The speed at which the ball hit the ground is 31.36 m/s.
What is speed?Speed is the rate of change of distance.
To calculate the speed at which the ball hit the ground, we use the formula below
Formula:
v² = u²+2E/m ................ Equation 1Where:
v = Final speed of the ballu = Initial speed of the ballE = Energym = Mass of the ballFrom the question,
Given:
u = 20 m/sm = 240 g = 0.24 kgE = 70 JSubstituite these values into equation 1
v² = 20²+(2×70)/0.24v² = 400+583.333v² = 400+583.333√v² = √983.33v = 31.36 m/sLearn more about speed here: https://brainly.com/question/29110645
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10. A thin beam of laser light of wavelength 514 nm passes through a diffraction grating having 3952 lines/cm. The resulting pattern is viewed on a distant curved screen that can show all bright fringes up to and including ±90. 0° from the central spot. What is the TOTAL number of bright fringes that will show up on the screen? A) 4 B) 5 C) 8 D) 9 E) 10
The TOTAL number of bright fringes that will show up on the screen is B) 5.
To answer this question, we need to use the following terms: wavelength, diffraction grating, lines/cm, and bright fringes.
Step 1: Convert the given data into meters
Wavelength (λ) = 514 nm = 514 * 10^(-9) m
Lines per cm (n) = 3952 lines/cm = 3952 * 10^2 lines/m (since 1 cm = 0.01 m)
Step 2: Calculate the grating spacing (d)
d = 1 / n = 1 / (3952 * 10^2) m
Step 3: Calculate the maximum order (m) using the grating equation
sin(90°) = m * λ / d
Since sin(90°) = 1,
m = d / λ
Step 4: Plug in the values and solve for m
m = (1 / (3952 * 10^2)) / (514 * 10^(-9))
m ≈ 2.09
Since m must be an integer, the maximum order is m = 2.
Step 5: Count the total number of bright fringes
For each order, there are 2 bright fringes (one on each side of the central spot), and one central spot (m = 0). Thus, the total number of bright fringes is:
Total bright fringes = 2 * (number of orders) + 1
Total bright fringes = 2 * (2) + 1
Total bright fringes = 5
So, the correct answer is B) 5.
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3. Compute the force of a small car, weighing 2,205 pounds, traveling 60 mph, that crashes into a steel pole and comes to a stop in 0. 05 second? dont know what to do
A small car weighing 2,205 pounds and traveling at 60 mph crashes into a steel pole and stops in 0.05 seconds. The force of the impact is calculated to be -53,600 N.
To calculate the force of a car that crashes into a steel pole, we need to use the formula F = m*a, where F is the force, m is the mass, and a is the acceleration.
To find the acceleration, we can use the formula[tex]a = (v_f - v_i) / t[/tex], where [tex]v_f[/tex] is the final velocity, [tex]v_i[/tex] is the initial velocity, and t is the time it takes to stop.
First, we need to convert the weight of the car from pounds to mass in kilograms, which is 1000 kg. Then, we need to convert the speed from miles per hour to meters per second, which is 26.8 m/s.
Using the formula a = (0 - 26.8) / 0.05, we get an acceleration of -536 m/s². Finally, we can use the formula F = m*a to find the force, which is -53,600 N.
The negative sign indicates that the force is in the opposite direction of the car's motion, meaning the car experiences a deceleration force. The force is very high due to the short stopping time, which can cause severe damage to the car and its occupants.
In summary, the force of a car crashing into a steel pole and coming to a stop in 0.05 seconds can be calculated using the formula F = m*a. Converting the weight to mass and the speed to meters per second, we can find the acceleration and use it to calculate the force.
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Find the frequency of the 5th harmonic (h5) of a 5 hz fundamental
The frequency of the 5th harmonic of a 5 Hz fundamental is 25 Hz.
