(hrwc11p41) a man stands on a platform that is rotating (without friction) with an angular speed of 2.0 rev/s; his arms are outreached and he holds a weight in each hand. the rotational inertia of the system of man, weights, and platform about the central axis is 7.00 kg m2. if by moving the weights the man decreases the rotational inertia of the system to 4.06 kg m2, what is the resulting angular speed of the platform?(rad/s)

To prove the given statement t(n) = 2^n - 1 using induction, we need to follow three steps: the base case, the induction hypothesis, and the induction step.

1. Base case (n=0):
Given that t(0) = 1. Let's check if it satisfies the formula t(n) = 2^n - 1:
t(0) = 2^0 - 1 = 1 - 1 = 0
Since t(0) = 1 and the formula gives t(0) = 0, there's a typo in the student question. The correct formula should be t(n) = 2^n - (-1), which makes t(n) = 2^n + 1.

Now, let's check the base case with the corrected formula:
t(0) = 2^0 + 1 = 1 + 1 = 2
The base case holds for the corrected formula since t(0) = 2.

2. Induction hypothesis:
Assume the statement is true for some n=k, i.e., t(k) = 2^k + 1.

3. Induction step (n=k+1):
We need to prove that the statement holds for n=k+1, i.e., t(k+1) = 2^(k+1) + 1.
Using the given recursive formula: t(n) = t(n-1) * 2n
t(k+1) = t((k+1)-1) * 2(k+1) = t(k) * 2(k+1)

Substitute the induction hypothesis into the equation:
t(k+1) = (2^k + 1) * 2(k+1)

Now let's show that this equals 2^(k+1) + 1:
t(k+1) = (2^k * 2(k+1)) + 2(k+1) = 2^(k+1) * 2 - 2 + 2 = 2^(k+1) + 1

Thus, we have proven the statement t(n) = 2^n + 1 by induction.

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Answer:

I think it might be umm... b

The correct answer is actually D

Explanation: i got it right on my district assignment! :)

Answer:

yes

Explanation:

velocity is vector though but speed is scalar

velocity requires direction

so velocity is literally speed with direction

The main advantage of using models in science is the chance to predict a given outcome and make new predictions.

The expression 'scientific models' makes reference to all advancements associated with the use of scientific claims, especially scientific theories that are well sustained by empirical evidence and the chance to prove these claims before their usage.

The scientific advantages are mainly associated with the possibility to predict the result of phenomena from the real world, which also allows for making new predictions.

In conclusion, the main advantage of using models in science is the chance to predict a given outcome and make new predictions.

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The scale will read 147N

The mass of the object, m = 15 kg

Since I am on the earth, the acceleration due to gravity on the earth is:

g = 9.8 m/s²

The scale will read the weight of the object, and is calculated below

The weight, W = mg

W = 15(9.8)

W = 147 N

Therefore, the scale will read 147N

The horizontal force that is required to make the shoe slide is 2.1658N.

Horizontal force = static friction

Static friction = uMg

u is coefficient of friction

g = acceleration due to gravity

M is the mass of the body that is .0425 kg.

Force required = (0.52 x 0.425 x 9.8) N

= 2.1658N

A horizontal force is a force that operates in a direction parallel to the horizon. The cycle's speed tends to slow down due to an opposing force called air resistance force, which acts in the opposite direction. Both the applied force and the air resistance force are considered horizontal forces when the direction is taken into account. Jumps and horizontal medicine ball throws can help increase the horizontal force produced. The Standing Long Jump, Standing Triple Jump, and horizontal jumps over hurdles or boxes are some of these jumps.

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Answer: r = 0.54m

Explanation: F=k(q1*q2)/r^2

Change micro charge by multiplying 10^-6

Manipulate the formula to find r.

r =√k(q1*q2)/F

r = √(8.99*10^9 N*m^2/c^2)(5.0*10^-6C)(2.7^10^-6C)/0.41N

r = 0.54m

The velocity of the ball when it strikes the ground, given the data is 21.56 m/s

From the question given above, the following data were obtained:

The velocity of the ball when it strikes the ground can be obtained as illustrated below:

v = u + gt

v = 0 + (9.8 × 2.2)

v = 0 + 21.56

v = 21.56 m/s

Thus, the velocity of the ball when it strikes the ground is 21.56 m/s

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The average force needed to accelerate an 8.00-gram pellet from rest to 155 m/s over a distance of 0.900 m along the barrel of a rifle is approximately 15.1 N.

