Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.

The dimension of the moment of inertia is \(ML^2\). Option A.

The moment of inertia represents the resistance of a body to rotational motion. It depends on the body's mass and the distribution of that mass around the axis of rotation.

The formula for the moment of inertia involves mass and distance and is expressed as:

I = mr^2

where

The dimension of mass is represented by M, and the dimension of distance is represented by L. Therefore, the dimension of moment of inertia is:

Moment of inertia = mass x distance^2 = M x L^2 = \(ML^2\).

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Answer:

i) 3.514 s, ii) 5.692 m/s

Explanation:

i) We can use Newton's second law of motion to find out how long does it take for the Eagle to touch down.

as the equation says for free-falling

h = ut +0.5gt^2

Here, h = 10 m, g = acceleration due to gravity = 1.62 m/s^2( on moon surface)

initial velocity u = 0

10 = 0.5×1.62t^2

t = 3.514 seconds

Therefore, it takes t = 3.514 seconds for the Eagle to touch down.

ii) use Newton's 1st equation of motion to calculate the velocity of the lunar module when it hits the surface of the moon

v = u + gt

v = 0+ 1.62×3.514

v= 5.692 m/s

Explanation:

6) newton

7) f =ma = 15*15 = 225N

8) a= 100/20 = 5ms^-2

Answer:

6 newton

7) f =ma = 15*15 = 225N

8) a= 100/20 = 5ms^-2

Explanation:

this is right pls mark as brainliest

Segment a, which is drawn from the center of the polygon perpendicular to one of its sides, is called the apothem.

The typical hexagon has a surface area of around 874.6 square meters.

To find the area of a regular polygon, use the formula:

Area = (1/2) x Perimeter x Apothem

Find the perimeter of the polygon. Since the polygon has n sides, use the formula:

Perimeter = n x s

where s = length of one side.

Since s = 18m, find n by using the formula:

n = 360° / (180° - (360° / n))

where n = number of sides.

Plugging in the values:

n = 360° / (180° - (360° / n))

n = 360° / (180° - (360° / 6))

n = 6

So the polygon has 6 sides, which makes it a hexagon.

Now find the perimeter:

Perimeter = n x s

Perimeter = 6 x 18

Perimeter = 108m

Next, find the apothem, use the formula:

Apothem = s / (2 x tan(π/n))

Plugging in the values:

Apothem = 18 / (2 x tan(π/6))

Apothem = 9√3 m

Now use the formula for the area:

Area = (1/2) x Perimeter x Apothem

Area = (1/2) x 108 x 9√3

Area ≈ 874.6 m²

Therefore, the area of the regular hexagon is approximately 874.6 square meters.

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The true statement is that the acceleration in the first two seconds is 6 m/s^2.

The term acceleration is defined as the rate of change of velocity with time. The graph as shown is a velocity time graph. The graph shows the changes that occur in the velocity over a given time interval.

Now  we have;

Initial velocity = 0 m/s

Final velocity = 12 m/s

Time taken = 2s

Acceleration = 12 - 0/2

= 6 m/s^2

Thus the true statement is that the acceleration in the first two seconds is 6 m/s^2.

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Answer:

B to C

Explanation:

The object height decreases

Potential energy= mass x height x gravitational force

Which means that potential energy is directly proportional to height

Thus, a decrease in height will cause a decrease in potential energy.

ENERGY cannot be wasted, it is transformed to another form, and here this form is kinetic energy as according to the gravitational force the speed increases as the object falls downward.

And kinetic energy = 1/2 mv2

Which again means that speed is directly proportional to kinetic energy

And thus an increase in speed will cause an increase in kinetic energy.

If a wave has an amplitude of 0.0800 m and is moving 7.33 m/s. The

wavelength of the wave is 1.69m.

The wavelength of a wave can be determined using the equation:

Wavelength = velocity / frequency

To determine the frequency we need to calculate the reciprocal of the time it takes for one complete oscillation.

frequency = 1 / time

frequency = 1 / 0.230

frequency ≈ 4.35 Hz

Substitute the values into the wavelength equation:

wavelength = velocity / frequency

wavelength = 7.33 / 4.35

wavelength ≈ 1.69m

Therefore the wavelength of the wave is approximately 1.69 meters.

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What is common among all the graphs is that they all show an object that is moving.

In the distance time graph, we have the distance on the vertical axis and we have the time on the horizontal axis and the shape of the plots may differ depending on the nature of the motion of the objects.

Graphs of distance vs time help us to examine motion by showing how an object has moved over time. All objects shown on a distance vs. time graph are shifting positions over time, regardless of the graph's specific shape or slope, and the graph reveals information about the direction and speed of their motion.