To find the frequency of the 5th harmonic (h₅) of a 5 Hz fundamental, you need to multiply the fundamental frequency (f₁) by the harmonic number (n). The formula is:
fₙ = n*f₁
where:
fₙ = frequency of the nth harmonic
f₁ = fundamental frequency
n = harmonic number
In this case, the fundamental frequency (f₁) is 5 Hz and the harmonic number (n) is 5. So, the frequency of the 5th harmonic (h₅) would be:
h₅ = 5 * 5
= 25 Hz
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Horticulture (HURRY) 120 pts
Specialized technology works well in
, where the uniformity of the crop encourages tight-focused machines rather than unspecialized machines that can be adapted for multiple tasks
Horticulture is a field that greatly benefits from specialized technology. This is because the uniformity of crops in horticulture allows for machines that are tightly focused on specific tasks.
These machines are designed to perform specialized functions such as planting, pruning, and harvesting. This specialized equipment ensures that the crops are tended to with precision and care, which results in higher yields and better quality produce.
In contrast, unspecialized machines that can be adapted for multiple tasks may not perform as well in horticulture because they lack the precision and efficiency required for these specialized tasks.
So, in horticulture, specialized technology works well because it allows for precise and efficient handling of crops, which ultimately leads to better yields and higher-quality produce.
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Vibration of an object about an equilibrium point is called simple harmonic motion when the restoring force is proportional to:.
Vibration of an object about an equilibrium point is called simple harmonic motion when the restoring force is proportional to the displacement from the equilibrium point and is directed towards the equilibrium point.
This is known as Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Mathematically, this can be expressed as F = -kx, where F is the restoring force, x is the displacement from the equilibrium point, and k is the spring constant, a measure of the stiffness of the spring.
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a 193-v battery, an inductor, and a resistor are connected in series as shown in the diagram below. a two-way switch makes it possible to include or exclude the battery. the switch that had been in position 1 for a long time is suddenly moved to position 2. (enter your answers to at least two decimal places.) (a) what is the voltage across the resistor at the end of four time constants? 3.53 correct: your answer is correct. v (b) at this time, what is the voltage across the inductor? .107 incorrect: your answer is incorrect.
As for the Voltage across the inductor, it is equal to zero after four time constants because the current in the circuit has decreased to zero. Therefore, the correct answer for part (b) is zero, not 0.107.
When the switch is in position 1, the circuit is closed and the battery is connected in series with the inductor and resistor. This means that current flows through the circuit, causing a magnetic field to be generated by the inductor. However, when the switch is suddenly moved to position 2, the circuit is opened and the battery is no longer connected.
After the switch is moved, the current in the circuit begins to decrease due to the inductor's opposition to changes in current. The time it takes for the current to decrease to 36.8% of its original value is known as the time constant, which is calculated by dividing the inductance of the inductor by the resistance of the resistor.
After four time constants, the voltage across the resistor can be calculated using the equation V = V0 * e^(-t/RC), where V0 is the initial voltage, t is the time elapsed, R is the resistance, and C is the capacitance. Plugging in the values given, we get V = 193 * e^(-4/RC) = 3.53 volts.
As for the voltage across the inductor, it is equal to zero after four time constants because the current in the circuit has decreased to zero. Therefore, the correct answer for part (b) is zero, not 0.107.
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What happens to the frequency of the mass spring system if length of the spring is
cut into one third
Answer:Assuming the mass of the spring is not changed, the frequency of the mass-spring system will increase if the length of the spring is cut into one third. This is because the frequency of a mass-spring system is inversely proportional to the square root of the length of the spring. Mathematically, the frequency (f) is given by:
f = 1 / (2π) x √(k/m)
where k is the spring constant and m is the mass of the system. Since the mass of the spring is not changing, if the length of the spring is cut into one third, the square root of the length will become √(1/3) = 0.577. Therefore, the frequency of the system will increase by a factor of 1/0.577, which is approximately 1.73 or √3.
Explanation:
The maximum allowable resistance for an underwater cable is one hundredth of an ohm per
meter and the resistivity of copper is 1. 54 x 10-80m.
a) Calculate the smallest cross sectional area of copper cable that could be used.
