Make a drawing of the problem situation including labeled vectors to represent the motion of the block as well as the forces on it. What measurements can you make with a meter stick to determine the angle of incline?
Draw a free-body diagram of the block as it slides down the track. Choose a coordinate system that will make calculations of energy transfer to and from the block easiest. What is your reason for choosing that coordinate system?
Transfer the force vectors to your coordinate system. What angles between your force vectors and your coordinate axes are the same as the angle between the track and the table?
In the coordinate system you have chosen, is there a component of the block’s motion that can be considered as in equilibrium? Use Newton’s second law in that direction to get an equation for the normal force in terms of quantities you know or can measure. Does the normal force increase, decrease, or stay the same as the ramp angle increases?
Write down the expression for the acceleration of the block in terms of quantities you know or can measure. Is the acceleration positive, negative, or zero? What is would be the difference between a positive and negative acceleration in this case?
Sketch a graph of the frictional force as a function of the normal force if the approximate relationship between them is good in this situation. How would you determine the coefficient of kinetic friction from this graph?
Restate the problem in terms of quantities you know or can measure. Beginning with basic physics principles, show how you get equations that give the forces you need to solve the problem. Make sure that you state any approximations or assumptions that you are making. Make sure that in each case the force is given in terms of quantities you know or can measure. Write down the approximate expression for friction that you are testing and sketch a graph of frictional force as a function of normal force for that equation.

Answers

Answer 1

First draw a free-body diagram of the block as it slides down the track. Then choose a coordinate system that will make calculations of energy transfer to and from the block easiest, and transfer the force vectors to your chosen coordinate system.

To determine the angle of incline, you can use a meter stick to measure the length of the ramp and the vertical height of the ramp, and then use basic trigonometry to calculate the angle. The expression for the acceleration of the block in terms of quantities you know or can measure is given by:

a=Fnet/m,

where Fnet is the sum of all forces acting on the block and m is its mass. The acceleration will be positive if the net force on the block is greater than zero, negative if the net force is less than zero, and zero if the net force is zero.  

Lastly, restate the problem in terms of quantities you know or can measure and use basic physics principles to show how you get equations that give the forces needed to solve the problem. Make sure that you state any approximations or assumptions that you are making, and write down the approximate expression for friction and sketch a graph of frictional force as a function of normal force for that equation.

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Related Questions

How would radiation occur in space?

Answers

Answer:

Space radiation is made up of three kinds of radiation: particles trapped in the Earth's magnetic field; particles shot into space during solar flares (solar particle events); and galactic cosmic rays, which are high-energy protons and heavy ions from outside our solar system.

Explanation:

A way of showing how energy moves through an ecosystem _________

Answers

Explanation:

Plants, as a autotrophs have chlorophyll to capture light energy from sun to make starch and sugar. Then, consumers eat plants, and the sugar is transferred to higher trophic level in a form of organic food. Nevertheless, energy is lost by uneaten food, indigestible food, unabsorbed food, excretory waste (eg co2) and heat loss by respiration.

Answer:

The Food Chain

Explanation:

The food chain is conducted of a web connected to three classifications. Each transfering energy to one a other when nutrients and living matter is passed from producers (one class) to consumers (another class), and is broken down by the decomposers (third class) lastly.

(03.07 MC)
A 660 kg car is travelling around a circular track of radius 55.0 m at 11.5 m/s.
Calculate the force and its direction that provides the centripetal force acting on the car to keep it
in the circular path. (3 points)
a) 24 N toward the center of the circle
b) 24 N along the line tangent to the circle
c) 1.587 E3 N along the line tangent to the circle
d) 1.587 E3 N toward the center of the circle

Answers

Answer: D) 1.587 E3 N toward the center of the circle

This is the same as saying 1.587*10^3 newtons, or we can say 1587 newtons

=================================================

Work Shown:

m = mass = 660 kilograms

v = velocity = 11.5 meters per second

r = radius of circle = 55.0 meters

-------------

F = centripetal force = inward pulling force toward center of circle

F = (m*v^2)/r

F = (660*11.5^2)/55

F = 1587

F = 1.587 * 10^3

F = 1.587 E 3

The "E 3" notation is what many calculators display scientific notation to be

The units for the force here are in newtons.

The force is pulling on the object toward the center of the circle, which helps keep the car on the circular path, rather than it going off on a tangent.