To calculate the average force, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a.

First, we need to convert the mass of the pellet from grams to kilograms: m = 8.00 g = 8.00 × 10⁻³ kg.

Next, we can calculate the acceleration using the equation of motion: v² = u² + 2as, where v is the final velocity, u is the initial velocity (which is 0 since the pellet starts from rest), a is the acceleration, and s is the distance traveled along the barrel.

Plugging in the given values, we have: 155² = 0² + 2 * a * 0.900.

Simplifying the equation: 24025 = 1.8a.

Solving for acceleration: a = 24025 / 1.8 ≈ 13347 m/s².

Finally, substituting the mass and acceleration into Newton's second law: F = 8.00 × 10⁻³ kg * 13347 m/s² ≈ 15.1 N.

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Answer:

B. Negative acceleration means this car is slowing down.

Explanation:

for the other screenshot

Average acceleration = change in velocity /change in time.

[a = ∆V/∆t] —this the formula.

NOTE:

u = initial velocity (velocity it started with)

v = final velocity (velocity it ended with)

t = time {the time you were given)

a = acceleration.

listing out our givens:

u =o —(the unit is m/s)

v = 40 —(the unit is also m/s)

t = 0.08 —(the unit is s) "s" means second(s).

Soo

a = 40-0 / 0.08 = 500 m/s² ( unit for velocity is m/s²)

( Remember when using the formula we subtract the initial from the final velocity.........I mean we remove the initial from final) if not you will get a negative answer or wrong answer).

also note: final velocity is always bigger in value than initial velocity EXCEPT it is in deceleration meaning for example a car that was speeding is gradually stopping then initial (the one it started with) will be bigger than the one it ended with (because as it gradually stops the speed reduces).

VELOCITY is speed in a specified direction.

you're super free to ask any questions

Good luck ✅.

The distance covered by Tiana is greater than the distance covered by the brother.

Distance is defined as the quantity that defines how far or near an object is from an observer which is normally measured in meters, kilometers and feet.

There are various ways by which distance can be measured which include the following:

From the scenerio created concerning Tiana and the brother, Tiana first left the doctors office to her friends house and they both left together to the school.

This shows that the distance covered by Tiana is greater than the distance covered by her brother.

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Answer:

the plane moves 495 kilometers per hour.

Explanation:

Because water molecules are cohesive, surface tension can be described as the quality of a liquid's surface that allows it to resist an external force.

Define Surface tension

Surface tension is the tension of a liquid's surface film brought on by the attraction of the liquid's bulk to the particles in the surface layer, which tends to reduce surface area.

In addition to the gas, solid, or liquid in contact with it, surface tension is primarily determined by the forces of attraction existing between the particles inside the given liquid. For instance, the weak attraction between the molecules in a drop of water. Large surface tension will be present in liquids when there is a strong attraction interaction between molecules.

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Answer:

88.2 J (I put 10kg instead of 3kg last time oops)

Explanation:

https://www.calculatorsoup.com/calculators/physics/gravitational-potential.php

Answer:

\(\boxed {\boxed {\sf 88.2 \ Joules}}\)

Explanation:

Potential energy is energy due to position. It is the product of the object's mass, height, and the gravitational acceleration.

\(E_p= m \times \ g \times h\)

The mass of the ball is 3 kilograms and the height is 3 meters. Assuming this is on Earth, the gravitational acceleration is 9.8 meters per square second.

Substitute these values into the formula.

\(E_p= 3 \ kg \times 9.8 \ m/s^2 \times 3 \ m\)

Multiply the first two numbers.

\(E_p=29.4 \ kg*m/s^2 \times 3 \ m\)

Multiply again.

\(E_p= 88.2 \ kg*m^2/s^2\)

\(E_p= 88.2 \ J\)

The ball has 88.2 Joules of potential energy.

The rockets average acceleration during these first 5 minutes is 33.33 m/s².

