5.1 5.2 5.3 QUESTION 5 (Start on a new page.) A skier of mass 60 kg skies from rest down a slope inclined at an angle of 15°. The length of the incline is 75 in. He reaches the end of the clined at a velocity of 15 m-s¹. A constant frictional force acts on the skier on his way down. 15:... 75 m Write down an expression for the magnitude of the normal force acting on the skier and then calculate its magnitude. Draw a labelled free-body diagram showing ALL the forces acting on the skier as he skies down the slope. Calculate the average frictional force acting on the skier during his motion down the incline. (2) (3) (7) [12]​

The impulses and changes in momentum are identical because equal forces are applied over equal periods of time.

The momenta of the two carts are identical since they both begin at rest and experience equal changes in momentum. We are aware that force is the same as mass multiplied by acceleration. Due to the initial resting state of both carts, u = 0 m/s, and the plastic cart moves 1 m. Newton's second law states that when the same force is applied to the two carts, the plastic cart will have more final momentum than the lead cart because of the momentum principle. Newton's third law states that every object feels the same force for the same length of time, which results in the same impulse and consequent change in momentum.

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Due to equivalent forces being delivered over equal times, the impulses and changes in momentum are identical.

The acceleration is determined by dividing the net force by the mass. An object's acceleration doubles if the net force exerted on it also doubles. Increased mass will result in a halving of acceleration.

Second Law of Motion: Force In accordance with his second law, a force is defined as the change in momentum (mass times velocity) per change in time. The definition of momentum is the product of the mass m and the velocity V of an object.

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( a ) 966 Ps is expressed in SI unit as 9.66 x 10⁻¹⁰ s

( b ) 966 fs is expressed in SI unit as 9.66 x 10⁻¹³ s

( c ) 48 ns is expressed in SI unit as 4.8 x 10⁻⁸ s

( d ) 640  μsis expressed in SI unit as 6.4 x 10⁻⁴ s

A standard way of expressing a derived quantity or fundamental quantity in terms of the SI unit is always in power of 10.

The standard form of the given quantity is calculated as follows;

( a ) 966 Ps = 966 x 10⁻¹² s = 9.66 x 10⁻¹⁰ s

( b ) 966 fs =  966 x 10⁻¹⁵ s = 9.66 x 10⁻¹³ s

( c ) 48 ns = 48 x 10⁻⁹ s = 4.8 x 10⁻⁸ s

( d) 640  μs = 640 x 10⁻⁶ s = 6.4 x 10⁻⁴ s

Thus, the standard form of a quantity in SI unit involves the power of 10.

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The electric field strength in FIGURE is not changing.

An great approach to see electric fields is with electric field lines.

At one point, a field line is drawn perpendicular to the net. As a result, the direction of the electric field at any place is the same as the tangent to the electric field line. Second, the relative strength (magnitude) of the electric field at a location is correlated with the relative density of the field lines around that point.

In the figure, density of  electric field line is same everywhere. Hence,  the electric field strength is not changing here.

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b) The strength of the apparent deflection varies with speed of Earth's rotation best describes the strength of Coriolis deflection where isobars are very close together.

The Coriolis deflection is a phenomenon of the Earth's rotation that affects the movement of air masses and ocean currents. The strength of the apparent deflection of these air and water masses varies with the speed of the Earth's rotation. Hence, option b is correct.

This is particularly noticeable when isobars, or lines of equal pressure, are very close together. The Coriolis deflection causes the air or water to be deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.

This deflection can result in the formation of cyclonic weather systems and gyres in the ocean.

Although a part of your question is missing, you might be referring to this question:

Which of the following best describes the strength of coriolis deflection where isobars are very close together?

a) Slowly moving objects are deflected more than rapidly moving objects.

b) The strength of the apparent deflection varies with speed of Earth's rotation.

c)Coriolis deflection occurs only along parallels, not meridians.

d) The Coriolis force is zero at the poles, increasing to maximum along the equator.

e)The amount of Coriolis deflection is uniform from equator to poles.

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In the circular motion, the system is open, because a net force is exerted on the ball as it travels in a circle. Option B

We know that the term circular motion would have to do with the kind of motion that is occurring in a circular path. We have to know that the velocity of the object may be constant but the object may still be said to be accelerating.

Given the fact that we know that the acceleration of the ball is not the same at all the points of the circle as we can see it then it follows that the system is an open system as the net force acts on it.