Pls help I'm desperate

If you place a hot piece of metal in a container of water, thermal energy flows from the metal to the water. What happens after the metal and the water reach the same temperature?

The flow of thermal energy stops, and the temperature remains constant.

The flow of thermal energy continues and causes both substances to become warmer.

The flow of thermal energy reverses and causes both substances to become warmer.

The flow of thermal energy reverses, and the water becomes colder.​

Answers

Answer:

I think your answer would be D

Explanation:

Are stairs a type of inclined plane?

Answers

Answer:

Inclined planes are simple machines used to make work easier. Ramps, ladders, and staircases are all inclined planes.

Explanation:

Answer:

imma say yes

Explanation:

Why does a person while firing a bullet holds the gun tightly to his shoulder? SHORT ANSWER ​

Answers

Answer:

They hold it tightly to their shoulder because the gun recoils and jumps back so by holding it to their shoulder it allows them to stablize the gun so that when it jumps in stead of the gun kicking back and flying the gun jumps and hit the shoulder.

Explanation:

Answer:helps to absorb most of the force produced by the recoil allowing the the shooter to steady his shoot and remain standing

Hope it helps

Explanation:

Answer this please ASAP!!

Answer this please ASAP!!

Answers

110 is the answer to the question

Answer:

dont run away

Explanation:

object with more momentum will take
What is the momentum of a 60 kg man running at a velocity of 4 m/s? -

Answers

Answer:

240 kg * m/s

Explanation:

Given

mass (m) = 60 kg

velocity (v) = 4 m/s

Momentum = ?

We know that

Momentum is the product of mass and velocity so

Momentum = m * v

                   = 60 * 4

                   = 240 kg * m/s

Hope it helps :)

Part II – Measuring distant objects [24 points] Parallax as
explained in the pre-lab activity, is an interesting way of
measuring the distance of an object by how much it appears to move
when viewed

Answers

wZAnswer:d

Explanation:

efwdx

Parallax is a valuable technique used in astronomy to measure the distances of nearby celestial objects accurately. It relies on the apparent shift in an object's position when viewed from different locations on Earth's orbit and utilizes trigonometry to calculate the distance to the object.

Parallax is the apparent shift or change in the position of an object when viewed from different perspectives. This effect occurs when an observer changes their viewing angle. In astronomy, parallax is used to measure the distances of stars, planets, and other celestial objects.

The principle behind parallax is simple: Observers on Earth have slightly different views of a nearby object compared to a distant one, due to the difference in the observer's location on the planet. By measuring the apparent shift in the position of an object when viewed from two different points (such as two different locations on Earth), astronomers can calculate the object's distance.

The baseline used for measuring the parallax is the distance between the two observing points. In the case of celestial objects, the baseline is the distance between two points on the Earth's orbit, which are six months apart. This is because the Earth's position is significantly different after half a year due to its revolution around the Sun.

To measure parallax accurately, astronomers use specialized instruments like telescopes and cameras to observe the position of stars or other celestial objects at different times of the year. By comparing the apparent shifts in the object's position, they can determine the parallax angle. Using trigonometry, they can then calculate the distance to the object.

The formula used to calculate the distance to the object is:

Distance (in parsecs) = 1 / Parallax (in arcseconds)

That 1 parsec is approximately equal to 3.26 light-years.

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The concept of inertia forms the basis for Newton's Third Law of Motion True False

Answers

Given

The concept of inertia forms the basis for Newton's Third Law of Motion

To find

The given statement is true or false

Explanation

The third law of motion states that every action has a equal and opposite reaction

Inertia is the property by virtue of which an object at rest tends to be at rest and object at motion tends to be at motion

Thus both the concept are not similar

Conclusion

The given statement is false

most interstellar hydrogen atoms emit only radio waves at a wavelength of 21cm, but some hydrogen clouds emit profuse amounts of visible light. what causes this difference?

Answers

The difference in the emission of interstellar hydrogen atoms between radio waves at a wavelength of 21cm and visible light is due to the physical conditions of the hydrogen clouds.

Hydrogen atoms emit radio waves at a wavelength of 21cm when their electrons change their spin state from parallel to anti-parallel. This transition corresponds to a change in energy that is characteristic of hydrogen atoms in interstellar space, where the density of particles is low and the temperature is cold.

