A spraying pump is used to spray water from a pool to a fountain.
a) Determine the power of the pump when the work done by the pump is 800Nm at 50ms to a distance of 20m
b) Determine the mass of the pump when the water is projected at acceleration of 10m/s?

According to Kirchhoff’s voltage law, the algebraic sum of the voltage around a closed loop in a circuit must be zero which is therefore denoted as option A.

This is also known as electric pressure, electric tension, or potential difference, and it is referred to as the difference in electric potential between two points.

Kirchhoff's Voltage Law states that the voltage around a loop equals the sum of every voltage drop in the same loop for any closed network and equals zero as a result of the absence of breaks.

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If we replace the incandescent bulb with a voltage meter and return the loop to its original configuration, then moving the bar magnet back and forth through the loop will induce an electrical current in the loop, as described by Faraday's law of electromagnetic induction.

A magnet is a material or object that produces a magnetic field, which is a force that can attract or repel certain other materials, such as iron or steel. The magnetic field is created by the motion of electric charges within the magnet, which align in such a way that they produce a net magnetic field. Magnets can be made from a variety of materials, including iron, cobalt, nickel, and certain alloys. They come in many different shapes and sizes, including bars, discs, horseshoes, and rings.

Here,

The type of current that is generated depends on the direction and rate of the magnet's motion. If the magnet is moved back and forth with a constant speed and in a straight line, the current induced in the loop will be an alternating current (AC), because the direction of the current will reverse every time the magnet changes direction. This can be observed by the voltage meter reading a voltage that periodically changes in direction.

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k = 2.8 x 104 lb/ft. is a constant-length linear spring that is parallel to a 700 lb over force-generating shock absorber.

The main determinant of an object's position and rate of motion is its velocity. It can be explained as the distance an object travels in one unit of time. The dispersion of the objects in a given amount of time is referred to as velocity. Vector sum (v) squared is equal to the sum of the beginning velocity (u) squared and the acceleration (a) times the displacement times two (s). In order to find v, we solve for v such that final velocity (v) = numerator of speed (u) divided plus two times accelerated (a) twice displacement (s).

To calculate kinetic energy of the car KE = (1/2)mv^2

to convert the mass of the car he velocity from mph to ft/s (1 mph = 1.47 ft/s), we get :KE = (1/2)(3600/32.2)(4.0 x 1.47)^2

KE = 13325 ft-lb, the potential energy will be calculated as PE = (1/2)kx^2

since the displacement of the spring is unknown, we can express it in terms of k and solve for k using the given information

we know that constant force of 700 lb is generated over a displacement of 0.25 ft.W = Fd

W = 700 lb x 0.25 ft

W = 175 ft-lb

e can equate the two expressions for potential energy and solve for k:

(1/2)kx^2 = 175

For the bumper with the shock-absorbing unit, the displacement x is 0.25 ft, so we get:

1/2)k(0.25)^2 = 175

k = 280000 Ib/ft

Therefore, the value of k for the simple linear spring is k = 2.8 x 10^4 lb/ft.

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The term "ordinary annuity" refers to the assumption made by the equation that payments are paid at the conclusion of each month.

The present value of an ordinary annuity may be calculated using the equation you've given.

PMT x 1 - [1 / (1+r)]n]r

In this case, PMT stands for the regular payment made at the end of each period, r for the interest rate per period, and n for the overall number of periods.

The present value of the annuity, which is the total present value of all the future payments, is determined by the numerator of the equation.

To account for the time value of money, the denominator of the equation determines the present value of one dollar.

The term "ordinary annuity" refers to the assumption made by the equation that payments will be made at the conclusion of each period.

The equation would have to be modified if the payments were made at the start of each period.

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When a dielectric material is inserted between the plates of a parallel-plate capacitor while it remains connected to a battery, the following quantities change:

(a) C: becomes bigger

C = A/d, where is the permittivity of the medium between the plates, A is the area of the plates, and d is the distance between the plates, gives the capacitance of the capacitor. A dielectric material placed between the plates raises the medium's permittivity, which in turn raises the capacitor's capacitance. As a result, the capacitance rises.

