The rotational inertia about an axis tangent to the sphere of the given mass and radius is ⁷/₅MR².
Parallel axis theoremAccording to parallel axis theorem, the moment of inertia of a body about any axis is equal to the sum of the product of its mass and the square of the distance between the two parallel axis and the moment of inertia of the body about a parallel axis passing through its centre of mass.
The moment of inertia of the sphere about its parallel axis passing through its centre of mass = ²/₅MR²
The product of its mass and the square of the distance between the two parallel axis = MR²
Rotational inertia about an axis tangent to the sphereMoment of inertia about an axis tangent to the sphere = MR² + ²/₅MR²
= ⁷/₅MR²
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The rotational inertia of a sphere of given mass and radius along a tangent axis is [tex]\rm \frac{7}{5} MR^2[/tex].
What is a moment of inertia?The sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation expresses a body's tendency to resist angular acceleration.
The given data in the problem is;
M is the sphere's mass.
R is the radius of a sphere
According to the parallel axis theorem,The rotational inertia of a sphere of given mass and radius along a tangent axis is found as;
[tex]\rm I=MR^2+\frac{2}{5} MR^2 \\\\ I=\frac{7}{5} MR^2[/tex]
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If a 5-kg object experiences a 10-N force for a duration of 0. 10-second then what is the impulse exerted by the force on the object? What is the momentum change of the object? What is the change in velocity for the object?
Answer:
orce = rate of change of momentum which is m a if the mass is constant
10 Newtons = change of momentum/0.10 second
so change of momentum = 1 kg m/s
by the way the change in speed would be 1/5 = .2 m/s
Explanation:
If a 5-kg object experiences a 10-N force for a duration of 0. 10-second then the impulse exerted by the force on the object would be 1 Ns, and the change in the momentum would be 1 Ns.
What is momentum?It can be defined as the product of the mass and the speed of the particle, it represents the combined effect of mass and the speed of any particle, and the momentum of any particle is expressed in Kg m/s unit.
As given in the problem If a 5-kg object experiences a 10-N force for a duration of 0. 10-second then we have to find out what the impulse exerted by the force on the object.
P = force × time
= 10 × 0.1
= 1 Ns
Thus, If a 5-kg object experiences a 10-N force for a duration of 0. 10-second then the impulse exerted by the force on the object would be 1 Ns, and the change in the momentum would be 1 Ns.
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Is the moons diameter about the same as the United States
Answer:
the Moon is smaller in diameter than the United States
however. The United States is 2,545 km / 1,582 mi from north to south, and thus, the Moon is smaller across than the United States is wide.
Answer:
The moon is smaller than the earth.
Explanation:
Moon's Diameter is 2,159.1 mi
Earth's Diameter is 7,917.5 mi
How you get a bucket of KFC past airport security?
Answer:
I am not sure in regards to other countries but USA let's anyone allow to take fried chicken.
Explanation:
Yes, the Transportation Security Administration (TSA) will allow you to bring fried chicken through airport security in your carry-on baggage. You can bring both homemade and takeout fried chicken through the TSA checkpoint. If the fried chicken isn’t already pre-packaged, it should be wrapped or placed in a resealable bag or container with a secure lid. There is no limit to the quantity of fried chicken you can bring in your carry-on: You can pack as much fried chicken as you’d like and will fit into your allowable hand luggage.
An object moving in the xy-plane is subjected to the force f⃗ =(2xyı^ 3yȷ^)n, where x and y are in m
The work done on the object moving in the xy-plane that is subjected to the given applied force is determined as (2ab²i + 3b²j) J.
Magnitude of the force on the objectThe magnitude of the force on the object is calculated as follows;
f = (2xyi + 3yj)
when;
x = a, and y = b
f = (2abi + 3bj)
Work done by the forceThe work done the applied force is the product of force and displacement of the object.
W = fΔs
where;
Δs is displacement of the objectΔx = a - a = 0
Δy = 0 - b = -b
Δs = √(Δx² + Δy²)
Δs = √(-b)²
Δs = b
W = (2abi + 3bj) x b
W = (2ab²i + 3b²j) J
Thus, the work done by the applied force on the object is (2ab²i + 3b²j) J.