However, some hydrogen clouds can emit visible light when the conditions are right for the excitation of the hydrogen atoms. This can happen, for example, when the density of particles is high enough for collisions to excite the electrons of the hydrogen atoms to higher energy levels, and then they release that energy as visible light when they return to their ground state.

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Suppose the Pathfinder moves at a rate of 0.2m/s for 20 seconds and then turns around and travels at the same speed for 3 seconds, what is the Pathfinder's current position?​

Answers

Answer:

PLEASE BE MORE SPECIFIC

Explanation:

The pathfinder is currently 3.4 m away from its initial position. Speed can be defined by the change in position of the object over time.

What is Speed?

It can be defined by the change in position of the object over time. The distance can be calculated by the formula,

\(d = s \times t\)

Where,

\(d\)- distance

\(s\) - speed

\(t\) - times -

Initially, Pathfinder moves,

\(d = 0.2 \times 20 \\\\d = 4 \rm \ m\)

Then he turns back and moves,

\(d' = 0.2 \times 3 = 0.6 \rm m\)

So the current position is:

\(D = d - d'\\\\D = 4 - 0.6 \\\\D = 3.4\rm m\)

Therefore, the pathfinder is currently 3.4 m away from its initial position.

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Describe the relationship between air time and range.

Answers

Answer: For the angles below 40, The air time and range are directly proportional meaning that if air time increases, the range increases. Like said earlier, the total traveled distance in the x-direction depends on the initial velocity and time.

Calculate the momentum elephant of a 2020 kg elephant charging a hunter at a speed of 7.49 m/s .

Answers

Answer:

15129.8 Kg•m/s

Explanation:

From the question given above, the following data were obtained:

Mass = 2020 kg

Velocity = 7.49 m/s

Momentum =?

Momentum is simply defined as the product of mass and velocity. Mathematically, it is expressed as:

Momentum = mass × velocity

With the above formula, we can obtain the momentum of the Elephant as follow:

Mass = 2020 kg

Velocity = 7.49 m/s

Momentum =?

Momentum = mass × velocity

Momentum = 2020 × 7.49

Momentum = 15129.8 Kg•m/s

Thus, the momentum of the Elephant is 15129.8 Kg•m/s

hey can anyone pls help me out in dis !

hey can anyone pls help me out in dis !

Answers

All of the above.

For example:

A glass plate is a solid. Particles vibrate in a solid and are closely packed. together.

It doesn’t change shape if you touch it.

It doesn’t change volume like it’s water.

Answer:

D: all of the above

Explanation:

particles in a solid do vibrate but they're tightly packed and move around fixed location

if another light bulb is connected in series to the first how would it affect the current in the power source?

Answers

When another light bulb is connected in series to the first, the current in the power source will remain the same, but the voltage will decrease, resulting in less light output for both bulbs.

The current in the power source will remain the same when another light bulb is connected in series. This is because the current will flow through both bulbs, dividing the same amount of current between them. When two bulbs are connected in series, each bulb has the same current running through it and so each bulb produces the same amount of light. The total resistance of the circuit will also increase as each light bulb adds resistance in series. The increase in resistance results in a decrease in voltage, thus each bulb produces less light.

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1:
a change in velocity?
Section 4.4
7. What is the acceleration of a car moving
along a straight-line path that increases its
speed from zero to 100 km/h in 10 s?
S
1
2

Answers

Initial velocity=u=0m/sFinal velocity=100km/h=v=100×5/18=500/18=2.7m/sTime=t=10s

\(\\ \tt\longmapsto Acceleration=\dfrac{v-u}{t}\)

\(\\ \tt\longmapsto Acceleration=\dfrac{2.7-0}{2}\)

\(\\ \tt\longmapsto Acceleration=\dfrac{2.7}{10}\)

\(\\ \tt\longmapsto Acceleration=27m/s^2\)

Answer:

Initial velocity=u=0m/s

Final velocity=100km/h=v=100×5/18=500/18=2.7m/s

Time=t=10s

⟼Acceleration=tv−u

⟼Acceleration=22.7−0

⟼Acceleration=102.7

⟼Acceleration=27m/s2

A source emits sound at a fixed constant frequency f. If the source moves away from you, and at the same time you run away from the source, the frequency you hear is the same as f.
higher than f.
lower than f.
unrelated to f.

