an airplane propeller is 1.80 m in length (from tip to tip) with mass 90.0 kg and is rotating at 2800 rpm (rev/min) about an axis through its center. you can model the propeller as a slender rod.
What is its rotational kinetic energy?
Suppose that, due to weight constraints, you had to reduce the propeller's mass to 75.0% of its original mass, but you still needed to keep the same size and kinetic energy. What would its angular speed have to be, in rpm?

Iron filings arrange around a U-shaped magnet because of the magnetic field generated by the magnet. The magnetic field creates invisible lines of force that extend out from the north pole of the magnet to the south pole. The iron filings align themselves along these lines of force, which form a pattern that is often described as "field lines." The U-shaped magnet has two poles, north and south, and the field lines extend from the north pole to the south pole, passing through the center of the U-shape. The filings align along these lines of force, forming a pattern that is often described as "field lines". As the filings come in contact with the magnetic field, they align in a pattern that is determined by the strength and direction of the magnetic field.

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Answer:

a. 16 kg m/s

b. -32 N (Newton)

c. 32 N

Explanation:

a. The momentum of an object is the product of its mass and velocity. The formula for momentum is: momentum = mass x velocity

So, in the case of an 8-kg bowling ball rolling at 2 m/s, the momentum would be: momentum = 8 kg x 2 m/s

= 16 kg m/s

The unit of momentum is kg m/s (kilogram meter per second). The momentum of this bowling ball is 16 kg m/s. It is important to note that the direction of velocity is also important when calculating momentum, so it is important to know the direction of the bowling ball.

b. To calculate the average force that the bowling ball exerts on the pillow, we can use the equation: force = change in momentum / change in time

The change in momentum is equal to the final momentum minus the initial momentum. Since the bowling ball is rolling at 2 m/s and stops in 0.5s, we can assume that its final momentum is 0 (since it stops moving) and the initial momentum is 16 kg m/s.

change in momentum = final momentum - initial momentum

= 0 - 16 kg m/s

= -16 kg m/s

change in time = 0.5s

So,

force = -16 kg m/s / 0.5 s

= -32 N (Newton)

The negative sign indicates that the force is opposite to the direction of motion of the bowling ball. This is expected as the force exerted by the pillow is acting in the opposite direction of the ball's motion, thus slowing it down and bringing it to a stop.

It is important to note that the force exerted by the pillow on the bowling ball is equal and opposite to the force exerted by the bowling ball on the pillow, this is Newton's third law of motion.

c. The average force that the pillow exerts on the ball is equal and opposite to the average force that the ball exerts on the pillow, as stated by Newton's third law of motion. This is because when the ball collides with the pillow, the pillow exerts an equal and opposite force on the ball to stop its motion. Therefore, the average force that the pillow exerts on the ball is 32 N, in the opposite direction of the ball's motion.

A pile of gunpowder can represent chemical potential energy , while a flying pulley can represent mechanical kinetic energy.

Thermal energy is kinetic energy associated with the random motion of atoms and molecules. Temperature is a quantitative measure of “hot” or “cold.” When the atoms and molecules in an object are moving or vibrating quickly, they have a higher average kinetic energy (KE), and we say that the object is “hot.”

The specific heat capacity (c) of a substance, commonly called its “specific heat,” is the quantity of heat required to raise the temperature of 1 gram of a substance by 1 degree Celsius (or 1 kelvin)..

Like matter, energy comes in different types. One scheme classifies energy into two types: potential energy, the energy an object has because of its relative position, composition, or condition, and kinetic energy, the energy that an object possesses because of its motion.

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(a) The rate of change of momentum of the water is 333.33 kgm/s².

(b) The force exerted by the building against the water is -333.33 N.

(c) The force exerted by water against the building is 333.33 N.

The rate of change of momentum of the water is calculated by applying the following equation as shown below.

ΔP/t = mv / t = (m/t)v

where;

ΔP/t = ( 1000 kg x 20 m/s ) / ( 1 min x 60 s )

ΔP/t = 333.33 kgm/s²

Based on Newton's third law of motion, action force and reaction force are equal and opposite. If the water exerts a certain force against the building, the building will exert equal and opposite force against the water.

The force exerted by water against the building, F = ma = (mv) / t

F = (mv) / t = 333.33 N

The force exerted by the building against the water;

F = - 333.33 N

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The lightning is formed by  two objects with different electric charges rub together Hence, option (D) is correct.