The complete question is below;
An object moving in the xy-plane is subjected to the force f = (2xyi + 3yj), where x and y are in m. The particle moves from the origin to the point with coordinates (a, b) by moving first along the x-axis to (a, 0), then parallel to the y-axis. How much work does the force do?
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The work done on an item moving in the xy-plane that is subjected to a particular force is found as (2ab²i + 3b²j) J.
What is work done?Work done is defined as the product of applied force and the distance through which the body is displaced on which the force is applied.
Work may be zero, positive, and negative.it depends on the direction of the body displaced. if the body is displaced in the same direction of the force, it will be positive.
The given data in the problem is;
F is the force applied; f⃗ = (2xyi + 3yj)
Work done is found as the product of force and the body displacement;
[tex]\rm W = F \triangle S[/tex]
As the object is moving in the xy- plane. Displacement in the x direction;
[tex]\rm \triangle x = a-a \\\\ \triangle x =0[/tex]
Displacement in the y direction;
[tex]\rm \triangle y = 0-b \\\\ \rm \triangle y = -b \\\\[/tex]
The net displacement in the xy plane is;
[tex]\rm \triangle s= \sqrt{(\triangle x)^2+(\triangle y)^2 } \\\\\ \rm \triangle s= \sqrt{(0)^2+(-b)^2 } \\\\\ \triangle s= \sqrt{b^2} \\\\ \triangle s=b[/tex]
The work done is found as;
[tex]\rm W= F \triangle S \\\\ W=( 2 ab \vec i+3b \vec j) \triangle S\\\\ W= W=( 2 ab \vec i+3b \vec j) b \\\\\ W=(2ab^2 \vec i + 3b^2 \vec j)\ J[/tex]
Hence, the work done on an item moving in the xy-plane will be,[tex]\rm W=(2ab^2 \vec i + 3b^2 \vec j)\ J[/tex]
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What happens when red, blue, and green light come together?
Answer:
I believe if red, blue, and green light come together it would produce White light.
Answer:
you get a light white
Explanation:
2. A spring has a spring constant of 80 N∙m−1. What is the force required to (a) compress the spring by 5 cm and (b) expand the spring by 15 cm?
Please show all your work.
#a
5cm=0.05mForce:-
F=-kxF=-80(0.05)F=-4N#b
15cm=0.15mForce:-
F=-kxF=-80(0.15)F=-12NPure substances can be made of atoms that are attracted to each other or atoms that are not attracted to each other. Which type of pure substance can create elaborate structures? (1 point)
Atoms that are attracted to each other because the bonds that form between them can support the creation of the structure.
Atoms that are attracted to each other because they will mix together to form a mixture with a different structure.
Atoms that are not attracted to each other because they will form bonds with each other and create a larger structure.
Atoms that are not attracted to each other because they will stay still and end up laying on top of each other.
Answer: atoms that are attracted to each other because the bonds that form between them can support the creation of the structure
Explanation:
A concave makeup mirror has a radius of curvature equal to 40 cm. How far away must your face be from the mirror so that your virtual image is twice the size of your actual face?.
Answer: 10 cm
Explanation:
[tex]$$The focal length is: \\ \\ \begin{aligned}f &=\frac{R}{2} \\&=-\frac{46}{2} \\f &=-20 \mathrm{~cm}\end{aligned}$$[/tex]
[tex]$$ Since the image is virtual: \\ \\ :\begin{aligned}\frac{v}{u} &=m \\\Rightarrow & v=m u \\\Rightarrow &v=2 u\end{aligned}$$[/tex]
[tex]$$ Using: \\ \\ \begin{aligned}&\frac{1}{l}=\frac{1}{v}+\frac{1}{u} \\&\frac{1}{20}=-\frac{1}{2 u}+\frac{1}{u} \\&\frac{1}{2 u}=\frac{1}{-20} \\&\Rightarrow u=-10 \\&\therefore u=10 \mathrm{~cm}\end{aligned}$$[/tex]
Therefore, you must be 10 cm away from the mirror so that your virtual image is twice the size of your actual face
After hearing about an accident on his normal route, mr. gujral checks for alternate routes to get to work. what type of circuit does this traffic situation model? a series circuit because there is more than one path a series circuit because there is only one path a parallel circuit because there is more than one path a parallel circuit because there is only one path
The type of circuit does this traffic situation model will be a parallel circuit because there is more than one path.