Answers

If a source emits sound at a fixed constant frequency f, and it moves away from the observer at the same time as the observer moves away from the source, the frequency the observer hears is lower than f. Hence option lower than f. is correct.

This is due to the Doppler effect. What is the Doppler effect? The Doppler effect is a phenomenon that occurs when a source of waves, such as sound or light, is moving relative to an observer. The Doppler effect causes the observed frequency of the waves to differ from the emitted frequency when the source and observer are moving relative to each other. This change in frequency is due to the compression or stretching of the waves that occurs as the source moves closer or farther away from the observer.

If a source of sound is moving away from an observer, the sound waves become stretched and the frequency of the sound decreases, resulting in a lower pitch. If the source of sound is moving towards the observer, the sound waves become compressed, causing the frequency of the sound to increase, resulting in a higher pitch. This is the reason why an ambulance siren sounds higher-pitched as it approaches the listener and then drops to a lower pitch as it moves away.

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Describe two uses for a member of each representative group.

Answers

Potassium and beryllium

Angular velocity magnitude from speed A point is currently at position x =-4 m, y =-5 m, z =-4 m and is rotating about the origin with angular velocity w. The speed of the particle is u = 10 m/s and w is parallel to the vector u = 5i + 3j + k. Matlab/Mathematica input: x =-4 y--5 z=-4 v=10 uvec [5,3,1] What is the magnitude of the angular velocity vector? w = | 1.324 rad/s Try question again Correct answer a = 2.7173454408164117 rad/s

Answers

The magnitude of the rotational velocity vector is approximately 2.72 rad/s (rounded to two decimal places). In the answer, A = 2.7173454408164117 rad/s.

How can you calculate the angular velocity's magnitude?

=t, where an angular rotation occurs during the course of time t. The angular velocity increases as the rotation angle increases over a particular period of time. The radians per second (rad/s) unit of measure for angular velocity.

proj v(x) is calculated as (x. v) / |v|2 * v, where ". " stands for the dot product. R = |x - proj v(x)| then.

Once we have determined r, we may apply the following formula to determine w:

w = u / r

Simplifying and plugging in the supplied values yields:

v = [3 -4 7]

r = [x - proj v(x)] = [4-9-28]/sqrt(35)] = [41/sqrt] (35)

The formula is w = u / r = 10 / (41/sqrt(35)) = 2.7173454408164117 rad/s.

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A car accelerates at -1 m/s2. What is its final speed (in m/s) at the end of 4 seconds if it started at 1 m/s? (round
to the nearest whole number)

Answers

The final velocity of the car at the end of 4 seconds would be -3 m/s. Negative velocity indicates that the car is slowing down.

This is an exercise in Rectilinear Uniformly Varied Motion (MRUV) is a type of motion in which an object moves in a straight line and experiences changes in its velocity at a constant rate. In this type of motion, the acceleration of the object remains constant over time.

The distinctive feature of the MRUV is that the velocity of the object changes uniformly, that is, its velocity increases or decreases by a constant amount in each unit of time. If the object experiences a positive acceleration, its velocity increases with time. On the other hand, if the object experiences a negative acceleration, its speed decreases.

In an MRUV, constant acceleration has a direct impact on displacement and the time it takes for the object to reach a certain speed. Also, the direction of the acceleration determines whether the object is accelerating or decelerating relative to its initial motion.

This type of movement is found in various situations of daily life, such as the launch of an object upwards and its subsequent fall, the movement of cars on a road with acceleration or braking, or even the study of bodies in free fall.

To solve this problem, we can use the kinematics formula for constant acceleration:

Vf = V₀ + a × t

Where:

Vf is the final speedV₀ is the initial velocitya is the accelerationt is the time

In this case, the initial velocity (vi) is 1 m/s, the acceleration (a) is -1 m/s^2 (negative because it indicates deceleration), and the time (t) is 4 seconds.

Substituting these values into the formula, we get:

Vf = V₀ + a × t

Vf = 1 m/s + (-1 m/s²) × 4 s

Vf = 1 m/s - 4 m/s

Vf = -3 m/s

The final velocity of the car at the end of 4 seconds would be -3 m/s. Negative velocity indicates that the car is slowing down.

ruby is in miami an texts her cousin, Xavier, in Seattel. her clock says 1:00 am

Answers

Answer:

so its 10pm in seattle

Explanation:

A slide projector has a magnification of 50. How wide will the projected image be if the slide is 2.8 cm wide?

