how can you maximize the torque applied to a given lever arm without applying more force?

The time will take a skateboard and dog with force 9N to stop the skateboard and dog is 8 seconds.

The force is defined as the push or pull of an object. The force equals the mass and acceleration of the object obtained from Newton's second law. Acceleration defines the change in velocity by the time taken. The force is defined as the rate of change of momentum and time. Momentum is defined as the product of mass and velocity and the unit of momentum is Kg.m/s.

From the given,

mass of dog (m) = 24 kg

The initial speed of dog (u) = 3 m/s

mass of skateboard and dog = 3 + 24 = 27 kg.

The final speed of dog (v) = 0 m/s

Force = 9N

time =?

F = dp/dt, rate of change of momentum and time.

F(dt) = dp

dt = (dp)/F

    =(Pf - Pi)/F

Pf is the final momentum and Pi is the initial momentum.

Pi = m×v = 24×3 = 72 kg.m/s²

Pf = m×v = 27×0 =0 kg.m/s²

dt = (0-72)/9

   = 8s

Thus, the time taken to stop the skateboard and dog is 8s.

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The final area of the plate is 4.0000352 [tex]m^2[/tex] if the temperature raised to 100 °C and the coefficient of linear expansion of iron is 1.1 x 10-7.

Expecting that the plate of iron is rectangular, we can involve the recipe for warm extension of solids to compute the last region of the plate. The equation for direct warm development is given by ΔL = αLΔT, where ΔL is the adjustment of length, α is the coefficient of straight extension, L is the first length, and ΔT is the adjustment of temperature.

Since the region of the plate is given by A = L*W, where L is the length and W is the width, we can involve the equation for straight warm extension to compute the adjustment of length of the plate and afterward use it to compute the last region.

ΔL = αLΔT = [tex](1.1 x 10^-7 m/oC)(2 m)(80 oC) = 1.76 x 10^-5 m[/tex]

The last length of the plate is L + ΔL = 2 m + 1.76 x [tex]10^-5[/tex] m = 2.0000176 m (approx.)

The last width of the plate is thought to be unaltered as it isn't impacted by the adjustment of temperature.

Thusly, the last region of the plate is A = L*W = (2.0000176 m)(2 m) = 4.0000352 [tex]m^2[/tex] (approx.)

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Answer: Weak or repulsive

Explanation: The amount of electrical force would be weak based on the distance between the two objects.

Based on the data in the table, the two objects will have a repulsive force of medium strength.

This is because the two objects have the same charge, and like charges repel each other. The force is calculated using the following formula:

F = k × (Q₁ × Q₂) / r²

where:

F = force in newtons

k = Coulomb's constant (8.988 x 10⁹ N m²/C²)

Q₁ and Q₂ = charges in coulombs

r = distance between the charges in meters

In this case:

F = medium

k = 8.988 x 10⁹ N m²/C²

Q1 = Q2 = +1 C

r = 10 mm = 0.01 m

Substituting these values into the formula gives:

F = (8.988 x 10⁹ N m²/C²) × (+1 C × +1 C) / (0.01 m)²

= 8.988 x 10⁶ N

Therefore, the two objects will have a repulsive force of medium strength.

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Answer:

To solve this problem, we can use the formula:

Work = Force x Distance x cos(theta)

where Work is the amount of work done on the pizza, Distance is the distance the pizza is lifted, theta is the angle between the force and the displacement, and cos(theta) is the cosine of the angle between the force and displacement.

We are given that the work done on the pizza is 116 kJ, the distance the pizza is lifted is 3.85 cm (which is 0.0385 m), and the angle between the force and the displacement is 0 degrees (since the force is applied in the same direction as the displacement).

Plugging in these values, we get:

116 kJ = Force x 0.0385 m x cos(0)

Simplifying and converting the units of work to joules, we get:

116,000 J = Force x 0.0385 m

Solving for Force, we get:

Force = 116,000 J / 0.0385 m

Force = 3,012,987.01 N

Therefore, the delivery man exerts a force of approximately 3,012,987.01 Newtons on the pizza to lift it 3.85 cm higher.

The density of the solid is (4.10 ± 0.78) × 10^3 kg/m^3.

To calculate the density of the cube below formula can be used:

ρ = m/V

where ρ is density, m is mass, and V is volume. For a cube, the volume is given by:

V = (side)^3

Therefore, the uncertainty in density can be calculated using the formula:

δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]

where δρ is the uncertainty in density, δm is the uncertainty in mass, δs is the uncertainty in side, and s is the value of the side.

