Suppose the worker pushing the oranges decides instead to attach a rope to the box of oranges and pull from the other side (the South side). Suppose she pulls in such a way that the pulling force has components of the same size as did the pushing force, except that the vertical component would now be upward instead of downward. What would be the resulting acceleration of the box of oranges

Answers

Answer 1

The resulting acceleration of the box of oranges would be upward, with the same magnitude as before. The change in direction of the pulling force would only affect the direction of the acceleration.

When the worker pushes the box of oranges, the downward force of gravity and the normal force cancel each other out, resulting in zero net vertical force. The horizontal force of the worker's push causes the box to accelerate horizontally.

When the worker pulls the box from the other side, the vertical component of the pulling force opposes the force of gravity. As a result, the net vertical force becomes the difference between the upward vertical component of the pulling force and the downward force of gravity. However, the magnitude of the vertical component of the pulling force remains the same as the magnitude of the pushing force. Therefore, the resulting upward acceleration of the box of oranges will have the same magnitude as before.

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Related Questions

Lexy throws a dart with an initial velocity of 25 m/s at an angle of 60° relative to the ground. What is the approximate vertical component of the initial velocity? 0. 5 m/s 0. 87 m/s 12. 5 m/s 21. 7 m/s.

Answers

The approximate vertical component of the initial velocity is `21.7 m/s`. The vertical component of an initial velocity in a projectile motion is given by the equation: `Vy = V₀sin(θ)` where `V₀` is the initial velocity of the projectile, `θ` is the angle at which the projectile was thrown and `Vy` is the vertical component of the initial velocity.

The vertical component of an initial velocity in a projectile motion is given by the equation: `

Vy = V₀sin(θ)`

With the given values `V₀ = 25 m/s` and `θ = 60°`,

The vertical component of the initial velocity is:
Vy = V₀sin(θ)
Vy = (25 m/s) sin(60°)
Vy ≈ 21.7 m/s
Therefore, the approximate vertical component of the initial velocity is `21.7 m/s`.

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The sun heats land faster than it heats water. As a result, the air above the water is usually cooler than that above land. Many times, early in the morning, the air above the water is very dense and is difficult to see through. What effect is observed from this difference in temperature?.

Answers

The effect that is observed from the difference in temperature is a sea breeze.

A sea breeze is a cooling wind that blows from the sea to the land and results from the difference in temperature between the land and the sea. The sun heats land faster than water, which causes the air above the land to heat up faster than the air above the water, as per the given statement.

As a result, the warm air above the land rises, creating low pressure over the land. On the other hand, the cool air above the sea sinks, creating high pressure over the sea. As a result, the cool air moves from the sea to the land, which is known as a sea breeze.So, the difference in temperature caused by the sun's heating land faster than water leads to the formation of a sea breeze.

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The electron and proton of a hydrogen atom are separated by a distance of approximately 5.3 x 10^-11m. Find the magnitude of the electric and gravitational force between the two particles.

Answers

The magnitude of the electric force is 8.21 × 10⁻⁸ N and the gravitational force is 3.61 × 10⁻⁸ N. The electric force acting between the electron and proton of hydrogen atom is given by: Coulomb's Law of electrostatics, F = 1 / 4πε₀ × q₁q₂ / r².

Given that, Distance between the electron and proton of a hydrogen atom, r = 5.3 × 10⁻¹¹m, Mass of an electron, m₁ = 9.1 × 10⁻³¹ kg, Mass of a proton, m₂ = 1.67 × 10⁻²⁷ kg, Charge of an electron, q₁ = -1.6 × 10⁻¹⁹ C, Charge of a proton, q₂ = +1.6 × 10⁻¹⁹ C.

Where,ε₀ = permittivity of free space = 8.854 × 10⁻¹² C²/N m²

F = 1 / 4π (8.854 × 10⁻¹²) × (1.6 × 10⁻¹⁹)² / (5.3 × 10⁻¹¹)²

F = 8.21 × 10⁻⁸ N

The gravitational force acting between the electron and proton of hydrogen atom is given by:

Newton's Law of gravitation, F = G × m₁m₂ / r², Where, G = gravitational constant = 6.67 × 10⁻¹¹ N m²/kg²

F = (6.67 × 10⁻¹¹) × (9.1 × 10⁻³¹) × (1.67 × 10⁻²⁷) / (5.3 × 10⁻¹¹)²

F = 3.61 × 10⁻⁸ N

Therefore, the magnitude of the electric force is 8.21 × 10⁻⁸ N and the gravitational force is 3.61 × 10⁻⁸ N.