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Answer:

a.) 12[tex]\frac{rad}{s^2}[/tex]

b.) 48[tex]\frac{rad}{s}[/tex]

c.) 23.87 rev

Explanation:

First, convert linear velocity to angular velocity.  The angular velocity can be calculated using the relationship v=rω, where v is the linear velocity, r is the radius, and ω is the angular velocity.  Rearrange the equation to solve for ω:

[tex]\omega=\frac{v}{r}[/tex]

For this problem, let v=30[tex]\frac{m}{s}[/tex] and r=0.5m.  So,

[tex]\omega=\frac{30\frac{m}{s}}{0.5m}\\\omega=60\frac{rad}{s}[/tex]

Next, to solve for angular acceleration use rotational motion equation #1, [tex]\omega_f=\omega_i+\alpha t[/tex].  For this problem, let

[tex]\omega_i=0.0\frac{rad}{s}\\\omega_f=60\frac{rad}{s}\\t=5s[/tex]

So,

[tex]60\frac{rad}{s}=0.0\frac{rad}{s}+\alpha(5s)\\(\frac{1}{5s})60\frac{rad}{s}=\alpha(5s)(\frac{1}{5s})\\12\frac{rad}{s^2}=\alpha[/tex]

Next, use the angular acceleration and the time given in part b in rotational motion equation #1 to solve for the angular velocity at t=4s:

[tex]\omega_f=\omega_i+\alpha t\\\omega_f=0.0\frac{rad}{s}+(12\frac{rad}{s^2})(4s)\\\omega_f=48\frac{rad}{s}[/tex]

To find the number of revolutions, use rotational motion equation #3, [tex]\theta=v_it+\frac{1}{2}\alpha t^2[/tex], to find the angular displacement at t=5s.  So,

[tex]\theta=0.0\frac{m}{s}(5s)+\frac{1}{2}(12.0\frac{rad}{s^2})(5s)^2\\\theta=0.0m+150\ rad\\\theta=150\ rad[/tex]

To convert the angular displacement in radians to revolutions, recall that one revolution equals 2π radians.  So,

[tex]150\ rad(\frac{1\ rev}{2\pi\ rad})=\frac{75}{\pi}\ rev\approx23.87\ rev[/tex]

The angular momentum of the particle in the x-component, y-component, and z-component are 3.12, 2.84, and 1.19 kg.m/s² respectively.

Angular momentum can be defined as the rotational form of linear momentum. Angular momentum is a physical conserved quantity.

The angular momentum in the terms of linear momentum can be represented as:

[tex]\displaystyle \vec L= \vec r\times \vec p = m\vec r \times \vec v[/tex]

Given, the mass of the particle, m = 70 Kg

The displacement of the vector of the particle, [tex]\vec r = (5.0, -5.5)[/tex]

The velocity of the vector of the particle, [tex]\vec u = (3.2, 0, -8.1)[/tex]

The angular momentum of the particle, L can be calculated as:

[tex]\displaystyle \vec L= m\vec r \times \vec u[/tex]

[tex]\displaystyle \vec L= m(5.0,-5.5, 0)\times (3.1,0,-8.1)[/tex]

[tex]\displaystyle \vec L= 0.070 \times (44.55, 40.5, 17.05) .Kg.m/s^2[/tex]

[tex]\displaystyle \vec L= (3.12, 2.84, 1.19) \; kg.m/s^2[/tex]

Therefore, the x-component of angular momentum = 3.12 kg.m/s²

The y-component of angular momentum = 2.84 kg.m/s²

The z-component of angular momentum = 1.19 kg.m/s²

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Answer: At least 100 billion stars, including our Sun, make up the Milky Way, a spiral galaxy with a diameter of around 100,000 light-years. In the Milky Way, where are we located? The Orion Arm, also known as the Orion Spur, is a short, incomplete arm between the Sagittarius and Perseus arms that is close to where our Sun is positioned.

Explanation:

1. The proximodistal pattern of development in the development of motor skills in infants involves the development of control and coordination of the head, neck, and trunk before control and coordination of the limbs. For example, an infant may first learn to lift their head and control its movements before learning to reach for and grasp objects with their hands.

2. The proximodistal pattern of development can also be seen in the development of language skills in children. Children typically learn to produce single words before they learn to put words together in simple phrases and sentences.

3. In the development of cognitive skills, the proximodistal pattern involves the development of more basic skills, such as perception and attention, before more complex skills, such as memory and problem-solving. For example, a child may first learn to identify basic shapes and colors before learning to solve more complex puzzles and games.

4. The proximodistal pattern of development can also be observed in the development of social and emotional skills in children. Children may first learn to express basic emotions, such as happiness and anger, before learning to recognize and understand the emotions of others.