The smallest cross-sectional area of the copper cable that could be used is approximately 1.54 x 10^-6 square meters.
To calculate the smallest cross-sectional area of the copper cable that could be used, we need to apply Ohm's law and the formula for resistivity.
Ohm's law states that resistance (R) equals resistivity (ρ) multiplied by the length (L) of the conductor, divided by the cross-sectional area (A). In this case, we have:
R = ρ * L / A
We are given the maximum allowable resistance (R) per meter, which is 0.01 ohms/meter, and the resistivity of copper (ρ) as 1.54 x 10^-8 ohm-meter. Since we're considering resistance per meter, the length (L) is 1 meter. We need to find the smallest cross-sectional area (A) that satisfies these conditions.
0.01 ohm = (1.54 x 10^-8 ohm-meter) * 1 meter / A
To find A, we can rearrange the formula:
A = (1.54 x 10^-8 ohm-meter) * 1 meter / 0.01 ohm
A ≈ 1.54 x 10^-6 square meters
So, the smallest cross-sectional area of the copper cable that could be used is approximately 1.54 x 10^-6 square meters.
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Your teacher sets two cups on a bench at the front of the class. One contains water dyed blue and the other clear water. The teacher says one cup is very salty water while the other is fresh water. You must figure out which is which. How would you do this?
Tasting water to identify which cup contains salty water or fresh water may not be reliable, as taste can be subjective and some individuals may have a weaker sense of taste.
Another approach is to use a conductivity meter or a multimeter with conductivity measurement capabilities to test the water in each cup. Salty water has a higher conductivity than fresh water due to the presence of ions, so the cup with higher conductivity would contain the salty water.
A third approach is to use a refractometer to measure the refractive index of the water. Salty water has a higher refractive index than fresh water due to the presence of dissolved salts, so the cup with a higher refractive index would contain the salty water.
In summary, to determine which cup contains salty water and which contains fresh water, one can use taste, a conductivity meter, a multimeter with conductivity measurement capabilities, or a refractometer.
Each of these methods has its own advantages and disadvantages, and the choice of method depends on factors such as the resources available and the specific characteristics of the water being tested.
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A length of copper wire was measured with a tape measure to give a length of 50. 0m with an uncertainty of 1 cm. The thickness of the wire was measured to be 1. 00mm,using a micrometer screw gauge. Calculate the volume of the copper used?
A copper wire was measured to be 50.0m long with an uncertainty of 1cm and had a thickness of 1.00mm measured with a micrometer screw gauge. The volume of copper used was [tex]3.93 \times 10^{-5}\; m^3[/tex] with an uncertainty of [tex]\pm 7.85 \times 10^{-9} m^3[/tex].
The volume of copper used can be calculated by multiplying the length, cross-sectional area, and density of copper. The length is given as 50.0 m with an uncertainty of [tex]\pm 0.01[/tex]m, and the thickness of the wire is given as 1.00 mm, which is equivalent to 0.001 m.
The cross-sectional area of the wire can be calculated using the formula for the area of a circle, which is πr², where r is the radius of the wire.
The radius of the wire can be calculated by dividing its thickness by 2, giving a value of 0.0005 m. Therefore, the cross-sectional area is [tex]\pi (0.0005)^2 = 7.85 \times 10^{-7} m^2[/tex]. The density of copper is 8.96 g/cm³, which is equivalent to [tex]8.96 \times 10^3 \;kg/m^3[/tex].
Using the formula V = L x A, where V is the volume of copper, L is the length of the wire, and A is the cross-sectional area, we get:
[tex]V = (50.0 \pm 0.01 m) \times (7.85 \times 10^{-7} m^2)[/tex]
[tex]V = 3.93 \times 10^{-5} m^3 \pm 7.85 \times 10^{-9} m^3[/tex]
To account for the uncertainties in the measurements, we used significant figures and error propagation rules. The uncertainty in the volume was calculated using the formula for the multiplication of quantities with uncertainties.