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A person standing atop a building drops a coin. How fast will the coin be traveling 2 seconds after she drops it? 3 seconds?

Answers

The speed of the coin when dropped from the top of a building, using free fall formula after 2 and 3 seconds are, 19.6 m/s and 29.4 m/s.

The speed of an object in free fall can be determined by multiplying the acceleration due to gravity (which is approximately 9.8 m/s²) by the time elapsed. In this case, after 2 seconds, the coin will have fallen a distance of 19.6 meters and will be traveling at 19.6 m/s. Similarly, after 3 seconds, the coin will have fallen a distance of 44.1 meters and will be traveling at 29.4 m/s.

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A call can supply circuit of 0. 4A and 0. 2A through a 4ohms and 10 ohms resistor respectively what is the internal resistant of the cell

Answers

A call can supply circuit of 0. 4A and 0. 2A through a 4ohms and 10 ohms resistor respectively what is the internal resistant of the cellThe internal resistance of the cell is 3 ohms.

According to Ohm's Law, the current in a circuit can be determined using the equation I = V/R, where I is the current, V is the voltage, and R is the resistance. In this case, we have two resistors connected in parallel. Let's assume the voltage of the cell is V.

For the 4-ohm resistor, the current is given as 0.4A. Using Ohm's Law, we can calculate the voltage across the resistor as V1 = I1 * R1 = 0.4A * 4ohms = 1.6V.

For the 10-ohm resistor, the current is given as 0.2A. Using Ohm's Law, we can calculate the voltage across the resistor as V2 = I2 * R2 = 0.2A * 10ohms = 2V.

Since the resistors are in parallel, the voltage across both resistors is the same, so V1 = V2. This means the internal resistance of the cell can be calculated as V = I * r, where r is the internal resistance. Substituting the values, we have 1.6V = 0.4A * r, which gives us r = 1.6V / 0.4A = 4 ohms.

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Question 5 (10 points)


The friction force depends on what two factors?



Question 5 options:



density and the spring constant




The normal force and distance




The coefficient of friction and the normal force




The coefficient of friction and height

Answers

The friction force depends on two factors: the normal force and the coefficient of friction. The normal force acts perpendicular to the surface of an object, while the coefficient of friction measures how difficult it is to slide one surface over another. F = N.

The friction force depends on two factors: the normal force and the coefficient of friction. The normal force is the force that acts perpendicular to the surface of an object, while the coefficient of friction is a measure of how difficult it is to slide one surface over another. The friction force depends on the coefficient of friction between the two surfaces in contact, which is given by the product of the coefficient of friction and the normal force. Mathematically, F = N, where F is the force of friction,  is the coefficient of friction, and N is the normal force.

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A projectile is launched horizontally from a height of 8. 0 m. The projectile travels 6. 5 m before hitting the ground. The velocity of the projectile the moment it was launched, rounded to the nearest hundredth, is m/s.

Answers

The initial velocity of a projectile launched horizontally can be calculated using the equation of distance covered horizontally (x) = Initial velocity (u)  Time of flight (t). The horizontal component of the initial velocity can be determined by x = u  t, t = 1.63 s, x = 6.5 mu = x / t = 6.5 m / 1.63 su = 3.99 m/s  4.00 m/s.

The initial velocity of the projectile that was launched horizontally can be calculated using the equation below: Distance covered horizontally (x) = Initial velocity (u) × Time of flight (t) where, Time of flight (t) can be found using the formula below: t = [2 × vertical height (h)] / g where ,g is the acceleration due to gravity = 9.8 m/s².The vertical height (h) of the projectile is 8.0 m. So the time of flight of the projectile will bet = [2 × 8.0 m] / 9.8 m/s²t = 1.63 s Therefore, the horizontal component of the projectile’s initial velocity can be determined by: x = u × tt = 1.63 s, x = 6.5 mu = x / t = 6.5 m / 1.63 su = 3.99 m/s ≈ 4.00 m/s. So, the projectile was launched horizontally with a velocity of 4.00 m/s (rounded to the nearest hundredth).Content loaded: The term “content loaded” is used to indicate that the contents of a webpage or app have finished loading and are ready for viewing or use.