A: remains the same (b)

Because the battery maintains a constant potential difference between the plates and the charge on the plates is equal and opposite, the charge on the capacitor stays constant. The charges on the plates are redistributed when the dielectric material is added, but the overall charge on the plates does not change.

(c) E between the plates: decreases

The electric field between the plates is given by E = V/d, where V is the potential difference between the plates. When a dielectric material is inserted between the plates, it reduces the electric field between the plates, as the voltage across the plates remains constant while the distance between them increases. Therefore, the electric field between the plates decreases.

(d) ΔV: decreases

The potential difference between the plates decreases when a dielectric material is inserted between them. This can be explained by the relationship V = Q/C, where V is the potential difference, Q is the charge on the plates, and C is the capacitance. Since the capacitance increases when the dielectric is inserted, the potential difference decreases for the same charge on the plates. Therefore, ΔV decreases.

(e) Energy stored in the capacitor: increases

The energy stored in a capacitor is given by U = (1/2)CV², where C is the capacitance and V is the potential difference between the plates. When a dielectric material is inserted between the plates, the capacitance increases and the potential difference decreases. Since the energy stored is proportional to the square of the potential difference, the decrease in ΔV is more than compensated by the increase in capacitance, leading to an overall increase in the energy stored in the capacitor. Therefore, the energy stored in the capacitor increases.

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The magnitude of the electric field inside the capacitor is: E = 93.53 x 10^3 N/C (or 93.53 kN/C)

An electric field is a physical quantity that describes the influence that an electric charge exerts on other charges within the space around it. It is defined as the force per unit charge that a test charge would experience at a given point in space, in the presence of an electric charge or charges.

Electric fields are typically represented by vectors, which have both magnitude and direction. The strength of an electric field is measured in units of volts per meter (V/m).

Electric fields are fundamental to understanding the behavior of electrical systems, including electronic circuits and power grids. They also play a critical role in the functioning of many natural phenomena, such as lightning, the aurora borealis, and the behavior of atoms and molecules.

Part (a) To find the charge on one of the plates, we can use the formula:

Q = C x V

where Q is the charge, C is the capacitance, and V is the potential difference.

Substituting the given values, we get:

Q = 0.072 F x 333 V = 23.976 C ≈ 2.4 x 10^-11 C

Therefore, the charge on one of the plates is approximately 2.4 x 10^-11 coulombs.

Part (b) To find the distance between the plates, we can use the formula:

C = ε0 x (A/d)

where ε0 is the permittivity of free space, A is the area of each plate, and d is the distance between the plates.

Solving for d, we get:

d = ε0 x A / C

Substituting the given values, we get:

d = (8.85 x 10^-12 F/m) x (0.29 m)^2 / 0.072 F = 3.56 x 10^-6 m = 3.56 micrometers (μm)

Therefore, the distance between the plates is approximately 3.56 μm.

Part (c) The electric field inside the capacitor can be calculated using the formula:

E = V/d

where V is the potential difference and d is the distance between the plates.

Substituting the given values, we get:

E = 333 V / (3.56 x 10^-6 m) = 93.53 x 10^3 V/m

However, the question asks for the magnitude of the electric field in newtons per coulomb. To convert from volts per meter to newtons per coulomb, we can use the formula:

1 V/m = 1 N/C

Therefore, the magnitude of the electric field inside the capacitor is:

E = 93.53 x 10^3 N/C (or 93.53 kN/C)

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If 3 circular bars made up of glass, steel, aluminium having equal cross section applied with muiltiaxial load at same point in same direction , The bar will produce more stress: glass

If 3 circular bars made up of glass, steel, aluminium having equal cross section applied with muiltiaxial load at same point in same direction, the bar made of glass will produce more stress.

This is because the modulus of elasticity of glass is lower than that of steel and aluminium. The modulus of elasticity is a measure of a material's resistance to deformation under load. A lower modulus of elasticity means that the material is more prone to deformation and therefore, will produce more stress under the same load.

In general, the stress produced in a material under load is given by the equation:

stress = load / cross-sectional area

Since the cross-sectional area of the bars is equal and the load applied is the same, the stress produced will depend on the modulus of elasticity of the material. Therefore, the bar made of glass will produce more stress under the same load as compared to the bars made of steel and aluminium.