What is a parallel circuit?A parallel circuit has branches that split the current such that just a portion of it passes through each branch.
The voltage or potential difference between each branch of a parallel circuit is the same, but the currents might differ.
A parallel circuit is having more than one path in order to reach it on time he has to take a different path.
Hence the type of circuit does this traffic situation model will be a parallel circuit because there is more than one path.
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Answer:
C) a parallel circuit because there is more than one path
Explanation: edge
The game starts with the serve on the left side of the court.
O
True
O
False
Answer:
Explanation:
well it depends what game are you talking about
Read the following statements, and then select ALL true statements about light.
Light travels in waves
Visible light is part of the
electromagnetic spectrum
Light travels in straight lines
Light is a form of energy
Read the following statements, and then select ALL true statements about light.
Light travels in waves
Visible light is part of the electromagnetic spectrum
Light travels in straight lines
Light is a form of energy
Light travels in straight lines
Light is a form of energy.
Light travels in waves.
The cooper family hijacks a UAV (Unmanned Aerial Vehicle). What do you know about UAVs and how they are used today?
Interstellar movie☝️
Interstellar is a movie about the human race being faced with a
civilization ending blight. A small group of brave individuals explore
possible new habitable worlds for humans. The following questions
will help guide you through the movie and hopefully get you
thinking about the future.
1. The Cooper family hijacks a UAV (Unmanned Aerial Vehicle).
What do you know about UAVs and how they are used today?
2. While at the parent-teacher conference, Murphy’s teacher
mentions that the Apollo program -- the same program that
landed humans on the Moon -- was just propaganda to
convince the Soviet Union to bankrupt themselves trying to do
the same. The reason for this was to encourage children to
take care of their own planet, rather than wasting precious
resources day dreaming of leaving it. Which side of the fence
would you sit on? Would you look for ways to save Earth and
our ability to stay there, or would you look to the sky, and find
a new planet to live on? Why?
3. A) What natural disaster(s) is Earth suffering from in the beginning of Interstellar?
B) If one of these happened now what actions would you take to protect yourself?
4. Cooper, Doyle, Romilly, and Dr. Brand (female) rendezvous with the Endurance in orbit around Earth. Once
onboard, they begin to spin the Endurance. Why? (Think about the physics happening here!) Draw a diagram.
5. Why or why isn’t space exploration important for the people in the movie interstellar? Why or why isn’t
space exploration important in today’s society? Defend your answers.
6. Explain time dilation as best as you can.
7. A) Estimate how long Dr. Mann went without human contact while on the ice planet:
The Lazarus mission was __________ years ago. It takes _______ years to get to Saturn from Earth. Cooper
and Dr. Brand were on Miller’s planet for approximately __________ years. This means the total time Dr.
Mann went without human contact is: ___________ years.
B) Consider the longest time away from human contact you've experienced. What did you do to keep yourself
occupied?
Useful Vocabulary
Blight: A specific symptom affecting plants in
response to infection by a pathogenic organism. The
potato famine of Ireland was caused by blight.
Event horizon: Is a point in which not even light can
escape the gravitational influence of the black hole.
Maroon: The intentional action of leaving someone
in a remote area such as an inhabitable island.
Rendezvous: When two objects meet and typically
dock together while in space.
Time dilation: A difference of elapsed time between
two events as measured by observers either moving
relative to each other or differently situated from
gravitational masses.
UAV: Unmanned Aerial Vehicles are remote
controlled or autonomous flying vehicles.
Unmanned aerial vehicles (UAVs) are typically used for a variety of purposes such as:
Monitoring and surveillance.Remote sensingPhotographyDisaster responseWhat is an unmanned aerial vehicle?An unmanned aerial vehicle (UAV) is also referred to as a drone and it can be defined as an aircraft that is designed and developed to be piloted or controlled by a remote control (ground-based controller) and on-board computer systems.
This ultimately implies that, an unmanned aerial vehicle (UAV) is a class of aircrafts that can fly without any human pilot, cabin crew, or passengers on board.