Now, putting in the given values:

s = (1.00 ± 0.06) cm = 0.01 ± 0.0006 m

m = (41.0 ± 0.4) g = 0.0410 ± 0.0004 kg

Volume, V = (0.01 m)^3

                  = 1.0 × 10^-6 m^3

Therefore, the density is:

ρ = m/V

  = 0.0410 kg/1.0 × 10^-6 m^3

  = 4.10 × 10^4 kg/m^3

Now substituting the values and calculating the uncertainty in density:

δρ/ρ = sqrt[(δm/m)^2 + 3(δs/s)^2]

δρ/ρ = sqrt[(0.0004/0.0410)^2 + 3(0.0006/0.01)^2]

δρ/ρ = 0.019

Therefore, the uncertainty in density is:

δρ = (0.019)(4.10 × 10^4 kg/m^3)

     = 779 kg/m^3

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Okay, here are the steps to solve this problem:

1) The seesaw is balanced when the sum of moments is 0.

2) The moment created by a force depends on the force and the perpendicular distance from the pivot point.

3) The 20 kg child sits 1 meter from the pivot. So its moment is 20 * 1 = 20 kg*m.

4) We want to find the distance for the 40 kg child to create a moment that balances the 20 kg child's moment.

5) So the moment of the 40 kg child must be 20 kg*m.

6) The moment depends on force and distance. We know the force is 40 kg.

7) So we set: 40 kg * distance = 20 kg*m

8) And solve for the distance: distance = 20 / 40 = 0.5 meters

Therefore, for the seesaw to balance with a 20 kg child 1 meter from the pivot and a 40 kg child on the other side, the 40 kg child should sit 0.5 meters from the pivot point.

Let me know if you have any other questions!

The point on the image that is the source of the sound / sound waves travelling would be B. 2.

When a sound is produced, such as a musical note or spoken word, it initiates a disturbance at the source, which sets the surrounding particles in motion. As these particles oscillate back and forth, they generate regions of compression and rarefaction, resulting in the formation of longitudinal waves.

The propagation of sound waves emanates from a central source, radiating outward in a spherical pattern, thereby creating an expanding wavefront. This fundamental principle of wave behavior stems from the point-source nature of sound waves, wherein they originate from a central locus and disperse in all directions.

This central source in the image is 2.

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A Stone Is Dropped Into a Deep Water Well. The Sound of The Stone Hitting The Water Is Heard After 3.4 Seconds. then The Depth of The Water Well is 56.6 m.

In terms of physics, sound is a vibration that travels through a transmission medium like a gas, liquid, or solid as an acoustic wave. Sound is the receipt of these waves and the brain's perception of them in terms of human physiology and psychology. Only acoustic waves with frequencies between about 20 Hz and 20 kHz, or the audio frequency range, may cause a human to have an auditory sensation. These correspond to sound waves in air with an atmospheric pressure of 17 metres (56 ft) to 1.7 centimetres (0.67 in) in wavelength. Ultrasounds are sound waves with a frequency higher than 20 kHz that are inaudible to humans. Infrasound refers to sound frequencies below 20 Hz. Animals of different species have different hearing ranges. Acceleration of the stone is 9.8 m/s²

according to kinematics,

s = ut + 1/2 at²

s =  1/2 ×9.8×3.4²

s = 56.6 m

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The depth of the barge below the waterline is 2.40 m.

To calculate the depth of the barge below the waterline, we need to consider the buoyancy force acting on the barge. The buoyancy force is equal to the weight of the water displaced by the barge.

First, we need to calculate the volume of water displaced by the barge.

Since the barge is flat-bottomed, we can assume that the shape of the displaced water is rectangular with a length of 20.0 m, a width of 10.0 m, and a depth of d (which is what we're trying to find).

Therefore, the volume of water displaced is V = 20.0 m x 10.0 m x d = 200.0 m³.

The weight of the displaced water can be calculated using its density and volume. In fresh water, the density of water is approximately 1000 kg/m³.

Therefore, the weight of the displaced water is W = 1000 kg/m³ x 200.0 m³ = 2.00 × 10⁵ kg.

Since the buoyancy force is equal to the weight of the displaced water, we have [tex]F_b[/tex] = W = 2.00 × 10⁵ kg.