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Lexy throws a dart with an initial velocity of 25 m/s at an angle of 60° relative to the ground. What is the approximate vertical component of the initial velocity? 0. 5 m/s 0. 87 m/s 12. 5 m/s 21. 7 m/s.

Answers

The approximate vertical component of the initial velocity is 21.7 m/s.

option D.

What is the approximate vertical component of the initial velocity?

The approximate vertical component of the initial velocity is calculated by applying the following equation as follows;

Mathematically, the formula vertical component of velocity is given as;

Vy = V sinθ

where;

V is the magnitude of the initial velocityVy is the vertical component of the velocityθ is the direction of the initial velocity

The approximate vertical component of the initial velocity is calculated as;

Vy = 25 m/s  x sin (60)

Vy = 21.7 m/s

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If the magnetic field in an electromagnetic field is doubled, by what factor does the electric field change?.

Answers

If the magnetic field in an electromagnetic field is doubled, the electric field remains unaffected. Therefore, the factor by which the electric field changes is 1, i.e., there is no change in the electric field.

What is an electromagnetic field?

An electromagnetic field refers to a combination of an electric field and a magnetic field. It is a field of energy produced by an electric charge in motion. These two fields are perpendicular to each other and exist perpendicular to the direction of the electromagnetic wave.

Magnetic fields can be generated from the presence of an electrical current. Conversely, a magnetic field may induce a current in a conductor if there is a time-varying magnetic flux that traverses a surface. On the other hand, an electric field is created by any charged particle, such as an electron, proton, or even a macroscopic charged object, like a balloon that has been rubbed on someone's hair.

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You have discovered and practiced the memory tools and study skills in this learning path.



Describe one specific tool or skill that has been most valuable for you to learn.


Describe how that specific tool or skill has been valuable.


Your answer should be at least two complete sentences.

Answers

One specific tool or skill that has been most valuable for me to learn is the technique of creating mnemonic devices. Mnemonic devices are memory aids that help me remember and recall information more easily. They involve associating the information I want to remember with vivid and memorable images, patterns, or acronyms.

This tool has been valuable because it has significantly improved my ability to retain and retrieve information. By using mnemonic devices, I can convert complex or abstract concepts into visual or auditory cues that are easier for my brain to process and store. It has helped me remember key facts, formulas, and sequences, making my studying more efficient and effective.

Additionally, mnemonic devices have made learning more engaging and fun, as I get to be creative in constructing mental associations that stick in my memory for a long time.

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3. A grating with 1555 lines/cm is illuminated with light of wavelength 565 nm. What


is the highest-order number that can be observed with this grating? (Hint:


Remember that sin can never be greater than 1 for a diffraction grating. )




important!

Answers

The highest-order number that can be observed with this grating using diffraction formula is 1/1555.

It is determined using the formula for diffraction: mλ = d sinθ. Where m is the order number, λ is the wavelength of light, d is the grating spacing, and θ is the angle of diffraction. In this case, the grating has 1555 lines/cm, which means the grating spacing is 1/1555 cm.

To determine the highest-order number, calculate m × (565 × 10^-9 meters) = (1/1555 cm) × sinθ, where θ must be less than or equal to 90 degrees to satisfy sinθ ≤ 1. Given the wavelength of light as 565 nm (or 565 × 10^-9 meters), we can proceed with the calculation. Since sinθ ≤ 1, the highest-order number (m) can be determined by substituting θ = 90 degrees into the equation: m = (1/1555 cm) × sin(90 degrees).

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geostationary satellite are placed in orbit of radius 4.2*10^4km use this information to deduce of at that height

Answers

To deduce the orbital period of a geostationary satellite at a given height, we can use the formula for the orbital period of a satellite:

T = 2π√(r³/GM),

where T is the orbital period, r is the radius of the orbit, G is the gravitational constant (approximately 6.67430 x 10^(-11) m³/(kg·s²)), and M is the mass of the Earth (approximately 5.972 x 10^24 kg).

First, we need to convert the radius of the orbit from kilometers to meters:

r = 4.2 x 10^4 km * 10^3 m/km = 4.2 x 10^7 m.

Now, we can calculate the orbital period:

T = 2π√((4.2 x 10^7)^3 / (6.67430 x 10^(-11) * 5.972 x 10^24)).