Answers

Answer:

hi = 12mm or 1.2cm

Explanation:

XOXO

Kit ^w^

A slide projector has a magnification of 50. 12mm or 1.2cm.

What is Magnification?

Bringing an object as close to the eye as feasible when wishing to observe an object's details is instinctual. The angle that an object subtends at the eye increases with proximity to the eye, making it appear larger.

However, if an item is too near, the eye will no longer be able to generate a distinct image. The creation of a "virtual image" that may be comfortably observed is made possible by the use of a magnifying lens between the observer and the object.

The magnifier should be positioned exactly in front of the eye to provide the clearest image possible. Once a clear image of the thing is present, the object of interest is brought closer to the eye.

Therefore, A slide projector has a magnification of 50. 12mm or 1.2cm.

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When light goes from one material into another material having a HIGHER index of refraction, Group of answer choices

Answers

Light passes from a material to another material with a higher refractive index, it undergoes refraction and bends towards the normal at the interface between the two materials.

When light goes from one material into another material with a higher index of refraction, it undergoes refraction. Refraction is the bending of light as it passes from one medium to another, caused by the change in its speed and direction.

In this scenario, the higher index of refraction indicates that the second material has a greater optical density than the first material. When light transitions from a lower to a higher refractive index material, it bends towards the normal (an imaginary line perpendicular to the surface) at the boundary between the two materials. This causes the light ray to change its direction.

The degree of bending, or the angle of refraction, is determined by Snell's law, which relates the incident angle, the refracted angle, and the refractive indices of the two materials. The exact amount of bending depends on the specific refractive indices of the materials involved.

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Please help quick

LaToya uses 50 newtons (N) of force to pull a 500 N cart. Which statements are correct about calculating LaToya's mechanical advantage? Select all that apply

A The input force is 50 N

B

The output force is 50N

с

The input force is 500 N

D

The output force is 450 N

E

The mechanical advantage is 10

F

The mechanical advantage is 100

Answers

F=ma

Newton's second law states that force is proportional to what is required for an object of constant mass to change its velocity. This is equal to that object's mass multiplied by its acceleration. We use Newtons, kilograms, and meters per second squared as our default units, although any appropriate units for mass (grams, ounces, etc.) or velocity (miles per hour per second, millimeters per second2, etc.) could certainly be used as well - the calculation is the same regardless.

The statements which are correct about calculating LaToya's mechanical advantage are—The input force is 50 N, the output force is 450 N and the mechanical advantage is 10.Therefore, the correct option is A, D and E.

What is mechanical advantage?

Mechanical advantage is the ratio of output force to input force. In this case, LaToya is using a force of 50 N to pull a cart that weighs 500 N. The output force is the weight of the cart minus the force LaToya exerts on it:

Output force = 500 N- 50 N = 450 N

To see why statement F is incorrect, note that the formula for mechanical advantage is:

Mechanical advantage = output force / input force

Substituting the values we found earlier, we get:

Mechanical advantage = 450 N / 50 N = 9

So the mechanical advantage is actually 9, not 100.

Therefore, the correct option is A, D and E.

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Calculate the answer to the correct
number of significant digits.
15.3 + 1.285

Calculate the answer to the correctnumber of significant digits.15.3 + 1.285

Answers

16.585 is the answer

As the diameter of the wire increases, the AWG number_____, and the resistance of the conductor_____.

Answers

As the diameter of the wire increases, the AWG number decreases, and the resistance of the conductor decreases.

AWG (American Wire Gauge) is a standard used to measure the diameter of wires, with smaller numbers indicating larger wire diameters.

Resistance is a measure of how difficult it is for an electric current to flow through a wire, with higher resistance causing a reduction in the amount of current that can pass through the wire.

When the wire diameter increases, the cross-sectional area of the wire also increases, which means there is more space for the electric current to flow through, resulting in lower resistance.

Therefore, a larger diameter wire has a lower AWG number and lower resistance, making it a more efficient conductor of electric current.

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Please someone help me with this!!! ​

Please someone help me with this!!!

Answers

Answer: Gravitational potential energy changes.