Charges created by rubbing can be used to explain lightning. The water droplets flow downhill during a thunderstorm while the air currents rise higher.

As a result of this process, the positive charges gather close to the cloud's upper edge, while the negative charges gather close to the cloud's lower edge and also close to the ground.

The charge's magnitude increases significantly as it builds up. Airborne water droplets serve as a conductor for this charge.

Lightning and thunder are produced when these charges flow to meet.

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Answer: C raindrops conduct electricity from clouds to the ground

Explanation:

After the collision, the final velocity of both balls will be (2.00 + 3.60) m/s in the same direction.

The outcome of the two things applying force to one another. The kinetic energy of the two objects is transformed into the other forms, such heat or sound, when they contact. Both elastic and inelastic collisions exist. Both the colliding objects maintain their original energy in an elastic collision.

The first ball has kinetic energy of (1/2)mv² where m is the mass of the ball and v is the velocity. The second ball has kinetic energy of (1/2)m(3.60)²

After collision, the final velocity of both balls in the same direction can be calculated using the conservation of momentum.

m1v1 + m2v2 = m1v'1 + m2v'2

where m1,m2 are the mass of the balls, v1 and v2 are the initial velocities of the two balls and v'1 and v'2 are the final velocities of the two balls.

Given that the mass of the two balls is equal, you can simplify this equation as:

v1 + (-v2) = v'1 + v'2

and solving for v'1 and v'2 gives v'1 = (v1+v2) and v'2 = (v1+v2)

Therefore, after the collision, the final velocity of both balls will be (2.00 + 3.60) m/s in the same direction.

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Yes, cycling up a hill is kinetic energy.

Kinetic energy refers to the energy of motion, which is observable as the movement of an object. Every move has kinetic energy. For instance, cycling up a hill can convert up to 90% of an individual's energy and movement into kinetic energy. The kinetic energy produced is then used to move the cycle up to the hill. Momentum, along with the balance of the rider, helps keep the cycle stable while traveling along the path up to the hill.

Therefore, it is concluded that cycling up a hill is kinetic energy.

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The speed of the child is 14.28 m/s at the bottom of the hill.

Energy cannot be created or destroyed, according to the law of conservation of energy. However, it is capable of change from one form to another. An isolated system's total energy is constant regardless of the types of energy present.

Initial potential energy = final kinetic energy

mass × acceleration of gravity × height = 1/2 × mass × speed²

Speed = √( 2 × 9.81 m/s² ×10.4 m)

Speed = 14.28 m/s

So, the speed of the child is 14.28 m/s at the bottom of the hill.

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The mass of the twig is determined as 7.5 g.

The mass of the twig is calculated by applying the principle of conservation of linear momentum as shown below.

This principle states that the sum of initial momentum of a system is equal to the sum of the final momentum of the system, provided the system is isolated.

Pi = Pf

where;

(0.4  x m ) = ( 1.2 x 2.5 )

m = ( 1.2 x 2.5 ) / ( 0.4 )

m = 7.5 g

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The statement describing point D is "The net force is zero, so the acceleration is zero."

Simple Harmonic Motion is the alternating motion of an object through its equilibrium point. In simple harmonic motion, the object accelerates in a direction toward the equilibrium point. Acceleration that occurs in simple harmonic motion is caused by a rebound force.

The speed of the object at the equilibrium point is maximum. Examples of simple harmonic motion are the alternating motion of a pendulum and the alternating motion of a mass-spring system.

The acceleration of an object will be proportional to the amount of force (force results) acting on the object and inversely proportional to its mass.

At point D we are in a situation where the spring passes its equilibrium position, so x=0, therefore the net force is zero and the acceleration is zero.

The question is multiple choice:

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Answer: The relationship between current, voltage and resistance is expressed by Ohm's Law. This states that the current flowing in a circuit is directly proportional to the applied voltage and inversely proportional to the resistance of the circuit, provided the temperature remains constant.

Explanation:

Answer:at night.

Explanation:

Meter is a metric unit of measure that measures length and distance because area is not any of the measurement unit.

We always measure the physical properties of a thing using particular units. For example, the unit for measuring your bodyʼs mass is the pound and the unit for measuring your height is inches. But, of course, itʼs not as simple as that. If you use the metric system you measure your mass in kilograms, not pounds, and you measure your height in centimeters.