The weight of the barge is [tex]W_b[/tex] = 4.80 × 10⁵ kg. According to Archimedes' principle, the buoyancy force acting on an object in a fluid is equal to the weight of the fluid displaced by the object, so we can write:

[tex]F_b[/tex] = [tex]W_b[/tex] - [tex]W_d[/tex]

where [tex]W_d[/tex] is the weight of the water displaced by the submerged part of the barge. Solving for [tex]W_d[/tex], we get:

[tex]W_d[/tex] = [tex]W_b[/tex] - [tex]F_b[/tex] = 4.80 × 10⁵ kg - 2.00 × 10⁵ kg = 2.80 × 10⁵ kg.

The volume of water displaced by the submerged part of the barge is equal to the volume of the rectangular prism with a length of 20.0 m, a width of 10.0 m, and a depth of d. Therefore, we can write:

[tex]V_d[/tex] = 20.0 m x 10.0 m x d = 200.0 m³ x (d/10.0)

The weight of the displaced water is also equal to its density times its volume, so we have:

[tex]W_d[/tex] = 1000 kg/m³ x [tex]V_d[/tex]

Substituting [tex]V_d[/tex] in terms of d and solving for d, we get:

d = ([tex]W_d[/tex] / (1000 kg/m³ x 200.0 m²)) x 10.0 m = (2.80 × 10⁵ kg / (1000 kg/m³ x 200.0 m²)) x 10.0 m = 2.40 m

Therefore, the depth of the barge below the waterline is 2.40 m.

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The distance of the screen from the mirror should be 60 cm in order to get a sharp image of the object.

To find the distance of the screen from the mirror, we can use the mirror formula:

1/f = 1/v + 1/u

where f is the focal length of the mirror, u is the distance of the object from the mirror, and v is the distance of the image from the mirror.

In this case, the focal length is given as -20 cm (negative sign indicates that the mirror is a concave mirror), and the object is placed at a distance of 30 cm from the mirror. Therefore, we have:

1/-20 = 1/v + 1/30

Solving for v, we get:

v = -60 cm

The negative sign of the image distance indicates that the image is formed behind the mirror, which means it is a virtual image.

Now, to find the distance of the screen from the mirror, we can use the magnification formula:

m = -v/u

where m is the magnification of the image, which is given as -1 in this case (since the image is virtual and inverted), and u is the distance of the object from the mirror.

Substituting the values, we get:

-1 = -60/u

Solving for u, we get:

u = 60 cm

Therefore, the distance of the screen from the mirror should be 60 cm in order to get a sharp image of the object. It's important to note that this solution assumes that the mirror and screen are both perpendicular to the optical axis of the mirror, and that the object is small compared to the size of the mirror. If these assumptions are not true, the solution may be more complex.

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Magnetic particle separation is a powerful tool for separating particles based on their velocities in a magnetic field, and it has significant practical applications in various scientific and technological fields.

To separate particles of different velocities moving in a magnetic field, one can utilize a technique called magnetic field separation or magnetic particle separation.

This method takes advantage of the fact that charged particles moving in a magnetic field experience a force called the Lorentz force, which acts perpendicular to both the velocity vector and the magnetic field.

The basic principle behind magnetic particle separation is to apply a magnetic field perpendicular to the motion of the particles. The Lorentz force will then cause the particles to curve in different directions based on their velocities and charges.

By carefully controlling the strength and direction of the magnetic field, particles with different velocities can be steered onto different paths and separated.

One common approach to achieve magnetic particle separation is to use a device called a magnetic separator. This device typically consists of a strong magnet or a series of magnets arranged to create a uniform magnetic field.

The particles to be separated are injected into a chamber or a flow system where the magnetic field is applied. As the particles move through the magnetic field, they experience the Lorentz force and deviate from their original trajectory. The degree of deviation depends on their velocity and charge.

By carefully adjusting the magnetic field strength, particle size, and other parameters, it is possible to optimize the separation process and achieve effective separation of particles with different velocities. This technique has various applications in fields such as biomedical research, environmental monitoring, and materials science.

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Answer: In this scenario, we have two carts colliding with each other. One cart weighs 250 kg and is moving at a speed of 8 m/s, while the other cart weighs 100 kg and is initially at rest.

After the collision, the 250 kg cart continues moving forward, but at a slower speed of 3 m/s. We want to find out the speed at which the 100 kg cart moves after the collision.

To solve this, we use the principle that the total "push" or momentum before the collision should be the same as the total momentum after the collision.