In conclusion, unmanned aerial vehicles (UAVs) carries no human pilot and are typically used for a variety of purposes such as:
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With a class 1 lever, does mechanical advantage increase or decrease as the fulcrum is moved closer to the load? Explain why.
Answer:
L1 F1 = L2 F2 explains balancing torques
F1 = load = counterclockwise torque
F2 = applied force - clockwise torque
L represents distances from fulcrum to the applied forces
F2 = F1 * (L1 / L2) (I)
MA mechanical advantage = (L2 / L1) load over applied force
We can rewrite equation (I) as
load force / applied force = applied distance / load distance
As the fulcrum is moved closer to the load L1 decreases and L2 increases which corresponds to an increase in MA
Is a dog barking an example of kinetic energy to potential energy
A block of mass m is suspended from two identical springs of negligible mass, spring constant k, and unstretched length l
The equation that shows the relationship between X₁ and X₂ in the springs is X₁ = 4X₂.
How to compute the equation?From the complete question, for case I, the two springs stretch up to the distance of X₁. Therefore, f = mg = kx₁.
For case 2, f = mg = kx₂.
Therefore, we'll equate the equations. This will be:
Kx₁ = Kx₂
(K/2)x₁ = (2k)x₂
K(x₁/2) = k(2x₂)
X₁/2 = 2x₂
X1 = 2 × 2x₂
X₁ = 4X₂.
In conclusion, X₁ = 4X₂.
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X₁ = 4X₂ is the equation that shows the connection between X₁ and X₂ in the springs.
What is spring force?The force required to extend or compress a spring by some distance scales linearly with respect to that distance is known as the spring force. Its formula is
F = kx
For case 1;
f=mg=kx₁
For case 2;
f=mg=kx₂
After equating the equation we get;
[tex]\rm Kx_1 = Kx_2 \\\\ \frac{K}{2}x_1 = (2k)x_2 = k(2x_2) \\\\ \frac{x_1}{2} =2x_2\\\\ x_1 = 4x_2[/tex]
Hence X₁ = 4X₂ is the equation that shows the connection between X₁ and X₂ in the springs.
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10. In the process of fusion, nuclear energy is
A. absorbed when a nucleus splits.
B. released when a nucleus splits.
C. released when nuclei join.
D. absorbed when nuclei switch places.
Answer:
B released when a nucleaus splits
A ray of light makes an angle of 25° with the normal to a plane mirror. If the mirror is turned through 6. 0°, making the angle of incidence 31°, through what angle is the reflected ray rotated?
The reflected ray of a ray of light that makes an angle of 25° with the normal to a plane mirror and its is turned through 60°, making the angle of incidence to be 31° is rotated through 12°.
What is reflection?Freflection can be defined as the turning back of a ray of light when its strikes a plane's surface.
There are 2 laws of reflection
Laws of reflection(1) The first law of reflection states that the incident ray the reflected ray and the normal all at the point of incidence lie in the same plane
(2) The second law of reflection states that the angle of incident is equal to the angle of reflection.
From the question, if the incidence ray is rotated through 6°, then the reflected ray is rotated through 12°
Hence, The reflected ray is rotated through 12°.
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The reflection resulting in a 31° angle of incidence and the angle is the reflected ray rotated will be 12°
What is the law of reflection?The law of reflection specifies that upon reflection from a downy surface, the slope of the reflected ray is similar to the slope of the incident ray.
The reflected ray is consistently in the plane determined by the incident ray and perpendicular to the surface at the point of reference of the incident ray.
When the light rays descend on the smooth surface, the angle of reflection is similar to the angle of incidence, also the incident ray, the reflected ray, and the normal to the surface all lie in a similar plane.
As a result, the reflected light is rotated by 12°.
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Which of the following is true about the horizontal component of a
projectile?
A: There is no acceleration
B: The change in displacement is always negative
C:The time is different than the vertical component
D:There is no initial velocity
Answer:
a
Explanation:
If a fast-moving car making a loud noise approaches and moves past a person, which of the following will happen as the distance between the two increases?
A) The pitch and frequency of the sound waves reaching the person's ear will remain unchanged.
B) The pitch of the sound being heard by the person will appear to be lower than the pitch of the source.
C) The frequency of the sound waves reaching the person's ear will be greater than the frequency of the waves leaving the car.