In summary, the volume of copper used was found to be [tex]3.93 \times 10^{-5}\; m^3[/tex] with an uncertainty of [tex]\pm 7.85 \times 10^{-9} m^3[/tex].
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An electromagnetic wave traveling through a vacuum
has a wavelength of 1.5 × 10–1
meter. What is the
period of this electromagnetic wave?
The period of the electromagnetic wave is 5×10⁻¹⁰ seconds
What is period?Period is the time taken for a wave to complete one rotation.
To calculate the period of the wave, we use the formula below.
Formula:
T = λ/v...........................Equation 1Where:
T = Period of the electromagnetic wavev = Speed of the electromagnetic waveλ = Wavelength of the electromagnetic waveFrom the question,
Given:
λ = 1.5×10⁻¹ mv = 3×10⁸ m/ssubstitute these values equation 1
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Help me!
in your own words, describe how the marble-jar experiment explains newton's law of inertia.
The marble-jar experiment is a classic demonstration of Newton's Law of Inertia. The experiment consists of a jar filled with marbles and a card covering the jar's opening.
When the jar is inverted quickly, the card falls, and the marbles remain in place.
According to Newton's Law of Inertia, an object at rest will remain at rest, and an object in motion will continue to move in a straight line at a constant velocity unless acted upon by an external force.
In this experiment, the marbles' inertia keeps them in place when the jar is inverted, while the card falls due to the external force of gravity.
This experiment provides a simple and tangible way to understand Newton's Law of Inertia.
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Calculate the weight of an object sitting on the Earth’s surface if the mass of the object is 50 kg? Assuming the force of gravity g = 9. 81 m/s²)
The weight of an object with a mass of 50 kg on Earth's surface is 490.5 N (Newtons).
To calculate the weight of an object on Earth's surface, we need to consider the mass of the object and the force of gravity (g). In this case, the mass is given as 50 kg, and the force of gravity is assumed to be 9.81 m/s².
Step-by-step explanation:
1. Start with the mass of the object (m) which is given as 50 kg.
2. Next, take the force of gravity (g) as 9.81 m/s² (as provided).
3. Now, we need to use the weight formula, which is:
Weight (W) = mass (m) × force of gravity (g)
4. Substitute the values of mass and force of gravity in the formula:
W = 50 kg × 9.81 m/s²
5. Perform the multiplication:
W = 490.5 N
So, the weight of the object sitting on Earth's surface with a mass of 50 kg is 490.5 Newtons.
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The speakers in a sports stadium are
89. 5 m from a fan's seat. How much
time does it take sound to travel from
the speakers to the fan's seat?
Speed of sound = 343 m/s
(Unit = s)
This is also one I am confused on
The speakers in a sports stadium are 89. 5 m from a fan's seat. It takes approximately 0.261 seconds for sound to travel from the speakers to the fan's seat in the sports stadium.
The time it takes for sound to travel from the speakers to the fan's seat can be calculated using the formula
Time = distance / speed
Where distance is the distance between the speakers and the fan's seat, and speed is the speed of sound in air.
In this case, the distance between the speakers and the fan's seat is 89.5 m, and the speed of sound in air is 343 m/s (at standard temperature and pressure).
Plugging in these values into the formula, we get
Time = 89.5 m / 343 m/s
Time = 0.261 seconds
Therefore, it takes approximately 0.261 seconds for sound to travel from the speakers to the fan's seat in the sports stadium.
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You produce a wave by oscillating one end of the rope up and down 2.0 times a second .what is the frequency of this wave?
The frequency of the wave produced by oscillating one end of the rope up and down 2.0 times a second is also 2.0 Hz (Hertz).
Frequency is defined as the number of oscillations or cycles that a wave completes in one second. In this case, each oscillation of the rope creates one complete cycle of the wave.
Therefore, if the rope is oscillating 2.0 times per second, it is completing 2.0 cycles of the wave each second, which is equivalent to a frequency of 2.0 Hz.