5. In the development of sensory and perceptual abilities, the proximodistal pattern involves the development of more basic abilities, such as visual acuity and auditory sensitivity, before more complex abilities, such as spatial awareness and depth perception. For example, a child may first learn to focus their eyes on objects close to them before being able to see objects in the distance.

The average acceleration of the object represented in the given graph above over eight seconds is equal to 0.5 m/s².

Acceleration can be defined as the rate change of velocity with respect to time. The acceleration is a vector parameter with both magnitudes as well as directions.

Acceleration can be determined as the first derivative of the velocity of an object w.r.t. time.

[tex]\displaystyle a =\frac{v_f-v_o}{t}[/tex]

From Newton's 2 law of motion, acceleration can be determined as:

a = F/m

Given, the initial velocity at time t = 0 is v = 0 m/s

The final velocity at time t = 8 is v = 4 m/s

[tex]\displaystyle a =\frac{4-0}{8}[/tex]

a = 0.5 m/s²

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The value of a, if the system of forces is in equilibrium​ is 2.

If the system of forces is in equilibrium​ the sum of all the forces will be equal to zero.

∑F = 0

2i -j + k +  3i + 4j + 4k + 5i + 3j + 3k - (3i+2k + 4i-5j + ak  -4i-2j+4k) = 0

The value of a is calculated by summing all the corresponding vectors and equating them.

10i + 6j + 8k - (3i -7j + 6k + ak ) = 0

10i + 6j + 8k - 3i + 7j - 6k - ak = 0

7i + 13 j + 2k - ak = 0

2k - ak = 0

ak = 2k

a = 2

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Find out your answer below:

The power, the resistor and time is I²₀R e-2Rt/L and - I₀²R  e-2Rt/L .

Work rate or energy delivery time is expressed as W/t, where W is the quantity of work completed or energy delivered, and t is the time interval.

A passive electrical device with two terminals that controls or limits the flow of electricity across electrical circuits. The main function of a resistor is to lower the voltage and reduce the current flow in a specific area of the circuit.

a) L di/dt + iR = 0 -Rt/L

= I = I₀ e

At t=0.  I = I₀

= Pr = I²R = I₀ R e = -2Rt/t

= Pr (t) = I²₀R e-2Rt/L

b) Energy of inductor = 1/2 L I²

= 1/2 L I₀²    e-2Rt/L

Power, Pl (t) = dE/dt

= d/dt (1/2 LI₀² e-2Rt/L)

= 1/2 t I₀² ( e-2Rt/L) e-2Rt/L

Pl (t) = - I₀²R  e-2Rt/L

Therefore, the power, the resistor and time is I²₀R e-2Rt/L and - I₀²R  e-2Rt/L .

I hoped this helped you!

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The aluminum ball has a higher density and contains more matter and would fill more space than the lead ball.

We know that in science, we can be able to define the density as the ratio of the mass per unit volume of the substance. The density is how we know the amount of material that is presence.

The fact that a substance has the greater density would have to mean that there is a lot more mass in the substance as we can see it and this is very important to the discussion that is going on here.

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Due to light refraction, any fish in the water can see a fisherman on the bank a little more clearly than one might anticipate. When the light hits the water's surface, it “bends” down by around 13 degrees, leaving the image. Thus option A is correct.

When it reaches the surface, light emanating from the fish refracts (changes direction). When viewed from above the water, a fish appears to be closer to the surface than it actually is.

Therefore, Fred the fisherman has been told that, because of refraction, a fish in water will appear.

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(a)  The average velocity of the sprinter for the first 4 seconds is 12 m/s.

(b) The instantaneous  velocity of the sprinter at time, t = 5 s is 12 m/s.

(c) The average acceleration of the sprinter between 0 and 4 s is 3 m/s².

(d) The time of race of the sprinter is 12 s.

The average velocity of the sprinter is the change in the total displacement of the sprinter with total time of motion.

From the given graph, the average velocity of the sprinter for the first 4 seconds is 12 m/s.

The instantaneous  velocity of the sprinter at time, t = 5 s from the graph corresponds to 12 m/s, since the velocity of the sprinter from 4 s to 12 seconds is constant.

The average acceleration of the sprinter between 0 and 4 s is calculated as follows;

a = ( 12 m/s - 0 m/s ) / ( 4 s - 0 s )

a = 3 m/s²

The total time of race of the sprinter according to the graph is 12 seconds.

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The reading on each of the scales on the right is 421.4 N.

The reading on each of the scales on the left is 156.8 N.

The reading on each scale is determined from the distribution of the weight of the woman.