Explanation: This is because depending on the amount of mass in an object that’s the amount of gravity pulling you down to the center of the earth

What is the angle of incidence if the total angle between the incidence ray and reflected ray is 70⁰​

What is the angle of incidence if the total angle between the incidence ray and reflected ray is 70

Answers

Answer:

35°

Explanation:

By laws of reflection,

Angle of incidence = Angle of reflection

Angle between incident ray and reflected ray = 70°

Angle of incidence + Angle of reflection = 70°

Since,

Angle of incidence = Angle of reflection

Angle of incidence + Angle of incidence = 70°

2 Angle of incidence = 70°

Divide 2 on both sides,

Angle of incidence = 70° / 2

Angle of incidence = 35°

A child shoots a 3.0 g bottle cap up a ramp 20° above horizontal at 2.0 m/s. The cap slides in a straight line, slowing to 1.0 m/s after traveling some distance, d. If the coefficient of kinetic friction is 0.40, find that distance.

Answers

Answer:

Approximately \(0.21\; {\rm m}\).

(Assuming that \(g = 9.81\; {\rm m\cdot s^{-2}}\).)

Explanation:

As the bottle cap slows down, it lost kinetic energy \((\text{KE})\): \(\Delta \text{KE} = (1/2)\, m\, (u^{2} - v^{2})\), where \(m\) is the mass of the cap, \(v = 1.0\; {\rm m\cdot s^{-1}}\), and \(u = 2.0\; {\rm m\cdot s^{-1}}\).

The amount of kinetic energy lost should also be equal to the sum of:

gain in gravitational potential energy (\(\text{GPE}\)), andwork that friction has done on the cap.

Let \(d\) denote the distance that the cap has travelled along the ramp. The height of the cap would have increased by:

\(\Delta h = d\, \sin(\theta)\), where \(\theta = 20^{\circ}\) is the angle of elevation of the ramp.

The \(\text{GPE}\) of the cap would have increased by:

\(\Delta \text{GPE} = m\, g\, \Delta h = m\, g\, d\, \sin(\theta)\).

To find the friction on the cap, it will be necessary to find the normal force that the ramp exerts on the cap.

Let \(\theta = 20^{\circ}\) denote the angle of elevation of this ramp. Decompose the weight of the cap \(m\, g\) (where \(m\) is the mass of the cap) into two directions:

Along the ramp: \(m\, g\, \sin(\theta)\),Tangential to the ramp: \(m\, g\, \cos(\theta)\).

The normal force on the cap is entirely within the tangential direction.

Since the cap is moving along the ramp, there would be no motion in the tangential direction. Forces in the tangential direction should be balanced. Hence, the normal force on the cap will be equal in magnitude to the weight of the cap in the tangential direction: \(F_{\text{normal}} = m\, g\, \cos(\theta)\).

Since the cap is moving, multiply the normal force on the cap by the coefficient of kinetic friction \(\mu_{\text{k}}\) to find the friction \(f\) between the ramp and the cap:

\(f = \mu_{\text{k}}\, F_{\text{normal}}\).

After a distance of \(x\) along the ramp, friction would have done work of magnitude:

\(\begin{aligned} (\text{work}) &= f\, s \\ &= (\mu_{\text{k}}\, F_{\text{normal}})\, (d) \\ &= \mu_{\text{k}}\, m\, g\, \cos(\theta)\, d\end{aligned}\).

Overall:

\(\begin{aligned} \Delta \text{KE} &= \Delta \text{GPE} + \mu_{\text{k}}\, m\, g\, \cos(\theta)\, d \\ &= m\, g\, \sin(\theta)\, d + \mu_{\text{k}}\, m\, g\, \cos(\theta)\, d \\ &= m\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))\, d\end{aligned}\).

At the same time:

\(\Delta \text{KE} = (1/2)\, m\, (v^{2} - u^{2})\).
Therefore:

\(\displaystyle \frac{1}{2}\, m\, (v^{2} - u^{2}) = m\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))\, d\).

\(\begin{aligned}d &= \frac{m\, (u^{2} - v^{2})}{2\, m\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))} \\ &= \frac{u^{2} - v^{2}}{2\, g\, (\sin(\theta) + \mu_{\text{k}}\, \cos(\theta))} \\ &= \frac{(2.0)^{2} - (1.0)^{2}}{2\, (9.81)\, (\sin(20^{\circ}) + 0.40\, \cos(20^{\circ}))}\; {\rm m} \\ &\approx0.21\; {\rm m}\end{aligned}\).

Other Questions
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