Since the 100 kg cart is initially at rest, its momentum is zero. The momentum of the 250 kg cart before the collision is 250 kg * 8 m/s = 2000 kg·m/s.

After the collision, the momentum of the 250 kg cart becomes 250 kg * 3 m/s = 750 kg·m/s.

To find the momentum of the 100 kg cart after the collision, we subtract the momentum of the 250 kg cart after the collision from the total momentum before the collision: 2000 kg·m/s - 750 kg·m/s = 1250 kg·m/s.

Now, we divide this momentum by the mass of the 100 kg cart to find its velocity: 1250 kg·m/s / 100 kg = 12.5 m/s.

Therefore, the 100 kg cart moves at a velocity of 12.5 m/s after the collision, in the opposite direction of the 250 kg cart's motion.

During Simple Harmonic Motion (SHM), an object at the mean position has potential energy (P.E)=0 and kinetic energy (K.E)=MAX. So, the correct option is (d).

In Simple Harmonic Motion (SHM), an object oscillates about a mean position, with the motion characterized by a restoring force proportional to its displacement from the mean position.

When the object is at the mean position, it has maximum kinetic energy (K.E) because it is at its maximum velocity, and it has zero potential energy (P.E) since it is not displaced from the equilibrium position.

As the object moves further from the mean position, its P.E increases, and K.E decreases. The correct answer to the question is option (d), where P.E=0 and K.E=MAX at the mean position.

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An example of a physical change of matter is (c) Melting ice.

Explanation: Melting ice is an example of a physical change of matter. When ice melts, it undergoes a change in state from a solid to a liquid, but its chemical composition remains the same. The water molecules in ice rearrange themselves to form liquid water, but no new substances are formed. This change can be reversed by cooling the liquid water to below its freezing point, causing it to solidify back into ice. Physical changes do not involve a change in the chemical identity of the substance, only a change in its physical properties, such as shape, size, or state.

In contrast, options a) Burning wood, b) Digesting food, and d) Rusting iron involve chemical changes. Burning wood involves a chemical reaction where wood reacts with oxygen to produce carbon dioxide, water vapor, and ash. Digesting food involves the breakdown of complex molecules into simpler ones through chemical reactions in the body. Rusting iron is a chemical reaction where iron reacts with oxygen and moisture in the air to form iron oxide.

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Note: The complete question is:

Which of the following is an example of a physical change of matter?

a) Burning wood

b) Digesting food

c) Melting ice

d) Rusting iron

When the given wave pulse meets, then the diagram C represents the superposition of the pulses. Therefore, option C is correct.

The superposition of wave pulses refers to the phenomenon that occurs when two or more wave pulses are present in the same medium simultaneously. When these pulses overlap, their displacements combine to create a resultant wave.

The principle of superposition states that when waves meet, their displacements add algebraically at each point of overlap. This means that at any given point in space and time, the displacements of the individual waves are added together to determine the net displacement at that point.

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The image distance is the distance of the image formed to the lens.

option C.

The distance between the point of incidence of a lens and the point where the image is formed is called image distance.

The image distance, that is the distance of the image formed by a lens for a given object distance (u) and the focal length (f) of the lens, is given by the following lens formula;

1/f = 1/v  + 1/u

where;

Thus, based on the formula and explanation given above, we can conclude that object distance is the distance of the object to the lens and image distance is the distance of the image formed to the lens.

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The electrical conductivity of copper at 300 K is 6.03 x 10⁷ Ω⁻¹m⁻¹.

Thermal conductivity is a property of a substance that describes its ability to conduct heat. Electrical conductivity is the ability of a material to conduct electricity. The two are related because both involve the movement of electrons in the material.

To calculate the electrical conductivity of copper at 300 K, we need to use the Wiedemann-Franz law, which states that the ratio of the thermal conductivity (κ) to the electrical conductivity (σ) is proportional to the temperature (T) of the material.

The Wiedemann-Franz law is given by:

L = κ/σT

Where L is the Lorenz number, which is a constant equal to 2.45 x 10⁻⁸ W Ω/K².

Rearranging this equation to solve for σ, we get:

σ = κ/(LT)

Plugging in the values for κ, L, and T, we get:

σ = 470.4 W/m K / (2.45 x 10⁻⁸ W Ω/K² x 300 K)
σ = 6.03 x 10⁷ Ω⁻¹m⁻¹

Therefore, the electrical conductivity of copper at 300 K is 6.03 x 10⁷ Ω⁻¹m⁻¹.