Evaluating this expression, we can find the orbital period of the geostationary satellite at that height.

Please note that the above calculation assumes a circular orbit and neglects the effects of other celestial bodies and atmospheric drag, which could slightly affect the satellite's actual orbital period.

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Susie estimated that she can run for hours at a steady rate of 8mph. She enters a marathon, a distance of 26miles. How long should it take her to complete the race? Give answers in hours and minutes.

Answers

To determine the time it would take Susie to complete the marathon, we can use the formula: Time = Distance / Speed

Given that the distance of the marathon is 26 miles and Susie's steady rate is 8 mph, we can substitute these values into the formula. Time = 26 miles / 8 mph. To calculate the time, we divide 26 miles by 8 mph: Time = 3.25 hours. Since there are 60 minutes in an hour, we can convert the decimal part of the time to minutes: 0.25 hours * 60 minutes/hour = 15 minutes.  Therefore, it would take Susie approximately 3 hours and 15 minutes to complete the marathon.

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A 5-kg object is moving to the right at 4 m/s and collides with another object moving to the left at 5 m/s. The objects collide and stick together. After the collision, the combined object:

Answers

After the collision, the two objects stick together and move as one. Their total mass is m1 + m2 = 5 kg + m2.

How to determine the effect of the collision

In this case, we can apply the principle of conservation of linear momentum

The initial momentum of the first object (P1_initial) is given by its mass (m1) times its velocity (v1), which is [tex]5 kg * 4 m/s = 20 kg*m/s.[/tex]

Therefore, the total initial momentum [tex](P_{total_initial}) is P1_{initial} + P2_{initial} = 20 kg*m/s - m2 * 5 m/s.[/tex]

After the collision, the two objects stick together and move as one.

Their total mass is m1 + m2 = 5 kg + m2.

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A stevedore slides a crate along a dock with a 50 kg horizontal force of 175 N. The opposing force of friction is 120 N. If started from rest, what is the crates’s final velocity after 0.5s?

Answers

To determine the crate's final velocity after 0.5 seconds, we can use the concept of Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.

In this scenario, the stevedore applies a horizontal force of 175 N to move the crate along the dock. However, there is also an opposing force of friction acting in the opposite direction, which has a magnitude of 120 N. The net force is the difference between these two forces, so we can calculate it as follows:

Net force = Applied force - Frictional force

Net force = 175 N - 120 N

Net force = 55 N

Now, using Newton's second law of motion, we can determine the acceleration of the crate. Rearranging the equation, we have:

Net force = mass * acceleration

55 N = 50 kg * acceleration

Solving for acceleration:

acceleration = 55 N / 50 kg

acceleration = 1.1 m/s²

Since we know the initial velocity of the crate is zero (as it starts from rest), and we want to find the final velocity after 0.5 seconds, we can use the equation of motion:

final velocity = initial velocity + (acceleration * time)

Plugging in the values:

final velocity = 0 + (1.1 m/s² * 0.5 s)

final velocity = 0.55 m/s

Therefore, the crate's final velocity after 0.5 seconds is 0.55 m/s. This means that after being subjected to a 175 N force and experiencing 120 N of friction, the crate gains a velocity of 0.55 m/s in the direction of the applied force.

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PLEASE ANSWER


Make the same observation of wave speed - the speed of the crest moving from left to right across the screen. Does this ten-fold increase in frequency - from


about 0. 1 Hz to about 10 Hz - have any noticeable and appreciable effect upon the wave speed? Explain


your answer and discuss your observations

Answers

While the frequency of a wave does not directly affect its wave speed, it can influence other wave properties.

The frequency of a wave is defined as the number of complete cycles or oscillations it completes in one second. The wave speed, on the other hand, refers to the speed at which the wave propagates through a medium.

In general, the frequency of a wave does not have a direct impact on its wave speed. Wave speed is primarily determined by the properties of the medium through which the wave is traveling, such as its density and elasticity.

Therefore, the ten-fold increase in frequency from about 0.1 Hz to about 10 Hz would not have a noticeable or appreciable effect on the wave speed itself. The wave speed would remain relatively constant unless there are changes in the properties of the medium.

However, it is worth noting that changes in frequency can affect other wave characteristics, such as wavelength and period. The wavelength is the distance between two consecutive crests or troughs of a wave, while the period is the time it takes for one complete cycle of the wave. These quantities are related to frequency through mathematical relationships.