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The steel bar will produce the most stress when applied with a multi-axial load at the same point in the same direction, as steel is the strongest of the three materials (glass, steel, and aluminium).

The bar made of steel will produce more stress under a multi-axial load at the same point in the same direction. This is because steel has a higher Young's modulus, or the measure of the ability of a material to withstand changes in length when under tension or compression, than glass or aluminum. Therefore, it will experience greater stress under the same loading conditions. Steel has a much higher Young's modulus than glass or aluminum, meaning it will experience greater stress under the same loading conditions.

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The child must use a wrench that is at least 20 centimeters long to remove the nut with the maximum force they can exert.

The torque exerted by the child must be equal to or greater than the required torque of 10 N·m to remove the nut. The formula for torque is torque = force x length x sin(theta), where theta is the angle between the force and the wrench.

Rearranging the formula, we can find the required length of the wrench by dividing the required torque by the force and the sin of the angle.

Length = Torque / (Force x sin(theta))

Using the given values, we get:

Length = 10 N·m / (50 N x sin(90°))

sin(90°) = 1

Length = 0.2 meters or 20 centimeters

Therefore, the child must use a wrench that is at least 20 centimeters long to remove the nut with the maximum force it can exert.

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Answer: the mass is18 kg

Explanation:

Answer:

Explanation:

Kinetic energy=1/2 *m *v^2

                      =1/2 * 18* 4.7*4.7=198.81J

The equation to calculate the distance between the plates of a capacitor can be derived from the given information:

Electric field strength (E) = Voltage (V) / Distance between plates (d)

Given that the electric field strength is 1.8 kV/cm and the voltage is 89.6 V, we can substitute these values in the equation:

[tex]1.8 kV/cm = 89.6 V / d[/tex]

To solve for the distance d, we can rearrange the equation:

[tex]d = 89.6 V / (1.8 kV/cm)[/tex]

Here, the voltage is expressed in volts and the distance is expressed in centimeters. This equation can be used to calculate the distance between the plates of the capacitor, given the voltage and the electric field strength.

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The earth's rotation generates the coriolis force, which makes objects hurled farther have more buoyant force.

The velocity Centripetal force is an outward force brought on by the rotation of the earth. In the northern hemisphere, the Coriolis force causes winds to be deflected to the right, and in the southern hemisphere, to the left. It is often referred to as "Ferrel's Law." When the wind speed is high, the deflection is greater.

The Coriolis force is most noticeable in the longitudinal course of an object. On Earth, an object traveling in a north-south direction will appear to be deflected to the north of the Equator and to left with in Southern Hemisphere.

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The speed of the bowling ball after the collision is 4 m/s.

The momentum is defined as the product of the mass and the velocity of the body.

We can use the law of conservation of momentum to solve this problem, which states that the total momentum of a system remains constant in the absence of external forces. The initial momentum of the system (bowling ball + bowling pin) is:

pi= m₁v₁ + m₂ v₂

= 10 kg x 10 m/s + 3 kg x 0 m/s

= 100 kg m/s

where m₁ is the mass of the bowling ball, v₁l is its velocity before the collision, m₂ is the mass of the bowling pin, and v'₂ is its velocity before the collision (which is zero since it's at rest).

After the collision, the momentum of the system is:

pf = m₁v'₁ + m₂  v'₂

Where v'₁  is the velocity of the bowling ball after the collision, and v'₂ is the velocity of the bowling pin after the collision.

Since momentum is conserved, we have:

pi= pf

Substituting the values we know, we get:

100 kg m/s = 10 kg x  v'₁ + 3 kg x 12 m/s

Solving for v'₁, we get:

v'₁ = (100 kg m/s - 3 kg * 12 m/s) / 10 kg

v'₁ = 4 m/s

Therefore, the speed of the bowling ball after the collision is 4 m/s.

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Throwing a 5kg stone with an initial vertical velocity of 8.0 m/s downward and an initial horizontal velocity of 7.0 m/s away from the cliff, without any air resistance. After the stone is in the air, its acceleration remains constant at 9.8 m/s² downward but its speed changes. The statement is true.