And even if you measure your height in inches, you are probably mix two different units: feet and inches. Although we can measure the mass and lengths of the devices and we deal with in computer architecture, we are typically more interested in a third property.

Time (measurement unit: the second) and the related properties of period and its reciprocal, frequency. Furthermore, computers manipulate physical representations of information, which has its own measurement unit.

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τnet = (TL ‐ TR)R is the needed net torque just on pulley about the axle.

A flexible line, cord, rope, chain, or belt is fastened to the rim of a wheel termed as a pulley. To transport motion and energy, pulleys may be employed singly or in combination.

If TL and TR are really the stresses pulling there at left and the sides of the pulleys, respectively, the net torque here on pulley would then be defined as net = (TL - TR)R, in which R represents the radius of pulley (see Fig. 1). It is believed that positive torque moves in a clockwise direction.

This means that  τnet = (TL ‐ TR)R is the necessary formula for net torque.

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Answer:

0.00088 kg/m³

Explanation:

Given:

[tex] \displaystyle{ \dfrac{8.8 \times {10}^{ - 3} \: \text{g} }{ \text{cm}^{3} }}[/tex]

Let's consider cm³ to m³ first. We know that m³ is 100 cm³. Therefore, cm³ would equal to m³ × 10 negative squared:

[tex] \displaystyle{ \dfrac{8.8 \times {10}^{ - 3} \: \text{g} }{ {10}^{ - 2} \: \text{m}^{3} }}[/tex]

And from the numerator, 1 kg = 10³ grams. Therefore, 1 gram would equal 10 to negative cube kg Hence:

[tex] \displaystyle{ \dfrac{8.8 \times {10}^{ - 3} \times {10}^{ - 3} \: \text{kg} }{ {10}^{ - 2} \: \text{m}^{3} }}[/tex]

Then evaluate using law of exponent where if same bases multiply each other, we add the exponents:

[tex] \displaystyle{ \dfrac{8.8 \times {10}^{ - 3 - 3} \: \text{kg} }{ {10}^{ - 2} \: \text{m}^{3} }} \\ \\ \displaystyle{ \dfrac{8.8 \times {10}^{ - 6} \: \text{kg} }{ {10}^{ - 2} \: \text{m}^{3} }} \\ \\ \displaystyle{ \dfrac{8.8 \times {10}^{ - 6 + 2} \: \text{kg} }{ \: \text{m}^{3} }} \\ \\ \displaystyle{ \dfrac{8.8 \times {10}^{ - 4} \: \text{kg} }{ \: \text{m}^{3} }}[/tex]

And 8.8 × 10^-4 is equal to 0.00088. Therefore, the answer is 0.00088 kg/m³

Answer:

Force=mass × acceleration

or, acceleration=Force/mass

=2000/1500

:. Acceleration=1.33 m/s²

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The shortest distant will be the diagonal of the square. The value of the diagonal of the square is 127.3 feet.

Square is a figure with a four sides that has the same value for each. The formula for its diagonal is sides√2. As per given sides is 90 feet. The calculation will be:

Diagonal = sides√2

Diagonal = 90√2

Diagonal = 90 x 1.41421356237

Diagonal = 127.279220613

Let round the value. So, the diagonal = 127.3 feet. You can also determine diagonal value from phytagoras theory by dividing the square into 4 triangle then calculate the diagonal.

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Answer:

The movement of a 2000-kg truck travelling at 19 m/s is 38,000 kgm/s.

Crash of two vehicles that are moving directly toward each other

This is a difficulty with momentum conservation. Each cart has a starting momentum equal to its mass multiplied by its velocity. When they hit and stick together, they become a single unit of combined mass of 4 kg + 5 kg, and their new velocity must account for momentum conservation.

Assume the 4 kilogram cart is coming from the left and the 5 kg cart is coming from the right. This results in a velocity of +12 m/s for the 4 kg cart and a velocity of -9 m/s for the 5 weight cart.

The carts’ early moments are

(4 kg * 12 m/s) = 48 kg * m/s

And

-45 (kg * m)/s = (5 kg * -9 m/s)

This results in a total starting momentum of 48 + (-45) = 3 (kg * m)/s.