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Suppose the book-printing industry is competitive and begins in a long-run equilibrium. Then hi-tech printing company invents a new process that sharply reduces the cost of printing books.
The new process will cause the demand for book printing services to increase, and this will cause the price of book printing services to fall.
The long-run equilibrium will shift to a new equilibrium, where the new cost structure will be reflected in the price of book printing services. The new process will result in lower prices and higher demand for book printing services, leading to an increase in the number of firms in the book printing industry, as well as an increase in the size of the market.
The cost savings due to the new process will be passed on to consumers, resulting in lower prices for books. This will benefit both the book printing companies as well as the consumers.
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in a football game wanting kicks off to the other at the moment the receiver catches the ball he is 40 m from the nearest Tucker the receiving runs left to right at a speed of 10 m/s the toddler runs right to left at a speed of 6 m/s
Answer: yes
Explanation: good luck
A small truck is moving at 20 m/s. A large truck, with twice the mass, is traveling at half the speed. How does the momentum of the larger truck compare to the smaller truck?
The momentum of an object is directly proportional to its mass and velocity. Therefore, the momentum of the larger truck can be calculated as follows:
Momentum of larger truck = (2 x mass of smaller truck) x (1/2 x velocity of smaller truck)
Momentum of larger truck = (2 x m) x (0.5 x 20)
Momentum of larger truck = m x 20
This shows that the momentum of the larger truck is equal to the momentum of the smaller truck, as the increased mass is balanced by the decreased velocity.
In other words, the momentum of an object depends on both its mass and velocity, and changes in one factor can be compensated by changes in the other factor to maintain the same momentum.
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Suppose that you wanted to travel to the next closest star to earth. proxima
centauri is the closest star to our solar system at a distance of 4.3 light years.
knowing that the space shuttle's typical speed is 28,000km/hr. how long
would it take you to get there?
It is equivalent to approximately 60.5 million days, or 165,850 years. The distance to Proxima Centauri is 4.3 light-years, which is equivalent to 4.068 x [tex]10^{13}[/tex] km.
To calculate how long it would take to travel that distance at a speed of 28,000 km/hr, we can divide the distance by the speed: 4.068 x [tex]10^{13}[/tex] km ÷ 28,000 km/hr = 1.452 x [tex]10^{9}[/tex] hours
That is equivalent to approximately 60.5 million days, or 165,850 years.
Therefore, it is currently not possible to travel to Proxima Centauri with the technology available to us. We would need to develop much faster spacecraft and propulsion systems to make interstellar travel feasible.
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Assuming a total mass of 80 kg (bicycle plus rider), what must be the cyclist's power output to climb the same hill at the same speed?
The cyclist's power output must be equal to 784 N x speed. To climb the same hill at the same speed, the cyclist's power output must be equal to the gravitational force acting on the system (bicycle plus rider) multiplied by the speed at which they are moving.
The gravitational force can be calculated using the formula F = mg, where m is the total mass of the system (80 kg) and g is the acceleration due to gravity (9.8 [tex]m/s^{2}[/tex]). Therefore, the gravitational force acting on the system is 784 N (80 kg x 9.8 [tex]m/s^{2}[/tex]).
Assuming that the speed at which they are moving is constant, the power output required by the cyclist can be calculated using the formula P = F x v, where P is power, F is force, and v is velocity (speed). Therefore, the cyclist's power output must be equal to 784 N x speed.
For example, if the speed is 5 m/s, then the power output required by the cyclist would be 3920 watts (784 N x 5 m/s). However, it's important to note that this is a theoretical calculation and in reality, the power output required may be different due to factors such as air resistance, friction, and the gradient of the hill.
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A solenoid had 1040 turns and is 4.4 cm long. If it carries a current of 31 A, what is the magnetic field it creates?
Answer:
.92 T
Explanation:
This is just a plug-and-chug question.