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In the circuit with two 10Ω resistors in parallel, ammeter A would show the greatest current. This is because, in a parallel circuit, the total resistance is lower than in a series circuit, which means that the current can flow more easily.

In this case, the two 10Ω resistors in parallel create a total resistance of 5Ω (1/Rtotal = 1/10 + 1/10 = 2/10, Rtotal = 10/2 = 5), while in the series circuit,https://brainly.com/question/11409042?referrer=searchResults the total resistance would be 20Ω (10 + 10). Ohm's law states that the current is directly proportional to the voltage and inversely proportional to the resistance, so the circuit with lower resistance will allow for greater current flow.

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--The complete Question is, In which circuit would ammeter A show the greatest current: a circuit with one 6V battery and two 10Ω resistors in parallel or a circuit with one 6V battery and two 10Ω resistors in series? --

Every action have equal and opposite reaction. for example when we fire bullet from a gun, the gun will recoil back and bullet moves forward. In case of rocket, rocket is fired, thrust is reaction of force applied by the gas on the floor.

A push or a pull that an object experiences as a result of interacting with another item is known as a force. Interactions result in forces! As was covered in Lesson 2, certain forces are the result of contact interactions (reaction, frictional, tensional, and applied forces are examples of contact forces), whilst other forces (gravitational, electrical, and magnetic forces) are the consequence of action-at-a-distance interactions. Newton postulated that whenever objects A and B interact, they exert forces on one another. You put a downward force on the chair when you sit on it, and the chair responds by exerting an upward force on your body. This contact creates two forces: one force on the chair and one force on your body.

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With a velocity of 45 m/s comes in to land at the start of the runway and brakes. The distance the plane will travel before coming to a stop is approximately 22.5a meters if the runway is 275 m long.

To determine how far the plane will travel before coming to a stop, we can use the equations of motion.

Let's assume the initial velocity of the plane is 45 m/s, the distance it travels before coming to a stop is 'd', and the length of the runway is 275 m.

Using the equation of motion:

v² = u² + 2as

where 'v' is the final velocity, 'u' is the initial velocity, 'a' is the acceleration, and 's' is the distance traveled.

Since the plane comes to a stop, the final velocity 'v' is 0 m/s.

Therefore, the equation becomes:

0 = 45² + 2a * d

Rearranging the equation, we get:

2a * d = -45²

d = (-45²) / (2a)

To find the value of 'a', we can use the equation:

a = (v - u) / t

where 't' is the time taken to stop.

Since the final velocity is 0 m/s and the initial velocity is 45 m/s, the equation becomes:

0 = (0 - 45) / t

Solving for 't', we find:

t = 45 / a

Now, substituting the value of 'a' into the equation for 'd', we get:

d = (-45²) / (2 * (45 / a))

Simplifying the expression, we have:

d = (-45² * a) / (2 * 45)

d = -45a / 2

d = -22.5a

Since the acceleration 'a' is negative (opposite direction to the initial velocity), the distance 'd' will also be negative. However, we are only interested in the magnitude of the distance traveled.

As for the time it takes to stop, we can use the equation t = 45 / a, where 'a' is the acceleration. The time taken to stop will be the same as the time taken to decelerate from the initial velocity of 45 m/s to 0 m/s.

In summary, the plane will travel approximately 22.5 times the acceleration distance before coming to a stop, and the time it takes to stop will be 45 divided by the acceleration.

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The sickle cell gene must be inherited from both parents for a kid to be born with sickle cell disease.

Haemoglobin synthesis in red blood cells is controlled by the genes linked to sickle cell disease.

Two typical genes are present in most persons for haemoglobin. Certain individuals have one gene for normal haemoglobin and one for sickle haemoglobin. Sickle cell trait refers to this.

In nearly every way, these people are normal. People who have sickle cell trait never develop into sickle cell disease.

Rarely did people with sickle cell trait have issues linked to their single sickle cell gene, and even then, only in rare cases.

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Refer to the attachment for solution

Answer:

Carbon dioxide and water vapour

Explanation:

So the products of a combustion reaction are primarily:

carbon dioxide + water vapour, however other gases such as nitrogen, methane, and sulphur dioxide are also produced in smaller concentrations.