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Answer:

0.27475 N

Explanation:

To find the net force acting upon q2, we need to find the force exerted by q1 to q2 and the force exerted by q3 to q2, and to do that we should apply the formula

[tex]F = |\frac{kq_{1}q_{2} }{r^{2} }|[/tex]

where in k is coulomb's constant ([tex]8.99*10^9 \frac{Nm^{2}}{C^{2}}[/tex])

q1 and q2 are the charges

and r is the distance between the two charges.

Finding the force exerted to q2 by q1:

[tex]F = |\frac{(8.99*10^{9} * (-5*10^{-6}) * (2.5*10^{-6})}{(0.500)^{2}}|[/tex]

F = 0.4995 N

q1 would be attracted to q2, so it would go to the right, so it's a positive force

Finding the force exerted to q2 by q3:

[tex]F =|\frac{(8.99*10^{9})*(-2.5*10^{-6})*(2.5*10^{6})}{0.250^{2}}|[/tex]

F = 0.22475 N

q3 would be attracted to q2, so it would go to the left, so it's a negative force

F = -0.22475N

Add-up the forces: 0.4995 + (-0.22475) = 0.27475 N

A 5.6kg ball has rolled down a hill. At the bottom of the hill, the ball is moving 2.4 m/s. The kinetic energy of the ball is 16.128 Joules.

The energy that an object possess as a result of motion is termed  as kinetic energy.KE is determined  as the effort needed to move a mass-determined body from rest to the indicated velocity for it motion. The body holds onto the kinetic energy it acquired while its acceleration until its speed changes.

Solution:

Given:

Mass of the ball = 5.6kg

g=9.8m/s

velocity=2.4 m/s

Kinetic energy =(1/2)mv^2,

Kinetic energy=(1/2)5.6*2.4^2

Kinetic energy=16.128 Joules

mgh=1/2 mv^2

h=1/2 mv^2/mg

h= 16.128 /5.6*9.8

h=28.224m

Hence, the hill was 28.224m high.

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Answer:

The height of the classroom can be determined using the equation:

height = (1/2) * g * t^2

Where:

g = the acceleration due to gravity (approximately 9.8 m/s^2 on Earth)

t = the time it takes for the penny to fall (0.8 seconds)

Plugging in the known values, we get:

height = (1/2) * 9.8 m/s^2 * (0.8 s)^2

height = 3.072 m

So the ceilings are approximately 3.072 meters tall.

Explanation:

Answer:

Which of the following is NOT TRUE about a longitudinal wave?

Explanation:

Inability of Wegener to provide adequate explanation of the forces responsible for continental drift and prevailing belief that the earth was solid and immovable resulted in scientific dismissal of his theories.

The primary reason that Wegener's hypothesis could not be accepted was because he suggested no mechanism for the moving of continents. He thought that the force of Earth's spin was sufficient enough to cause continents to move, but geologists knew that rocks are too strong for this to be true.

Wegener is not qualified to propose theories in the fields of geology and  history of Earth because there was no mechanism available to endorse his proposals and offer convincing and truthful explanation.

The fossils could naturally be located in the places Wegener found them because fossils are mostly found where sedimentary rocks of the right age are exposed, such as river valleys, cliffs and hillsides.

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The force with which the second astronaut is pushing is 11.25 N in the problem given.

We have to note that force is a vector and because that force is a vector, we know that the direction of the force that has been applied is also very important.

As we know, it is clear that;

Force of an astronaut Fₓ = 42 N

Angle θ = 15º

Then we can write that;

F = 42 tan 15

= 11.25 N

Thus, the force that acts as the second astronaut is pushing is about 11.25 N.

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Answer:

  about 0.365 m/s

Explanation:

You want to know the velocity of an astronaut who starts from rest and fires a thruster that expels 35 g of gas at 875 m/s.

The total momentum of the system is the same before and after the thruster is fired: 0.

If v is the velocity of the astronaut, it must satisfy the equation ...

  (84)v +(0.035)(875) = 0

  v = -(0.035)(875)/(84) ≈ -0.3646

The velocity of the astronaut is about 0.365 m/s in the direction opposite of the expelled gas.

__

Additional comment

We have used (kg·m/s) as the units of momentum. 35 g = 0.035 kg. We have also assumed that the mass of the system before firing is a total of 84.035 kg

Answer: A, B, and C

Explanation: A standard room-vacuuming robot doesn't unpack itself from the box it comes in.