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A stone is(4i+5j) find the height maximum and the range

Answers

The maximum height of the stone is approximately 1.27 meters and the range is approximately 2.04 meters.

To find the maximum height and range of a projectile, we need to consider the motion of the object in the x and y directions.

Given that the initial velocity of the stone is (4i + 5j), we can break it down into its x and y components:

Initial velocity in the x direction (Vx) = 4

Initial velocity in the y direction (Vy) = 5

The maximum height (H) can be determined using the formula:

H = (Vy^2) / (2 * g)

where g is the acceleration due to gravity. Assuming g = 9.8 m/s^2, we can calculate the maximum height:

H = (5^2) / (2 * 9.8)

H = 25 / 19.6

H ≈ 1.27 meters

The range (R) can be calculated using the formula:

R = (Vx * Vy) / g

R = (4 * 5) / 9.8

R = 20 / 9.8

R ≈ 2.04 meters

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A 20. Kilogram rock is lifted 7. 0 meters above the ground. What is the gravitational


potential energy of the rock?

Answers

The gravitational potential energy of the rock is 1,372 Joules.

The gravitational potential energy (PE) of an object can be calculated using the formula:

PE = m * g * h, where:

m is the mass of the object,

g is the acceleration due to gravity, and

h is the height or distance above the reference point.

In this case, the mass of the rock (m) is 20 kilograms, and the height (h) is 7.0 meters.

The acceleration due to gravity (g) is approximately 9.8 m/s².

Now we can calculate the gravitational potential energy:

PE = 20 kg * 9.8 m/s² * 7.0 m

PE = 1,372 Joules

Therefore, the gravitational potential energy of the rock is 1,372 Joules.

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What is the energy of a photon with a frequency of 1. 7 × 1017 Hz? Planck’s constant is 6. 63 × 10–34 J•s. 1. 1 × 10–17 J 1. 1 × 10–16 J 8. 3 × 10–16 J 8. 3 × 10–15 J.

Answers

The energy of the photon is determined as 1.1 x 10⁻¹⁶ J.

What is the energy of the photon?

The energy of the photon is calculated by applying the following formula as follows;

E = hf

where;

h is the Planck's constantf is the frequency of the photon

The given parameters include;

frequency of the photon = 1. 7 × 10¹⁷ Hz

Planck’s constant is 6. 63 × 10⁻³⁴ J•s

The energy of the photon is calculated as follows;

E =  6. 63 × 10⁻³⁴ J•s  x 1. 7 × 10¹⁷ Hz  

E = 1.1 x 10⁻¹⁶ J

Thus, the energy of the photon is determined as 1.1 x 10⁻¹⁶ J.

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The international astronomical union has identified 88 what?.

Answers

The International Astronomical Union (IAU) has identified 88 constellations.

A constellation is an area of the celestial sphere as defined by the International Astronomical Union (IAU).

There are 88 constellations, each with a particular area and a list of stars associated with it. The majority of constellations are named after ancient Greek and Roman mythological characters, with a few named after animals, scientific instruments, and seasonal objects like planets and the zodiac, as well as a handful named after navigational tools and historical figures. The concept of constellations dates back thousands of years, and their use in astronomy has allowed astronomers to create a map of the sky and chart the motions of celestial objects.

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Two rows of fluorescent lamps are installed in an office on the same branch circuit, with each row drawing 12.5 amperes. The source voltage is 277 volts, and the total line resistance of the circuit conductors is 0.5 Ω. The wire used has a constant (k) of 12.6. What is the percentage of voltage drop? (Round the FINAL answer to one decimal place.)

Answers

According to the solving the percentage of voltage drop is 2.8%

Let V = Source voltage

= 277 volts

Let R = Total line resistance of the circuit conductors

= 0.5 Ω

Let A = Each row drawing

= 12.5 amperes

Let k = 12.6

The voltage drop formula is given by:

Vdrop = kRA

Where; Vdrop = Voltage drop

= Constant of the wire

= Total line resistance

A = Load Current

Putting the given values in the voltage drop formula, we get;

Vdrop = 12.6 x 0.5 Ω x (12.5 + 12.5) amps

Vdrop = 12.6 x 0.5 Ω x 25 amps

Vdrop = 7.875 volts

Percentage of Voltage drop = (Vdrop / V) x 100%= (7.875 / 277) x 100%

Percentage of Voltage drop = 2.8427 % ≈ 2.8%

Therefore, the percentage of voltage drop is 2.8%.