The weight of the board is distributed uniformly and each scale with have equal reading of the weight of the board.

weight of the board = 10 kg x 9.8 m/s² = 98 N

Reading of each due to weight of the board is calculated as;

W₁ = ¹/₂ (98 N) = 24.5 N

The distribution of the weight of the woman on the right scale is calculated as;

W (R) = ( 1.5 m / 2 m) x ( 54 x 9.8 )

W (R) =  396.9 N

The distribution of the weight of the woman on the left scale is calculated as;

W (L) = ( 0.5 m / 2 m) x ( 54 x 9.8 )

W (L) =  132.3 N

Total reading on the scale on the right = 396.9 N + 24.5 N = 421.4 N

Total reading on the scale on the left = 132.3 N + 24.5 N = 156.8 N

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The segment of the graph represents the squirrel heading toward its nest is S. The correct option is A.

The graph of a function f in mathematics is the collection of ordered pairs, where display style f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space, and so form a subset of this plane in the typical situation when x and f(x) are real integers.

They are employed to arrange data in order to highlight patterns and correlations. This information is displayed as a shape on a graph.

Therefore, the correct option is A. S.

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Answer:

I expect that approximately half of the class will have unattached earlobes, while the other half will have attached earlobes. This is because the trait for having attached or unattached earlobes is determined by a single gene with two alleles, and these alleles are equally common in the population. Therefore, the probability of an individual having attached earlobes or unattached earlobes is roughly equal. Therefore, I would expect that about half of the class will have each type of earlobe.

B. Noise decreases the loudness of analog signals but does not affect the loudness of digital signals.

Noise is any extraneous interference that can affect the quality of a signal being transmitted.

Noise can cause analog signals to become weaker or distorted, which can reduce the loudness of the signal and make it more difficult to interpret. In contrast, noise does not affect the loudness of digital signals in the same way.

Digital signals are transmitted using a series of ones and zeros, which can be easily distinguished from noise. This means that digital signals are less susceptible to the effects of noise, and are generally considered to be more reliable than analog signals for this reason.

Other reasons to use digital signals instead of analog signals include the fact that digital signals are easier to store and transmit over long distances, and that they can be more easily processed by computers.

[tex]\bold{ \: \purple{Hope \: This \: Helps \: You!}}[/tex]

B. Noise decreases the loudness of analog signals but does not affect the loudness of digital signals.

Noise is any extraneous interference that can affect the quality of a signal being transmitted. Noise can cause analog signals to become weaker or distorted, which can reduce the loudness of the signal and make it more difficult to interpret. In contrast, noise does not affect the loudness of digital signals in the same way.

Digital signals are transmitted using a series of ones and zeros, which can be easily distinguished from noise. This means that digital signals are less susceptible to the effects of noise, and are generally considered to be more reliable than analog signals for this reason.

Other reasons to use digital signals instead of analog signals include the fact that digital signals are easier to store and transmit over long distances, and that they can be more easily processed by computers.

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The cannonball lands 68.73 meters from the base of the wall.

The time it takes for the cannonball to fall from the castle wall to the ground is given by:

t = sqrt(2h/g)

= sqrt(210.5/10)

= sqrt(2.1)

= 1.45 seconds

The distance the cannonball travels horizontally in this time is given by:

d = vt

= 47.4 * 1.45

= 68.73 m

The total distance from the base of the wall is therefore 68.73 m.

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The points in the above graph that are possible long-run equilibria include B. A and B.

A and B are the equilibria. This is because long run equilibrium occurs where the aggregate demand intersects the long run aggregate supply curve. The long run equilibrium will always occur at long-run aggregate supply curve.

The other options are incorrect because they lie at the intersection of short-run aggregate supply curve and aggregate demand curve. They do not lie on long run aggregate supply curves and hence are not long-run equilibrium points.

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The magnitude of charge q₁ is equal to magnitude of charge q₂.

The magnitude of charge q₁ is calculated by applying Coulomb's law of electrostatic force as shown below.

The electric force between q₁ and q is calculated as follows;

F₁ = kq₁q / r²

where;

F₁ = ( 9 x 10⁹ x 4.4 x 10⁻⁹ x q₁) / (0.1)²

F₁ = 3960q₁

The electric force between q₂ and q is calculated as follows;

F₂ = kq₂q / r²

F₂ = ( 9 x 10⁹ x 4.4 x 10⁻⁹ x q₂) / (0.1)²

F₂ = 3960q₂

Since the charge q₂ is in static equilibrium with q and q₁, then

F₁ + F₂ = 0

3960q₁ = - 3960q₂

q₁ = -q₂

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Electrons occupy neutral oxygen atom has 8 electrons.