Carbon dioxide and water vapour are the main byproducts

Answer:

Carbon dioxide

Explanation:

The major byproduct of fossil fuel combustion is carbon dioxide. When fossil fuels such as coal, oil, and natural gas are burned, they release carbon dioxide into the atmosphere. This is because fossil fuels are made up of hydrocarbons, which are compounds made up of carbon and hydrogen. When these compounds are burned, they react with oxygen in the air to produce carbon dioxide [tex]\rm (CO_2)[/tex] and water vapor [tex]\rm (H_2O)[/tex].

Methane is also produced during fossil fuel combustion, but in smaller amounts compared to carbon dioxide. Sulfuric acid is not a byproduct of fossil fuel combustion, but rather a product of the reaction between sulfur dioxide [tex]\rm (SO_2)[/tex] and water vapor in the atmosphere. While water vapor is also produced during fossil fuel combustion, it is not considered a major byproduct, as it is a natural component of the air and atmosphere.

The time taken by the cars to meet is 5.4 x 10³ s.

Speed of car A, v₁ = 45 km/h = 12.5 m/s

Speed of car B, v₂ = 55 km/h = 15.27 m/s

Distance between the cars, d = 150 km = 15 x 10⁴m

The expression for the time taken by the cars to meet can be given as,

Time = Distance/Average speed

t = d/(v₁ + v₂)

Applying the values of d, v₁ and v₂.

t = 15 x 10⁴/(12.5 + 15.27)

t = 15 x 10⁴/27.77

t = 5.4 x 10³ s

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The charge R is positive and the charge L is negative hence, the correct option is option D.

The electric charges are of two types and they are positive and negative charge. There is an attractive force between the two charges. The electric field is formed around the charges and the electric field is denoted by using field lines around it.

The field lines are emerging from positive charge and end up in a negative charge. The field lines never intersect with each other. Hence, from the given, the field lines emerging from the positive charge(R) and end up in the negative charge(L).

Hence, the ideal solution is option D.

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Answer:

C. does not change the velocity of an object.

Explanation:

Centripetal force is the force that acts on an object moving in a circular path and is directed towards the center of the circle. It is responsible for changing the direction of the object's velocity towards the center of the circle, but it does not change the magnitude of the velocity, which means that it does not affect the speed of the object. Therefore, option B and D are incorrect. The direction of the velocity is constantly changing due to the centripetal force, but the magnitude of the velocity, or speed, remains constant. Option A is also incorrect because centripetal force is not responsible for increasing the speed of the object, but rather for changing the direction of its velocity.

The amount of heat required to change the ice cube of mass 720 g from ice at a temperature of -10 ˚C to water at temperature of 15 ˚C is 300963.6 J

First, we shall obtain the heat required to change the ice from -10 ˚C to 0 °C. Details below:

H₁ = MCΔT

H₁ = 0.72 × 2220 × 10

H₁ = 15984 J

Next, we shall obtain the heat needed to melt the ice. Details below:

H₂ = m × ΔHf

H₂ = 0.72 × 333000

H₂ = 239760 J

Next, we shall determine the heat required to change the water from 0 °C to 15 °C. Details below:

H₃ = MCΔT

H₃ = 0.72 × 4187 × 15

H₃ = 45219.6 J

Finally, we shall determine the heat required to change the ice from -10 ˚C to water at temperature of 15 ˚C Details below:

Q = H₁ + H₂ + H₃

Q = 15984 + 239760 + 45219.6

Q = 300963.6 J

From the above calculations, we can conclude that the heat required to change the ice from -10 ˚C to water at 15 ˚C is 300963.6 J

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1. Diagram and Variables:

                                   Maximum Height

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                                          |

                                          |

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------------------------ Ground ------------------------>

Variables:

Initial velocity (v₀) = 90 m/s

Launch angle (θ) = 45°

Maximum height (H)

Time of travel at maximum height (t_max_height)

Horizontal displacement at maximum height (d_max_height)

Time of travel at maximum range (t_max_range)

Horizontal displacement at maximum range (d_max_range)

2. For when the round reaches maximum height:

a) Time of travel (t_max_height):

At the maximum height, the vertical velocity (v_y) becomes zero. To find the time it takes for the round to reach the maximum height, we can use the equation for vertical motion:

v_y = v₀ * sin(θ) - g * t

0 = v₀ * sin(θ) - g * t_max_height

Solving for t_max_height:

t_max_height = v₀ * sin(θ) / g

Substituting the values:

t_max_height = 90 m/s * sin(45°) / 9.8 m/s²

Calculating the value:

t_max_height ≈ 6.12 s

b) Horizontal displacement (d_max_height):

The horizontal displacement at maximum height can be calculated using the equation:

d_max_height = v₀ * cos(θ) * t_max_height

Substituting the values:

d_max_height = 90 m/s * cos(45°) * 6.12 s

Calculating the value:

d_max_height ≈ 385.94 m

Therefore, at the maximum height, the time of travel is approximately 6.12 seconds, and the horizontal displacement is approximately 385.94 meters.