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A web browser is open on yur screen. The lengh of the monitor is x+7. The area of the browser windw is 24 inches. The dimensions of the browser window are x-2 and x. Find the length of the browser window x. Part B. The browser covers 3/13 of the screen. What are the dimensions of the screen

Answers

The length of the browser window (x) is 6. The dimensions of the screen are approximately 3 inches (width) and 18/13 inches (height).

Let's solve the equations step by step:

Part A:

The area of the browser window is given by the equation:

(x - 2) * x = 24

Expanding the equation:

[tex]x^{2}[/tex] - 2x = 24

Rearranging the equation to standard quadratic form:

[tex]x^{2}[/tex] -  2x - 24 = 0

Factoring the quadratic equation:

(x - 6)(x + 4) = 0

Setting each factor to zero:

x - 6 = 0 or x + 4 = 0

Solving for x:

x = 6 or x = -4

Since the length of the monitor cannot be negative, we discard the solution x = -4.

Therefore, the length of the browser window (x) is 6.

Part B:

The dimensions of the screen can be calculated using the length of the monitor (x+7) and the coverage ratio of the browser window (3/13).

The width of the screen is given by:

Width = (3/13) * (x + 7)

The height of the screen is given by:

Height = (3/13) * (x)

Substituting the value of x = 6:

Width = (3/13) * (6 + 7) = (3/13) * 13 = 3

Height = (3/13) * 6 = 18/13

Therefore, the dimensions of the screen are approximately 3 inches (width) and 18/13 inches (height).

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PLEASE USE KINEMATIC EQUATION!



You are asked to do an experiment to measure g. You set up a device that drops a metal ball from


rest from a height of 1.650 m. Using an accurate timing device that detects the release of the ball


and its landing on the floor, you measure the average time of the falling ball to be 0.585s.




a. What do you measure the value of g as?


b. Write an explanation as to the error from the accepted value of 10 m/s^2 (or 9.8)

Answers

1. The value of g measured from the experiment is approximately 5.646 m/s^2.

How to solve for the experiment

To determine the value of acceleration due to gravity (g) using the given information, we can utilize the kinematic equation for the motion of a falling object:

h = 0.5 * g * t^2

where:

h is the height (1.650 m),

g is the acceleration due to gravity (what we want to find), and

t is the time taken (0.585 s).

a) To find the value of g, we rearrange the equation to solve for g:

g = 2h / t^2

Substituting the given values:

g = 2 * 1.650 m / (0.585 s)^2

g = 5.646 m/s^2

Therefore, the value of g measured from the experiment is approximately 5.646 m/s^2.

2. Air resistance: In real-world scenarios, the presence of air resistance can affect the motion of falling objects. The simplified equation used assumes no air resistance, which may result in a deviation from the accepted value.

Imperfect timing device: The accuracy of the timing device used in the experiment can introduce errors. Even small errors in measuring the time can lead to significant differences in the calculated value of g.

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Suitable cross section shape of a dam wall diagram

Answers

Trapezoidal shapes are used for dams with a height of 20 to 80 meters. Rectangular shapes are used for dams with a height of more than 80 meters. The cross-sectional shape of a dam wall is an important consideration in the design of a dam as it affects the safety and stability of the dam wall.

The cross-section shape of a dam wall is determined by the hydraulic forces that the dam will experience. The suitable cross-section shape of a dam wall diagram should have a wide base with a gradual reduction in width as it approaches the top. It should be designed in such a way that the dam can withstand the force of water pressure and the load of the content loaded. The width of the base should be at least 2 to 3 times the height of the dam. Additionally, the dam wall should have a curvature at the upstream face that minimizes the water pressure at the base of the wall. The most common types of dam cross-section shapes include triangular, trapezoidal, and rectangular shapes. Triangular shapes are preferred for small dams with a height of less than 20 meters. Trapezoidal shapes are used for dams with a height of 20 to 80 meters. Rectangular shapes are used for dams with a height of more than 80 meters. The cross-sectional shape of a dam wall is an important consideration in the design of a dam as it affects the safety and stability of the dam wall.