Once the stone is released from your hand, it will experience a constant acceleration of 9.8 m/s² downward due to the force of gravity. This means that its speed will change over time as it falls.

In the vertical direction, its speed will increase at a rate of 9.8 m/s², so it will be moving faster and faster as it falls. In the horizontal direction, the stone will continue to move with a constant velocity of 7.0 m/s, as there is no force acting in that direction to change its speed.

The motion of the stone can be analyzed using kinematic equations, which describe the relationships between distance, time, acceleration, and velocity. The equations for motion in one dimension (vertical) are:

d = vit + (1/2)at²

vf = vi + at

where d is the distance traveled, vi and vf are the initial and final velocities, a is the acceleration, and t is time. Using these equations, you can calculate the stone's speed and distance fallen at any point in time.

In summary, the stone will experience a constant acceleration of 9.8 m/s² downward due to gravity once it is released from your hand, and its speed will change over time as it falls.

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The semilunar valves will open when the pressure within the ventricles exceeds the pressure within the great arteries.

The heart valve located at the base of the aorta and the pulmonary artery is known as a semilunar valve. It is made up of cusps or flaps that prevent the blood from flowing backwards during the systole phase of the heart's beat. The semilunar valves are responsible for controlling the flow of blood between the ventricles and the main arteries, which directs blood flow away from the heart and towards the organs that are necessary for survival.

Mitral and tricuspid valves prevent blood from flowing backwards into the atria. This is necessary because blood travels from the atria to the ventricles. Pressure differences between the chambers are the driving force behind the opening and closing of semilunar valves, which are controlled by how they are operated.

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The force on the force sensor can be calculated as 2.25 kg x 9.8 m/s² = 22.05 kg If the ramp angle is 90 degrees and the cart mass is 2.25 kg,

Then the force on the force sensor can be predicted using a simple equation. The force on the force sensor is equal to the mass of the cart multiplied by the acceleration due to gravity, which is 9.8 m/s². Therefore, the force on the force sensor can be calculated as 2.25 kg x 9.8 m/s² = 22.05 kg. This means that the force on the force sensor when the ramp angle is 90 degrees and the cart mass is 2.25 kg will be 22.05 kg. This calculation is based on the assumption that there is no friction or other external force acting on the cart. If there are other external forces such as friction, then the force on the force sensor may change.

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Communication cannot be undone once it has been sent, hence it is impossible to undo any effects it may have had on the recipient.

Interpersonal communication is an irreversible process; you can later apologize for something you said and wish you hadn't said it, but you can't take it back. We frequently act and speak with people depending on prior communication experiences.

In passive sentences, the typical word order is reversible. The two stamps were turned on their sides by him. A second vehicle backed out of the drive. He drove away after doing a U-turn. Driving backwards directly at the officer of the law, he.

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The electric field due to a charged rod of length 2a with total charge q uniformly distributed along its length, placed along the z axis with its center at the origin.

To find the electric field everywhere due to the charged rod, we can use Coulomb's law and the principle of superposition. The electric field due to a small segment of the rod at a point P in space is given by:

dE = k dq / r^2

where k is Coulomb's constant, dq is the charge on the segment, r is the distance from the segment to the point P, and dE is the electric field due to the segment. To find the total electric field at P, we integrate this expression over the entire length of the rod, from -a to +a, as follows:

E = ∫ dE = k ∫ dq / r^2

where the integral is taken over the length of the rod. We can express dq in terms of the charge density λ, which is the charge per unit length of the rod, as dq = λ ds, where ds is an infinitesimal length element along the rod. We can also express r in terms of the distance s from the origin to the segment, as r = √(s^2 + z^2), where z is the distance from the segment to the z axis.