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Answer:

1- bounce rule

2- left

3-11,2

4-true

5- whiffle ball

6- kitchen

7-false

8- ping pong

9- true

10- true

Explanation:

I'm pre5sure they are all right. brainliest please

Answer: I had the same quiz too I’m only doing so the other guy can get brainliest

Explanation:Kfkfkfjgjggj

The bike is travelling at 22.5 m/s after 2.5 s

This is defined as the rate of change of velocity which time. It is expressed as

a = (v – u) / t

Where

a = (v – u) / t

a = (15 – 0) / 5

a = 3 m/s²

a = (v – u) / t

3 = (v – 15) / 2.5

Cross multiply

v – 15 = 3 × 2.5

v – 15 = 7.5

Collect like terms

v = 7.5 + 15

v = 22.5 m/s

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The excess amount of water that moved up the small tube attached to the lid is 2.60 cm³ in linear expan- sion of Pyrex glass.

Water expands or gains capacity when it is heated. Water loses density as its volume rises. Water shrinks and loses volume as it cools. Water becomes denser as its volume diminishes.

We can apply the formula:

ΔV = V₀(β₁ΔT - αΔT)

where:

ΔV = excess amount of water that moved up the tube

V₀ = initial volume of water = 200 cm³

β₁ = volume expansion coefficient of water = 0.21 x 10³ K⁻¹

α = linear expansion coefficient of Pyrex glass = 3.3 x 10⁻⁶ K⁻¹

ΔT = change in temperature = 83°C - 21°C = 62°C

Plugging in the values, we get:

ΔV = 200(0.21 x 10³)(62) - 200(3.3 x 10⁻⁶)(62)

= 2.602 cm³ (rounded to three significant figures)

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These waves are traveling at the same speed.  The wave with the highest frequency is option C, "A wave frequency with line crossing in the middle."

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To find

Which of the following has units of velocity

Explanation

The unit of velocity is m/s

Conclusion

So the correct option are

-120 m/s

9.8m/s downward

Answer:

The net force on the hanging mass is thus

2 T Mg     18 6.6 N 11.4 N

, enough to accelerate it upward at

17 m/s2

. The angular acceleration of the pulley is thus

   

2 2

Explanation:

The tension in the rope on both sides of the pulley 20.21N.

To solve this problem, we'll need to consider the forces acting on both sides of the pulley and apply Newton's second law of motion. Let's break it down step by step:

(a) Is the tension in the rope the same on both sides of the pulley?

No, the tension in the rope is not the same on both sides of the pulley. The side with the greater mass attached will experience a greater tension in the rope.

(b) Find the tension in the rope on both sides of the pulley:

Calculate the gravitational force on each mass:

Gravitational force on the pulley: Fpulley = mpulley * g, where mpulley is the mass of the pulley and g is the acceleration due to gravity (approximately 9.8 m/s²).

Gravitational force on the hanging mass: Fhanging = mhanging * g, where m_hanging is the mass of the hanging mass.

Calculate the net force on the pulley:

Net force on the pulley is the difference between the tension forces on either side: Fnet = TLeft - Tright.

Apply Newton's second law to the pulley:

For the pulley, Fnet = mpulley * a, where a is the acceleration of the pulley. Since the pulley is assumed to be massless, we can use the relationship a = α * r, where α is the angular acceleration and r is the radius of the pulley.

Use the relationship between linear acceleration and angular acceleration:

α = a / r.

Equate the torque due to the tension to the moment of inertia times the angular acceleration:

τ = I * α, where τ is the torque, I is the moment of inertia of the pulley, and α is the angular acceleration.

Substitute the expression for α and solve for the net tension:

Tnet = (τ / r) = (I * α) / r = (1/2 * mpulley * r² * α) / r = (1/2 * mpulley * r * a).

Now, substitute the expression for a from step 3 and solve for the net tension:

Tnet = (1/2 * mpulley * r * α) = (1/2 * mpulley * r * (a / r)) = (1/2 * mpulley * a).

Substitute the expression for a from step 2 (Fnet = mpulley * a) and solve for the net tension:

Tnet = (1/2 * Fnet).

Now, you can find the tensions on each side of the pulley:

Tleft = Tnet + Fhanging

Tright = Tnet - Fpulle

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Answer:

An ultralight car weighs less than Honda at 940kg or about 63% less

Answer:

14.1seconds approx

Explanation:

Given data

Distance= 59.1m

Your velocity= 2.35m/s

Walkway velocity= 1.85m/s

Total velocity= 2.35+1.85= 4.2m/s

We know that

Velocity= distance/time

time= distance/velocity

substitute

time= 59.1/4.2

time= 14.07

time=14.1seconds approx

Hence the time is 14.1seconds approx

Answer:

Explanation:

Formula (Force)

We have the values of :

Substitution

A truck weighing 5 x 10³ kg force.

A cart weighing 500 kg force.

Moving with the same speed complete their

kinetic energies.

As we know that,

Formula of:

→ Kinetic energy = 1/2 x m x v².

Using this formula in the equation, we get.

(1).

→ For truck = 1/2 x 5 x 10³ x v².-----

→ For cart = 1/2 x 500 x v². -----(2).

Divide equation (1) and (2), we get.

⇒ KE₁/KE₂ = 5 x 10³/5 x 10².

➡ KE₁/KE₂ = 10/1.

⇒ KE₁/KE₂ = 10:1.

Answer:

Net force

Explanation:

When several forces act on an object, the forces combine to act as a net force.

The minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.

To maintain equilibrium, the torques acting on the meter stick must balance each other. The torque is given by the formula:

τ = r * F * sin(θ)

where τ is the torque, r is the distance from the pivot point to the point where the force is applied, F is the force applied, and θ is the angle between the force vector and the lever arm.

In this case, the meter stick is in equilibrium when the torques on both sides of the pivot point cancel each other out. The torque due to the weight of the meter stick itself is acting at the center of mass of the meter stick, which is at the 50.0 cm mark.

Let's denote the mass to be placed on the 0.00 cm mark as M. The torque due to the weight of M can be calculated as:

τ_M = r_M * F_M * sin(θ)

where r_M is the distance from the pivot point to the 0.00 cm mark (which is 30.0 cm), F_M is the weight of M, and θ is the angle between the weight vector and the lever arm.

Since the system is in equilibrium, the torques on both sides of the pivot point must be equal:

τ_M = τ_stick

r_M * F_M * sin(θ) = r_stick * F_stick * sin(θ)

Substituting the given values:

30.0 cm * F_M = 20.0 cm * (0.0400 kg * 9.8 m/s^2)

Solving for F_M:

F_M = (20.0 cm / 30.0 cm) * (0.0400 kg * 9.8 m/s^2)

F_M = 0.0264 kg * 9.8 m/s^2

F_M = 0.25872 N

Finally, we can convert the force into mass using the formula:

F = m * g

0.25872 N = M * 9.8 m/s^2

M = 0.0264 kg

Therefore, the minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.

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Answer:

Chelsea F.C

Explanation:

Chelsea F.C

Soccer

Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.  

The dome will have approximately 0.1176% more interior space in the summer than it does in the winter.
The dome will have approximately 88.6 m³ more interior space in the summer than it does in the winter.

The dome will have more interior space in the summer due to thermal expansion of the aluminum framework. To calculate the change in volume, we can use the coefficient of thermal expansion for aluminum, which is approximately 2.4 x 10⁻⁵ /°C.

The temperature change from -15°C to 34°C is a difference of 49°C. So, the fractional change in volume is:

ΔV/V = αΔT

ΔV/V = (2.4 x 10⁻⁵/°C) x 49°C

ΔV/V = 0.001176

As a result, the dome will have 0.1176% more internal area in the summer than it does in the winter.

To find the actual change in volume, we can use the formula for the volume of a hemisphere:

V = (2/3)πr³

The diameter of the dome is 58.0 m, so the radius is 29.0 m. Therefore, the volume of the dome is:

V = (2/3)π(29.0 m)³

V = 75344 m³

Increasing the volume by 0.1176% gives us:

ΔV = 0.001176 x 75344 m³

ΔV = 88.6 m³

As a result, the dome will have 88.6 m³ more internal room in the summer than it does in the winter.

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The minimum coefficient of static friction with the floor is 0.3846.

To find the minimum coefficient of static friction with the floor, we need to consider the forces acting on the couch. In this case, the force of gravity is pulling the couch downward with a magnitude of mg, where m is the mass of the couch (40 kg) and g is the acceleration due to gravity (9.8 m/s²).

Since the couch does not move, the force of static friction between the couch and the floor must be equal in magnitude but opposite in direction to the horizontal pushing force of 150 N.

Therefore, we have the equation F_friction = F_push, where F_friction is the force of static friction.

The force of static friction can be calculated using the formula F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.

Since the couch is on a level floor and is not accelerating vertically, the normal force N is equal in magnitude but opposite in direction to the force of gravity, which is mg.

Substituting the values into the equation, we have μs * mg = 150 N.
Solving for μs, we get μs = 150 N / (mg).
Substituting the given values, we have μ_s = 150 N / (40 kg * 9.8 m/s²).
Simplifying, we find that μs = 0.3846.

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A C and D

C because ofc when electric charge flow electric field is produced

Answer:

A & D

Explanation:

Answer:

Sound waves travel through the air.

Step-by-step explanation:

As a sound wave travels through a medium, it will often reach the end of the medium to encounter an obstacle or perhaps another medium through which it could travel. In a sound wave, a portion of the energy carried by the sound wave will pass across the boundary and out of the transmission, and a portion of the energy carried by the sound wave will reflect off the boundary, remain in the transmission, and travel in the opposite direction.

The force is 400.2 N

The work done is 120 J

The power is 48W

Force is a physical concept that describes the influence that one object has on another object, causing it to accelerate or deform. Force can be defined as any influence that changes the motion of an object, such as a push or a pull.

How to solve:

under equilibrium condition

F * 1.45 m =68 kg * 9.81 m/s^2 *0.87 m

F =400.2 N

b)

work done = m*g*h =68 kg*9.81 m/s^2*0.180 m =120.0744 J =120 J

c)

power =120.0744 J *(24 /60 s) =48.02976 W = 48 W

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Answer:

Matter can exist in one of three main states: solid, liquid, or gas. Solid matter is composed of tightly packed particles. A solid will retain its shape; the particles are not free to move around. Liquid matter is made of more loosely packed particles.