Now you can statistic out how many electrons, protons and neutrons Oxygen has: Atomic number which is all the time smaller of the two numbers is 8. Hence 8 protons. Because the atom is impartial, there are also 8 electrons. Oxygen likes to have two extra electrons to make it happy. Each lithium atom provides one.

the first two electrons will inhabit the 1s orbital while the next two electrons will occupy the 2s orbital. The endure four electrons will occupy the 2p orbital. The correct design for a neutral oxygen atom.

So we can conclude that Oxygen is the eighth element with a total of 8 electrons. In writing the electron layout for oxygen the first two electrons will go in the 1s orbital.

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The final speed would be equal because they don't depend on the mass or the radius.

The mass, gravitational pull, and height above the earth all affect how much potential energy an item has. This energy is transformed into kinetic or indeed the change in momentum, when you fall the thing. An object's mass and speed affect its kinetic energy.

The quantity of work performed on an object as well as its velocity following an inertia moment caused by external forces are two aspects that affect the overall kinetic energy about an object. The most crucial variables that affect kinetic energy are the motion calculated in terms of the object's mass and velocity.

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The loop-the-loop works in the same way, with the highest point of the loop representing the roller coaster's potential energy. It converts to kinetic energy on the way down and out of the loop-the-loop and rolls onto the next stomach-churning thrill.

Potential energy is the energy held by an object as a result of its position in relation to other objects, internal stresses, electric charge, or other factors.

Because of its position, an object can store energy. When a demolition machine's heavy ball is held in an elevated position, it stores energy. This stored positional energy is known as potential energy. Similarly, the position of a drawn bow allows it to store energy.

When potential energy is released, it is propelled into motion by gravity or elastic forces, among other catalysts.

Thus, The loop-the-loop works in the same way, with the highest point of the loop representing the roller coaster's potential energy.

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The moment of the force about point A is 66.13 Nm.

Moment is the product of a force and its perpendicular distance.

To calculate the magnitude of the moment produce about point A, we use the fornula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the moment of the force is 66.13 Nm.

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The difference between the string's tension at the bottom of the circle and at the top of the circle is 2mg.

Given the mass of the ball is m

radius of circle = r and constant speed is maintained = v

At the top of the circle, ΣF = FT + mg = mv^2/r, where F is the force acting on the string, T is tension, m is mass and g is gravitational acceleration.

Here as the ball moves in circle it carries centripetal force = mv^2/r.

Then FT = mv^2/r – mg.

At the bottom of the circle, ΣF = FT – mg = mv^2/r, So

FT = mv^2/r + mg

By comparing these two equations we get:

The difference is (mv^2/r + mg) – (mv^2/r – mg) = 2mg.

Hence the  required difference is 2mg.

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There is a 2mg difference in string tension between the circle's bottom and top points.

the mass of the ball is m

radius of circle = r and constant speed is maintained = v

At the top of the circle, ΣF = FT + mg = mv^2/r, where F is the force acting on the string, T is tension, m is mass and g is gravitational acceleration.

Here as the ball moves in circle it carries centripetal force = mv^2/r.

Then FT = mv^2/r – mg.

At the bottom of the circle, ΣF = FT – mg = mv^2/r, So

FT = mv^2/r + mg

By comparing these two equations we get:

The difference is (mv^2/r + mg) – (mv^2/r – mg) = 2mg.

Hence the  required difference is 2mg.

When the centripetal force and the gravitational force are exactly equal at the peak of the swing, the minimum speed will occur. The tension would then be exactly zero, and the ball would hardly be able to keep rolling in a circle.

The weight of the body operates vertically downward while the centrifugal force acts vertically downward at the lowest position. As a result, the string's tension is at its highest. The weight of the body acts vertically downward and the centrifugal force acts vertically upward at the highest point.

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A dog running is the best example of Kinetic energy.

In simple terms, Kinetic energy is defined as the energy due to motion. Any object in motion is said to possess kinetic energy.

Kinetic energy is formulated as [tex]E = 1/2 mv^{2}[/tex]

The energy possessed due to the state of rest is Potential Energy. It is represented using the symbol U.

Picture of sun shining on a field of flowers - is not an example of kinetic energy as no motion is involved, The picture is a still object.

An owl - is not an example of kinetic energy as it does not specify whether own is in motion or at rest.

A dog running - is an example of kinetic energy as the dog is in motion.

Rocks on grass - is not an example of kinetic energy as the rocks and grass are in the state of rest thus no motion is involved.

Thus, a dog running is the best example of Kinetic energy.

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Answer:

Resistivity and conductivity are reciprocal quantities.

Doubling one will cause the other to be reduced to one half.