Substituting these expressions into the integral, we obtain:

E = k ∫ dq / r^2 = k ∫ λ ds / (s^2 + z^2)

To evaluate this integral, we use a trigonometric substitution, letting s = z tan θ. Then, ds = z sec^2 θ dθ, and the limits of integration become -arctan(a/z) and arctan(a/z). Substituting these expressions into the integral, we obtain:

E = k λ z ∫_{-arctan(a/z)}^{arctan(a/z)} dθ / (1 + (a/z)^2 tan^2 θ)

This integral can be evaluated using the substitution u = tan θ, which gives:

E = k λ z / (2πε_0) ∫_{-a/z}^{a/z} du / (1 + u^2)

where ε_0 is the permittivity of free space. This integral can be evaluated using the inverse tangent function, giving:

E = k λ z / (2πε_0) [arctan(a/z) - arctan(-a/z)]

Simplifying this expression using the identity arctan(-x) = -arctan(x), we obtain:

E = k λ a / (2πε_0 z√(a^2 + z^2))

This is the expression for the electric field due to a charged rod of length 2a with total charge q uniformly distributed along its length, placed along the z axis with its center at the origin. The electric field points radially away from the rod, and its magnitude decreases as 1/r^2 with distance from the rod

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The equilibrium force vector would need to be equal in magnitude and opposite in direction to the resultant force vector.

The equilibrium force vector is a third force vector that is added to a system in order to place it in a state of equilibrium. Equilibrium means that the net force acting on the system is zero, so the system remains at rest or moves with a constant velocity.

In general, the concept of an equilibrium force vector can be applied to any system that is subject to multiple forces or other influences, and the equilibrium force vector is the force that is needed to balance out those forces or influences and maintain a state of equilibrium. However, the concept of equilibrium and the equilibrium force vector remain useful for understanding and analysing the forces and dynamics of a system.

In the context of a stationary object subject to two force vectors, the equilibrium force vector is the force that is needed to balance out the other two forces so that the net force on the object is zero, and the object remains stationary in equilibrium. The magnitude and direction of the equilibrium force vector must be carefully calculated to ensure that it cancels out the net force on the object.

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Calcium is released from the breakdown of potassium ion. Thorium atom is released from the degradation of Uranium atom through alpha decay. The beta decay of Uranium form Neptunium. Radium is released from the alpha decay of thorium and P(15) is released from the beta decay of Silicon atom.

Alpha decay is a common mode of radioactive decay in which a radioactive nucleus emits an alpha particle such as a helium-4 nucleus.

Beta decay is a common mode of radioactive decay in which the nucleus emits beta particles. The daughter nucleus in this decay will have a higher atomic number than the original nucleus.

Calcium is released from the breakdown of potassium ion. Thorium atom is released from the degradation of Uranium atom through alpha decay. The beta decay of Uranium form Neptunium. Radium is released from the alpha decay of thorium and Phosphorus(15) is released from the beta decay of Silicon atom.

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The maximum speed at that a car can travel around the curve without slipping is 13.7 m/s.

In this situation, the coefficient of static friction (μs) is 0.34 and the coefficient of kinetic friction (μk) is 0.29. The radius of the curve (r) is 56.0m.

We can use these values to calculate the maximum speed that a car can travel around the curve without slipping. This is determined by the centripetal force (Fc) required to keep the car on the curve and the frictional force (Ff) that keeps the car from sliding off the curve.

The equation for centripetal force is

Fc = mv^2/r,

where m is the mass of the car and v is the speed of the car.

The equation for frictional force is

Ff = μsFn,

where Fn is the normal force.

Since the car is on a level surface,

Fn = mg,

where g is the acceleration due to gravity.

Setting Fc equal to Ff and solving for v gives us the maximum speed that the car can travel around the curve without slipping:

mv^2/r = μsmg v^2

=> μsrg v

=> √(μsrg) v

=> √(0.34 * 56.0m * 9.8m/s^2) v

=> 13.7 m/s

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A acceptable acceleration for a jet plane in these circumstances is 25 m/s2. The jet in this problem accelerates quickly from cruising speed to a higher speed.

Velocity is the term for the rate at which a displacement changes. Acceleration is the term for the measurement of a change in velocity.

a. To determine the jet's acceleration, we can apply the equation for constant acceleration:

v_f² = v_i + 2ad

Substituting the given values, we get:

(400 m/s)² = (320 m/s)² + 2a(4.0 km)

Simplifying and solving for a, we get:

a = [(400 m/s)² - (320 m/s)²] / (2 × 4.0 km)

≈ 25 m/s²

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Conventionally, the field strength around a charged object is the direction of the force acting on a "positive test charge".