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Josh is playing pool. During his shot, an orange billiard ball with a momentum of 135 g · m/s hits a green billiard ball at rest. After the collision, the orange billiard ball continues in the same direction with a momentum of 60 g · m/s. What is the momentum of the green ball right after the collision?

Answers

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision, assuming no external forces are acting on the system.

Let's denote the momentum of the orange ball before the collision as p1, and the momentum of the green ball after the collision as p2.

Given:

Initial momentum of the orange ball (p1) = 135 g · m/s

Final momentum of the orange ball (p1') = 60 g · m/s

Momentum of the green ball after the collision (p2) = ?

Since momentum is a vector quantity, we need to consider both the magnitude and direction. In this case, the orange ball continues in the same direction after the collision, so the magnitude of its momentum decreases from 135 g · m/s to 60 g · m/s.

Using the principle of conservation of momentum:

p1 + 0 = p1' + p2

Substituting the given values:

135 g · m/s + 0 = 60 g · m/s + p2

Simplifying the equation:

p2 = 135 g · m/s - 60 g · m/s

p2 = 75 g · m/s

Now, we need to convert the momentum of the green ball from grams to kilograms:

1 g = 0.001 kg

p2 = 75 g · m/s * 0.001 kg/g

p2 = 0.075 kg · m/s

Therefore, the momentum of the green ball right after the collision is 0.075 kg · m/s.

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If the surface of a moon is impacted by meteorites at a constant rate, the density, or quantity per unit of area, of impact craters on the moon’s surface will increase over time. How can this information be used to determine the relative age of a moon’s surface?.

Answers

The information about the increasing density of impact craters on a moon's surface over time can be used to determine the relative age of the moon's surface.

This concept is based on the principle of superposition, which states that in undisturbed layers of rock or regolith, the oldest layers are at the bottom, and the youngest layers are at the top. When meteorites impact the surface of the moon, they create craters. Over time, new craters form on top of older craters. Therefore, the density of impact craters on the moon's surface can be an indicator of its relative age. If a specific region of the moon has a high density of impact craters, it suggests that the region is older because it has been exposed to meteorite impacts for a longer time, accumulating more craters.  On the other hand, a region with a lower density of impact craters indicates a relatively younger surface with less time for meteorite impacts to accumulate. By comparing the density of impact craters on different regions of the moon's surface, scientists can make relative age determinations. Areas with higher crater density are considered older, while areas with lower crater density are considered younger. It's important to note that this method of age determination assumes a constant rate of meteorite impacts over time and that there have been no major geological events or processes that could have reset or altered the surface. Additionally, the age determination based on crater density is a relative dating technique and does not provide an exact or absolute age for the moon's surface.

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An elastic wire expands by 2cm when load of 40g hangs from it. What additional load will be required to cause a further extension of 4cm

Answers

To solve this problem, we can use Hooke's Law, which states that the extension of an elastic material is directly proportional to the force applied to it.

First, let's convert the mass of the load from grams to kilograms:
Mass of the load = 40 g = 0.04 kg

Next, we need to find the spring constant of the wire. The spring constant (k) is a measure of the stiffness of the wire and represents the force required to produce a unit extension. We can find it by dividing the force (weight) by the extension.

Given:
Extension 1 = 2 cm = 0.02 m
Force 1 = Weight = 0.04 kg × 9.8 m/s^2 (acceleration due to gravity) = 0.392 N

Using Hooke's Law, we can calculate the spring constant:
k = Force 1 / Extension 1
k = 0.392 N / 0.02 m
k = 19.6 N/m

Now that we have the spring constant (k), we can calculate the additional load required to cause a further extension of 4 cm.

Given:
Extension 2 = 4 cm = 0.04 m

Using Hooke's Law:
Force 2 = k × Extension 2
Force 2 = 19.6 N/m × 0.04 m
Force 2 = 0.784 N

Therefore, an additional load of 0.784 N will be required to cause a further extension of 4 cm.
Answer:
An additional load of 80g will be required to cause a further extension of 4cm.

Step by step explanation:
To find the additional load required to cause a further extension of 4cm, we can use the concept of proportionality.

The extension of the wire is directly proportional to the load applied. This means that the ratio of the extension to the load remains constant.