D) The pitch of the sound being heard by the person will appear to be higher than the pitch of the source.
Answer:
(B) Probably - Pitch will appear to be lower than the source
Pitch differences occur because of relative motions between the source and observer - it does not depend on distance measurements
Answer:
(B) Probably - Pitch will appear to be lower than the source
Pitch differences occur because of relative motions between the source and observer - it does not depend on distance measurements
Explanation:
Three 20W resistors are connected in series across a 120 V generator. What is the total resistance of the circuit and what current flows in the circuit?
The total resistance and current flowing through the circuit is equal to 60 Ohms and 2 Amperes respectively.
Given the following data:
Resistors = 20 Ohms.
Voltage = 120 Volts.
How to determine the total resistance.Since the three resistors are connected in series, we would calculate their total resistance by adding them up as follows:
RT = R1 + R2 + R3
RT = 20 + 20 + 20
RT = 60 Ohms.
Next, we would determine the current that is flowing through the circuit by applying Ohm's law.
From Ohm's law, we have:
V = IR
I = V/R
I = 120/60
I = 2 Amperes.
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An aircraft is in a steady climb, at an airspeed of 100 knots, and the flight path makes a positive 10 degree angle with the horizontal. Find the Rate of Climb.
The rate of climb of the aircraft in a steady climb making a 10 degree angle with the horizontal is : 17.36 knots
Given data
Airspeed = 100 knots
Angle with the horizontal ( ∅ ) = 10°
Determine the rate of climb of the aircraftwe will apply the formula below
Vy ( rate of climb ) = Airspeed * sin ∅
= 100 * sin ( 10 )
= 17.36 Knots
Hence we can conclude that rate of climb of the aircraft in a steady climb is : 17.36 knots.
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What does the text mean when it says “naming an elements is like creating history
Answer: When you name an element, it's usually because the element is newly discovered. So by naming an element you are creating something that will last throughout history.
Explanation:
Item 1
The figure presents a block on a horizontal surface attached to a horizontal spring. The other end of the spring is attached to a wall. The spring is labeled 50 newtons per meter, and the box is labeled 0.5 kilogram. The horizontal position of the center of spring is x equals negative 0.3 meter. The horizontal position of the center of the box is x equals 0 meters. When the spring is stretched the box will be at a horizontal position of x equals 0.3 meter.
A block of mass 0.5kg on a horizontal surface is attached to a horizontal spring of negligible mass and spring constant 50N/m. The other end of the spring is attached to a wall, and there is negligible friction between the block and the horizontal surface. When the spring is unstretched, the block is located at x=0m. The block is then pulled to x=0.3m and released from rest so that the block-spring system oscillates between x=−0.3m and x=0.3m. What is the magnitude of the acceleration of the block and the direction of the net force exerted on the block when it is located at x=0.3m?
Magnitude of Acceleration Direction of Net Force
30m/s2 Positive
, Magnitude of Acceleration Direction of Net Force 30 meters per second squared Positive
Magnitude of Acceleration Direction of Net Force
30m/s2 Negative
, Magnitude of Acceleration Direction of Net Force 30 meters per second squared Negative
Magnitude of Acceleration Direction of Net Force
0 m/s2 Positive
, Magnitude of Acceleration Direction of Net Force 0 meters per second squared Positive
Magnitude of Acceleration Direction of Net Force
0 m/s2 Negative
Explanation:
No need to calculate the force you can just find by Hookes law
Hookes law states that
F=-kxWhere
F is force ,k is spring constant x is distanceSo
force remains negative as per it
Acceleration=50/0.5÷1/3=100/3=33≈-30m/s²Option B
A 20 kg child and a 80 kg man are standing 10 meters apart on frictionless ice. How far from the man is the center of mass of the system?
1 meter?
2 meters?
3 meters?
4 meters?
5 meters?
6 meters?
7 meters?
8 meters?
9 meters?
The illustrations show soccer balls of different masses being kicked with equal force.
Which ball will have the greatest acceleration?
You just explored speed. Now test your understanding. A car travels 85 km from Town A to Town B, then 45 km from Town B to Town C. The total trip took 1.5 hours. What was the car’s average speed? A. 65 km/h B. 87 km/h C. 131.5 km/h D. 2 km/h
Answer:
B. 87 km/h
Explanation:
We can find the average speed by using the relationship between speed, distance, and time.