3. For when the round reaches maximum range:

a) Time of travel (t_max_range):

To find the time it takes for the round to reach the maximum range, we can consider the symmetry of projectile motion. The time of flight (t_flight) is twice the time it takes to reach maximum height:

t_flight = 2 * t_max_height

Substituting the value of t_max_height:

t_max_range = 2 * 6.12 s

Calculating the value:

t_max_range ≈ 12.24 s

b) Horizontal displacement (d_max_range):

The horizontal displacement at maximum range can be calculated using the equation:

d_max_range = v₀ * cos(θ) * t_max_range

Substituting the values:

d_max_range = 90 m/s * cos(45°) * 12.24 s

Calculating the value:

d_max_range ≈ 868.63 m

Therefore, at the maximum range, the time of travel is approximately 12.24 seconds, and the horizontal displacement is approximately 868.63 meters.

When a mortar is fired at an angle of 45 degrees, it will reach its maximum height in 6.49 seconds and its maximum range in 12.98 seconds. The horizontal displacement of the mortar when it reaches its maximum height will be 413.02 meters, and its horizontal displacement when it reaches its maximum range will be 826.53 meters.

1. To draw a diagram of the described scenario, you can start by drawing a coordinate system. The x-axis represents the horizontal direction, and the y-axis represents the vertical direction. Place the origin (0, 0) at the point of launch. Since the mortar is angled 45 degrees from the horizontal, you can draw a line representing the initial direction of the round at a 45-degree angle from the x-axis.

Next, label the variables along the x and y dimensions. For the x-dimension, you can label the variable as "horizontal displacement" or simply "x." For the y-dimension, you can label the variable as "vertical displacement" or "height" and indicate that it is measured in meters.

2. When the round reaches maximum height:

a)

The time of ascent  can be calculated using the following formula:

time = ( initial velocity * sin(angle)) / acceleration due to gravity

In this case, the initial velocity is 90 meters per second, and the angle is 45 degrees. The acceleration due to gravity is typically considered to be approximately 9.8 meters per second squared.

Plugging in the values:

time = (90 * sin(45)) / 9.8  = 6.49s

b) The horizontal displacement at maximum height is :

horizontal displacement = initial velocity * cos (45) * time of ascent

Plugging in the values:

horizontal displacement=90* cos (45) * 6.49s= 413.02m

3. When the round reaches maximum range:

a) The time of travel can be calculated using the following formula:

time = (2 * initial velocity * sin(angle)) / acceleration due to gravity

The initial velocity and angle remain the same.

Plugging in the values:

time = (2 * 90 * sin(45)) / 9.8= 12.98s

b) The horizontal displacement at maximum range can be calculated using the following formula:

horizontal displacement = (initial velocity^2 * sin(2*angle)) / acceleration due to gravity

Plugging in the values:

horizontal displacement = (90^2 * sin(2*45)) / 9.8= 826.53m

Therefore, A mortar will reach its maximum height and distance when shot at a 45-degree angle in 6.49 and 12.98 seconds, respectively. When the mortar achieves its maximum height, its horizontal displacement will be 413.02 meters, and when it reaches its maximum range, it will be 826.53 meters.

To learn more about projectile motion click:

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Our intrepid hero has done 2,332,000 joules of work pushing the crate on the frictionless surface of the new planet.

To compute the work done by the space wayfarer, we want to involve the recipe for work, which is work = force x distance. For this situation, the power can be determined utilizing the recipe force = mass x speed increase, which gives us force = 220 kg x 2 m/s^2 = 440 N.

The distance moved by the traveler is given as 5.3 km, however we want to change this over completely to meters by duplicating by 1000, which gives 5300 m.

Accordingly, the work done by the wayfarer is work = 440 N x 5300 m = 2,332,000 J.

Thus, our fearless legend has completed 2,332,000 joules of work pushing the container on the frictionless surface of the new planet.

To learn more about work, refer:

https://brainly.com/question/20627720

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