The average acceleration of an object refers to the rate at which the velocity changes with time of motion of the object.

a = Δv/Δt

where;

The given parameters include;

v = 10 km/s = 10 km/s x 1000 m/1km = 10,000 m/s

t = 5 minutes = 5 x 60 s = 300 seconds

a = 10,000 / 300

a = 33.33 m/s²

Thus, the rockets average acceleration during these first 5 minutes is 33.33 m/s².

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We are given a series circuit with two resistors and a voltage source. Since the resistor are in series this means that the total resistance is the sum of both resistances. Applying Ohm's law we get

Where:

V is voltage, I is current and R1 and R2 are the resistance of the radio and the variable resistance respectively.

Now we solve for the variable resistance, R2, first by dividing both sides by I:

Now we subtract R1 to both sides:

Replacing the values:

Solving the operations:

Therefore, the resistance needed is 135 Ohms.

Answer: Budding is one of the methods of asexual reproduction in organisms.

Explanation:

The asexual reproduction is the process in which new organisms are produced from the parent organism without the formation of gametes. The budding is one of the methods of asexual reproduction in which from a mature organism a bud develops as an outgrowth. The bud obtains the nutrition from the parent organism and increase in size. On maturity the bud dissociate or detach from the parent organism and lives as separate individual organism. Budding can be seen in the case of Hydra, and Yeast.

Answer:

175

Explanation:

its for Acellus

The potential difference is V=1.743*10^-7

The voltage is generally referred to as the electric potential difference and  it can be measured using a voltmeter. The electrical potential difference between the two plates is expressed as q=CV.

CALCULATION

we know,

q=CV

q={EA/d}*V

here q= 5.24*10^-8C

       A=8.22*10^-5m^2

       d=2.42*10^-8m

therefore , C={( 8.85*10^-12)*(8.22*10^-5)}/(2.42*10^-8)

                 C=3.006*10^-1

q=CV

q/C=V

V=1.743*10^-7

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Answer:

The acceleration of the smaller cart is 50 m/s²

Explanation:

The given masses of the carts are 0.1 kg and 0.2 kg

The direction in which the small cart bounces = In the revers to its initial direction

The force exerted by the larger cart on the small cart = 5 N

Therefore, we have;

Force acting on smaller cart = Mass of smaller cart  × Acceleration of the smaller cart

∴ The acceleration of the smaller cart = Force acting on smaller cart/(Mass of smaller cart)

The acceleration of the smaller cart = 5 N/(0.1 kg) = 50 m/s²

The acceleration of the smaller cart = 50 m/s².

Turn the dial either clockwise to make the unit colder or anticlockwise to make the unit warmer to set the thermostat to any temperature.

A thermostat is a part of a regulating mechanism that senses the temperature of a physical system and takes action to keep it close to a desired setpoint.

Any system or gadget that heats or cools to a setpoint temperature uses a thermostat. Examples include central heating systems for buildings, air conditioners, HVAC systems, water heaters, kitchen appliances like refrigerators and ovens, and incubators for use in science and medicine.

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The charge q must be placed at the origin so that the electric field vanishes at x = 0, y = 3.0 m will be q₃ = -2.83x10⁻⁶

tan θ = 3/3 = 1

As a result of this, θ = 45°

The distance between q1 (or q2) and the point (0,3) is calculated by

d² = 3² + 3² = 18m²

Let us calculate the magnitude of q1 or q2's electric:

E = Kq1 /d² = Kq2/d²

E = 9.10⁹ X 4.10⁻⁶/8

E = 2000N/c

Both fields' vertical components are given by

Ey = 2000 cos 45°

= 1414.21

The total field generated by q1 and q2 is twice that amount.

Eyt = 2828.42 N/c

That should be the value of E3 to make the entire field disappear (equal to 0)

E₃ = Kq₃/d²₃ = 2828.42

Trying to figure out q3

q₃ = 2828.42.d²₃ = 2828.42 x 3²/9.10⁹

q₃ = -2.83x10⁻⁶

We already knew that the sign of q3 had to be negative.

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H=132.3m and U=29.4ms−1 are height and velocity respectively.

What is motion?

Motion is a change in position of an object over time. It occurs when an object moves from one point to another. Motion can be described in terms of displacement, distance, speed, velocity, and acceleration. Motion can also be described using Newton's laws of motion which state that an object in motion will remain in motion unless acted upon by an external force. Motion also describes the motion of particles in a fluid or gas, as well as the motion of waves in a medium. Motion is an essential part of the physical world and is essential for understanding the fundamental laws of nature.