Distance = Speed * Time
Reaarange this to obtain:
Speed = Distance/Time
Speed = (85+45)/1.5
Speed = 87 km/h
What is the wavelength of an electromagnetic wave?
a
The number of waves that pass a point in a certain
amount of time.
b
The distance a wave can travel through empty
space
c The height of the wave from top to bottom
d
The distance between the peaks of two waves that
are next to each other
Answer: (A) The number of waves that pass a point in a certain amount of time.
Explanation:
Electromagnetic waves are categorized according to their frequency f or, equivalently, according to their wavelength λ = c/f. Visible light has a wavelength range from ~400 nm to ~700 nm.
Frequency: Is the number of waves that pass a certain point in a specified amount of time.
Trough: The low point of the wave cycle.
Wavelength: The distance between two successive peaks.
Electromagnetic wave: One of the waves that are propagated by simultaneous periodic variations of electric and magnetic field intensity.
A thin rod of length d on a frictionless surface is pivoted about one end
The magnitude of the angular momentum of the rod immediately after the collision is given as (pf + pi) * d. (Option A).
What is Angular Momentum?
Angular Momentum may be defined or described as the vector quantity of the rotation of a body, which is arrived at by multiplying its moment of inertia by its angular velocity.
The formula for Angular Momentum is given as:
L = mvr; Where
L = Angular Momentum
m = mass
v = velocity; and
r = radius.
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[tex]\rm( P_f+P_i)d[/tex] is the magnitude of the rod's angular momentum immediately after the contact. Option A is correct.
What is the definition of Angular Momentum?Angular Momentum may be defined as the vector quantity of a body's rotation, which is calculated by multiplying its moment of inertia by its angular velocity.
The Angular Momentum formula is as follows:
[tex]\rm L=I\omega[/tex]
[tex]\rm L = mvr[/tex]
Where,
L is the angular momentum
m stands for mass.
v stands for velocity, and
r stands for radius.
Hence option A is correct.
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If a FM radio station broadcasts at 80. 3 MHz (megahertz), what is its wavelength in m (speed of light 3. 0 x 108 m/s)
Answer:
Wavelength = 3.74 m
Explanation:
In order to find wavelength in "metres", we must first convert megahertz to hertz.
1 MHz = 1 × 10⁶ Hz
80.3 Mhz = x
x = 80.3 × 1 × 10⁶ = 8.03 × 10⁷ Hz
The formula between wave speed, frequency and wavelength is:
v = fλ [where v is wave speed, f is frequency and λ is wavelength]
Reorganise the equation and make λ the subject.
λ = v ÷ f
λ = (3 × 10⁸) ÷ (8.03 × 10⁷)
λ = 3.74 m [rounded to 3 significant figures]
A builder drops a brick from a height of 15 m above the ground. The gravitational field strength g is 10 N/ kg. What is the speed of the brick as it hits the ground?
The speed of the brick dropped by the builder as it hits the ground is 17.32m/s.
Given the data in the question;
Since the brick was initially at rest before it was dropped,
Initial Velocity; [tex]u = 0[/tex]Height from which it has dropped; [tex]h = 15m[/tex]Gravitational field strength; [tex]g = 10N/kg = 10 \frac{kg.m/s^2}{kg} = 10m/s^2[/tex]Final speed of brick as it hits the ground; [tex]v = \ ?[/tex]
Velocityvelocity is simply the same as the speed at which a particle or object moves. It is the rate of change of position of an object or particle with respect to time. As expressed in the Third Equation of Motion:
[tex]v^2 = u^2 + 2gh[/tex]
Where v is final velocity, u is initial velocity, h is its height or distance from ground and g is gravitational field strength.
To determine the speed of the brick as it hits the ground, we substitute our giving values into the expression above.
[tex]v^2 = u^2 + 2gh\\\\v^2 = 0 + ( 2\ *\ 10m/s^2\ *\ 15m)\\\\v^2 = 300m^2/s^2\\\\v = \sqrt{300m^2/s^2}\\ \\v = 17.32m/s[/tex]
Therefore, the speed of the brick dropped by the builder as it hits the ground is 17.32m/s.
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