35 m/s in a -22.0 direction. A hockey stick pushes it for 0.215 s, changing its velocity to 6.42 m/s in a 50 degree direction. What was the direction of the acceleration?
Answer:
48.9 is the answer I think !
Answer:
28.4
Explanation:
A conducting sphere of radius R carries an excess positive charge and is very far from any other charges. Draw the graphs that best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere?
Answer:
See annex
Explanation:
By convention potential at ∞ V(∞ ) = 0
As the distance from the sphere decreases the potential increases up to the point d = R ( R is the radius of the sphere. That potential remains constant while d = R and becomes 0 inside the sphere where there is not free charges and therefore the electric field is 0 and so is the potential.
I am sorry I could not make a better graph
The graph that best illustrates the potential (relative to infinity) produced by this sphere as a function of the distance r from the center of the sphere is attached as an image below
[tex]V = \frac{KQ}{R}[/tex]
for r <= R
[tex]V = \frac{KQ}{r}[/tex]
for r > R
Therefore the graph will be
For more information on potentials as function of distance
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