Motion in a straight line

Let,

u = Initial velocity of stone

H = Maximum height attained by the stone

v = final velocity at maximum height = 0

t = time taken to attain maximum height = 3s

a=−g= acceleration due to gravity

a. We know that,

V=u+at

0=u−g×3

U=3g=3×9.8ms−2

U=29.4ms−1

b. From the equations of motion, we know that,

S=ut+ ½ a t2

H=29.4×3+½ * 9.8 *32

H=88.2+44.1

H=132.3m

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Answer:

Explanation:

Now

Look at it this way. This box is in equilibrium... Meaning forces around balanced out.

Now...

The Earth's pull on it is 98N

What Minimum external forces is needed to pick this up....

Now... The Minimum Force is 98N

Why?

Since This Box is under the influence of gravity...

Gravity is acting as a resistance

If you apply a force less than 98N... Let's say 50N on this box... It won't budge because your applied force is less than the resisting force on it(98N).

So We need a force ≥98. So the least force is 98N. Nothing below this will move the Box

Answer 98N.

Answer:

See image

Explanation:

Plato

Formula for force:

\(F=ma\)

force(measured in newtons) = mass(measured in kg) * acceleration(measured in m/s^2)

Formula for work:

\(w=Fd\)

work(measured in joules) = force(measured in newtons) * distance(measured in meters)

__________________________________________________________

Given:

\(m=3.4kg\)

\(d=1613m\)

\(a=9.8m/s\) (due to gravity)

\(w=?\)

__________________________________________________________

Finding force:

\(F=ma\)

\(F=3.4\times9.8\)

\(F=33.32N\)

__________________________________________________________

Finding work:

\(W=Fd\)

\(W=33.32\times1613\)

__________________________________________________________

Answer:

\(\fbox{w = 53745.16 Joules}\)

Answer:

The momentum bar chart is a tool used to track the changes in momentum of objects in a system over time.

(a) With one cart as the system:

Initial Momentum: m1v1

Final Momentum: m1v1'

Change in Momentum: m1(v1' - v1)

(b) With both carts as the system:

Initial Momentum: m1v1 + m2v2

Final Momentum: m1v1' + m2v2'

Change in Momentum: (m1 + m2)(v1' + v2' - v1 - v2)

The above expressions represent the changes in momentum of the carts, where m1 and m2 are the masses of the carts, v1 and v2 are their initial velocities, and v1' and v2' are their final velocities. The expressions can be used to calculate the net force acting on the carts using Newton's second law, F = Δp/Δt, where Δp is the change in momentum and Δt is the change in time.

Physical quantities that can be calculated from this scenario include the initial and final momentum of the carts, the change in momentum, the net force acting on the carts, and the acceleration of the carts.

Within the subject of technology, radiogenic heat may be described because of the type of warmth that is released when radioactive isotopes disintegrate. consequently, we say that the thermal strength is launched by means of the nuclear disintegration of the radioactive isotopes.

Approximately 50% of the Earth's inner warmness originates from radioactive decay. four radioactive isotopes are chargeable for the general public of radiogenic warmness because of their enrichment relative to different radioactive isotopes uranium-238 (238U), uranium-235 (235U), thorium-232 (232Th), and potassium-40 (40K).

Radioactive heating refers back to the power dissipated within the interiors of planets, satellites, or asteroids as a consequence of the radioactive decay of radioactive isotopes (see radiochemistry). Radioactive isotopes are characterized by their decay energies and their half-lives.

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Answer:

hydraulic lift pump moves the lift piston out in a series of movements. and a hydraulic brake moves it out in one short break.

The quantities that are unknown final separation of the particles and initial speed of the protoninitial speed of the alpha particlefinal speed of the protonfinal speed of the alpha particles.

Alpha particles are positively charged particles consisting of two protons and two neutrons. They are the heaviest and most energetic of the common types of radiation emitted by radioactive materials. Alpha particles can be emitted by the decay of heavy elements such as uranium, radium, and plutonium. T

hey are relatively large and heavy, which means that they have a short range and are easily stopped by even thin materials such as paper or human skin. However, they can be dangerous if they are inhaled or ingested, as they can cause damage to living tissue and increase the risk of cancer

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