This convention is used because positive charges and negative charges experience opposite forces in an electric field, so the direction of the field is defined based on the force experienced by a positive charge. By convention, a positive test charge is used to define the direction of the field, even though in reality the direction and magnitude of the field would be the same for a negative test charge. This convention helps to avoid confusion and ensure consistent understanding of the direction and properties of electric fields.

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The Gibbs Free Energy (ΔG) at 298 K for the conversion of A to B can be calculated using the equation ΔG = ΔH - TΔS.

Here, ΔH is the enthalpy of the reaction and ΔS is the change in entropy. Therefore, the Gibbs Free Energy for the conversion of A to B at 298 K is given by: ΔG = ΔH - (298 K)(-26.8 J K^-1 mol^-1)

Therefore, the value of the Gibbs Free Energy for the conversion of A to B at 298 K is equal to 7.54 kJ mol^-1. This value indicates that the conversion of A to B is thermodynamically favourable at 298 K, since the Gibbs Free Energy is negative.

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The Gibbs free energy is a thermodynamic potential in thermodynamics that can be used to determine the maximum amount of non-volume expansion work that a thermodynamically closed system is capable of performing at constant temperature and pressure.

The formula  ΔG =  ΔH - T ΔS can be used to determine the Gibbs Free Energy ( ΔG) at 298 K for the conversion of A to B.

Here, ΔH represents the reaction's enthalpy and ΔS represents the entropy change.

Therefore, 7.54 kJ mol^-1 is the value of the Gibbs Free Energy for the conversion of A to B at 298 K. Given that the Gibbs Free Energy is negative, this number shows that the conversion of A to B is thermodynamically advantageous at 298 K.

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To verify whether you accurately pipette 950l of water into each tube, measure the actual weight of water and compare it with calculated weight.

To verify if you accurately pipetted 950 mL of water into each tube, you can weigh each tube before and after adding the water. Since you know the density of water, you can calculate the expected weight of the water in each tube, which should be equal to 950 g or 0.95 kg.

By subtracting the weight of an empty tube from the weight of a tube filled with water, you can determine the actual weight of the water added to the tube. If the actual weight is close to 0.95 kg, then the pipetting was accurate.

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Some ice-rich objects in the Kuiper belt (such as Pluto or Eris) would have grown to larger sizes these are consequences solar wind to clear away the solar nebula.

Eventually, 4 effects clear away the nebula: the Sun's radiation pressure, the solar wind, the gravitation of the individual planets, and close encounters between planets and planetessimals. METEORS, COMETS, ASTEROIDS are left as residues of the planet formation process. Theoretical models for the solar nebula indicate a decreasing temperature with increasing distance from the Sun.

Shock waves from the explosion compressed the cloud of gas and dust. Compression made the cloud collapse, as gravity pulled the gas and dust together, forming a solar nebula. Just like a dancer that spins faster as she pulls in her arms, the cloud began to spin as it collapsed

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Vegetable oil does not burn if we use it while frying it because liquid oil itself does not burn. Rather, it is the vapor from oil that has reached its boiling and vapor point that ignites.

There are three things, for our purposes, to understand. The flash point, the fire point, and the ignition point. The ignition point is responsible for burning. To avoid oil burns, carefully and gently lower the food into the oil with your hands or tongs, and make sure that it drops away from you.

When oil starts to smoke it will impart a burnt, bitter flavor thanks to a substance released called acrolein. During this process, harmful compounds called polar compounds may also be released as a byproduct of the breakdown of that oil as it's exposed to heat.

Therefore, vegetable oil does not burn if we use it while frying it because liquid oil itself does not burn.

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The initial speed of the car was approximately 24.9 m/s.

We can use the equation for the work done by kinetic friction to find the initial speed of the car. The work done by kinetic friction is given by:

W_friction = F_friction * d

where;

The force of kinetic friction is given by:

F_friction = m * g * μ

where;

The work done by kinetic friction is equal to the change in kinetic energy of the car:

W_friction = (1/2) * m * v^2

where;

Setting these two equations equal to each other and solving for v, we get:

(1/2) * m * v^2 = F_friction * d

(1/2) * m * v^2 = m * g * μ * d

v^2 = 2 * g * μ * d

v = √(2 * g * μ * d)

Substituting the given values, we get:

v = √(2 * 9.81 m/s^2 * 0.85 * 45 m)

v = 24.9 m/s

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The peak wavelength of light coming from a star with a temperature of 5300 K is 550 nm.