In this case, we have an initial extension of 2cm when a load of 40g is applied. We can set up the following proportion:

2cm / 40g = 4cm / x

Cross-multiplying, we get:

2cm * x = 40g * 4cm

2x = 160g cm

To find the additional load required, we need to solve for x:

x = 160g cm / 2
x = 80g

Therefore, an additional load of 80g will be required to cause a further extension of 4cm.

A boy ties a stone to the end of a string which he then whirls above his head round a circular path of radius 2 metre. If the stone makes 10 oscillations in 4 seconds, calculate the angular and linear speed of the stone.

Answers

The angular and linear speed are 5π rads/ seconds and 10π meter/ seconds.

How to calculate the angular and the linear speed

In order to calculate the angular speed of the boy, we will use the equation below.

w =2πn/ T

Where

radius is 2 meter

number of oscillation is 10.

time is 4 s

So, we have

w = 2π * 10/4

w = 5π rads/ seconds.

To calculate the linear speed.

v = r *w

v = 2 * 5π

v = 10π meter/ seconds

Therefore, the angular and linear speed are 5π rads/ seconds and 10π meter/ seconds.

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A small sphere of mass 2. 5 × 10–5 kg carries a total charge of 6. 0 × 10–8 c. The sphere hangs from a silk thread between two large parallel conducting plates. The excess charge on each plate is equal in magnitude, but opposite in sign. If the thread makes an angle of 30° with the positive plate as shown, what is the magnitude of the charge density on each plate?.

Answers

The magnitude of the charge density on each plate for the given mass, charge and angle is 1.38 × 10⁻⁴ C/m².

The angle at which the sphere makes with the vertical = 90 – 30 = 60°. Therefore, the force on the sphere is the weight of the sphere – the tension in the thread, Tsinθ which acts towards the negative plate.The force towards the positive plate is qE. Therefore we have,

Tsin60° = mg – qE ...(1)

qE = mg – Tsin60° ...(2)

E is the electric field at a point between the plates.

For the electric field between the plates, we have,d = 4.0 mm = 4.0 × 10⁻³ mV = 500 VQ = 6.0 × 10⁻⁸ C.

Electric field strength = V/d = 500/(4.0 × 10⁻³) = 1.25 × 10⁵ V/m

Charge density = σ

Charge density of the positive plate = charge density of the negative plate= σ

Charge on a sphere is given by q = 4πε₀r²σ

Sphere charge = q = 6.0 × 10⁻⁸ C

Radius of the sphere = r

Mass of the sphere, m = 2.5 × 10⁻⁵ kg

Charge density, σ = q/4πε₀r²

Therefore, σ = 6.0 × 10⁻⁸ / (4π × 8.85 × 10⁻¹² × (6.25 × 10⁻⁶)²)

σ = 1.38 × 10⁻⁴ C/m²

The charge density on the positive plate is the same as that of the negative plate.

Therefore, the magnitude of the charge density on each plate is 1.38 × 10⁻⁴ C/m².

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A man weighing 70 kg runs alongside railroad tracks with a


velocity of 18 km/h, and jumps into a car of weight 100 kg


standing on the tracks. Calculate the velocity with which the


car and man will start moving.


a 2.06 m/s


b 1.47 m/s


С


2.31 m/s


d 3.02 m/s

Answers

The velocity with which the car and man will start moving is d.) 3.02 m/s. Hence, option d) is the correct answer. The formula for the momentum is p= mv.

Initially, the momentum of the man is given by: mv = 70 kg × (18 km/h) × (1 h/3600 s) × (1000 m/1 km)

= 35/18 m/s × 70 kg

= 1225/18 kg m/s

The momentum of the car is given by: p = mv

= 0 kg × v

= 0

Since the total momentum before the man jumps into the car is zero and the total momentum after the man jumps into the car is conserved, the total momentum is given by: mv + mv' = 0

where v' is the velocity of the car and man after they combine. Rearranging the equation above gives: v' = -mv / m' where m is the mass of the man and m' is the combined mass of the car and man: v' = -70 kg × 35/18 m/s / (70 kg + 100 kg)

= -35/26 m/s

≈ -1.35 m/s

Note that the negative sign implies that the velocity of the man is opposite to that of the car. The magnitude of the velocity is obtained by taking the absolute value: v' = 35/26 m/s ≈ 1.35 m/s

Therefore, the velocity with which the car and man will start moving is 3.02 m/s (to two decimal places).

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