The peak wavelength of light coming from a star with a temperature of 5300 K can be calculated using Wien's law. According to Wien's law, the peak wavelength of a blackbody is inversely proportional to its temperature. The peak wavelength of a blackbody with a temperature of 5300 K can be calculated using the equation: λpeak = 0.0029/T, where T is the temperature in K. Plugging in the temperature of 5300 K into the equation results in a peak wavelength of 0.00055 μm or 550 nm. Therefore, the peak wavelength of light coming from a star with a temperature of 5300 K is 550 nm.

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The peak wavelength coming out of a star which has a temperature of 5300 K is 547 if 1 nm=  10-9 m

Peak wavelength is the one wavelength at which the light source's radiometric emission spectrum is at its broadest. Simply put, it represents photo-detectors rather than the human eye's perception of any emission from the light source.

To calculate a peak wavelength, we have to divide Wien's displacement constant by the absolute temperature

The Wien's displacement law, which states that the absolute temperature of a black body is inversely proportional to the electromagnetic wavelength at its maximal radiation intensity, is the law for which Wien's constant is well known.

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The ball must be thrown with a initial speed of 31.30 m/s from the ground level to rise it to a maximum height of 50m and it will in the air for 6.38 seconds.

Given, we have the distance ball needs to travel = 50m and we know that the final velocity at the maximum height when thrown vertically will be 0. And the acceleration will be 9.8m/s²  which is acceleration due to Earth's gravity. Now, using the equations of motion we can find the initial velocity needed :

⇒ v² -  u²  = 2as where v stands for final velocity, u stands for initial velocity , s stands for the distance travelled and a stands for the acceleration. Therefore,

⇒ -u² = 2 x (-9.8m/s²) x 50m

⇒  u²= 980         (taking square roots on both sides of the equation)

⇒ u  = 31.30 m/s  

Now, we can easily find the duration for which the ball stays in the air using the equation v = u + at.

⇒ 0  = 31.30 + (-9.8)t     (solve the equation for t)

⇒ 31.30 = 9.8t

⇒31.30 / 9.8 = t

⇒t = 3.19 seconds

Now, this is the time required by the ball to reach the maximum height, the total time for which the ball stays in air will be twice of this because we also have to take account of the time required by the ball to reach to the ground from the maximum height which is equal to the time we calculated since this is a free fall situation.

Therefore, total time for which the ball stays in the air after throwing it with a speed of 31.30 m/s : 2 x 3.19 seconds. The graphs are attached below.

⇒  6.38 seconds

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The maximum altitude is 40km . The range of projectile is 3398.28 m and the displacement is 2575.12 m.

(a) Angle θ = 30°

altitude=40 km

Time = t = 20 s

Time of flight of a projectile is given by the expression,

  t = (2usinθ/g)

  20 = (2 X usin30 / 9.81)

  u = 196.2 m/s

(b) Maximum altitude is given by H =

  H = u²sin²θ / 2g

  H = 196.2² X sin² 30 / 2 X 9.81

  H = 490.6 m

(c)  Range of projectile is given by = R =

  R = u²sin2θ / g

  R = 196.2² X sin 2 X 30 / 9.81

  R = 3398.28 m

(d) Horizontal velocity = ucosθ = 196.2 x cos 30 = 169.91 m/s

Vertical velocity = usinθ = 196.2 x sin 30 = 98.1 m/s

We have equation of motion s = ut + 0.5 at²

Horizontal motion;

u = 9.81 m/s

a = 0

t = 15 s

Substituting,

= s = 169.91 x 15 + 0.5 x 0 x 15² = 2548.71 m

Vertical Motion;

= s =  98.1 x 15 + 0.5 x -9.81 x 15² = 367.88 m

Total displacement = √ ( 2548.71² + 367.88²) = 2575.12 m

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