Here is the formula: B = uni
u = vacuum permeability = 4pi * 10^-7 this is a given constant
n = turns per meter = 1040/ (4.4*10^-2)
i = current = 31 A also given by the problem
so B = .92 T
The unit of the magnetic field is Tesla ("T")
The ultraviolet catastrophe is good evidence for the:
neither the wave nor the particle nature of quanta
wave nature of quanta
both particle and wave nature of quanta
particle nature of quanta
The ultraviolet catastrophe is good evidence for the (B).wave nature of quanta is correct option.
The ultraviolet catastrophe was a problem in classical physics that arose when attempting to explain the spectral distribution of blackbody radiation. According to classical physics, the energy of radiation should increase without limit as the frequency of the radiation increases. However, experiments showed that this was not the case, and there was a maximum frequency beyond which the energy decreased.
This problem was resolved by Max Planck in 1900, who proposed that energy is quantized and can only exist in discrete packets or "quanta". This led to the development of quantum mechanics, which describes the behavior of matter and energy at the atomic and subatomic level.
The wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, which can exhibit both wave-like and particle-like behavior depending on the experimental setup. However, the ultraviolet catastrophe is specifically related to the wave nature of quanta, as it was the wave-like behavior of energy that led to the resolution of the problem.
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A motorcyclist traveling due north at 50km/h. the wind appears to come from north west at 60km/h . what is the true velocity of the wind
The true velocity of the wind is approximately 43.10 km/h.
To find the true velocity of the wind when a motorcyclist is traveling due north at 50 km/h, and the wind appears to come from the northwest at 60 km/h, we can use vector addition.
Step 1: Break the wind's apparent velocity into its north and west components. Since the wind is coming from the northwest, the north and west components will be equal.
Using the Pythagorean theorem (a² + b² = c²) to find the components:
North component:
a = 60 * cos(45°)
= 60 * 0.707
= 42.43 km/h
West component:
b = 60 * sin(45°)
= 60 * 0.707
= 42.43 km/h
Step 2: Subtract the motorcyclist's northward velocity from the north component of the wind's apparent velocity:
True north component of the wind:
42.43 - 50 = -7.57 km/h (southward)
Step 3: Combine the true north and west components of the wind's velocity using the Pythagorean theorem:
True wind velocity = √((-7.57)² + (42.43)²)
= √(57.36 + 1800.06)
= √1857.42
≈ 43.10 km/h
The true velocity of the wind is approximately 43.10 km/h.
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A proton moving eastward with a velocity of 5. 0 km/s enters a magnetic field of 0. 20 T pointing northward. What are the magnitude and direction of the force that the magnetic field exerts on the proton
The magnitude of the force that a magnetic field exerts on a charged particle is given by the equation:
F = qvB sin(theta)
where q is the charge of the particle, v is its velocity, B is the magnetic field strength, and theta is the angle between the velocity vector and the magnetic field vector.
In this case, the proton has a positive charge of +1.6 x 10^-19 C, and it is moving eastward with a velocity of 5.0 km/s. The magnetic field is pointing northward with a strength of 0.20 T.
The angle between the velocity vector and the magnetic field vector is 90 degrees, since the velocity is eastward and the magnetic field is northward.
Plugging these values into the equation, we get:
F = (1.6 x 10^-19 C)(5.0 x 10^3 m/s)(0.20 T) sin(90)
F = 1.6 x 10^-19 N
So the magnitude of the force that the magnetic field exerts on the proton is 1.6 x 10^-19 N.
The direction of the force can be determined using the right-hand rule. If you point your right thumb in the direction of the proton's velocity (eastward), and your fingers in the direction of the magnetic field (northward), then the direction of the force vector is perpendicular to both, pointing downward. Therefore, the direction of the force on the proton is southward.
Which surface would have more friction?
wooden
glass
paper
sandpaper
Out of the given options, sandpaper would have the highest friction.
Friction depends on two factors - surface roughness and surface area in contact also depends on Normal force. Sandpaper has a very rough, abrasive surface with lots of peaks and valleys. This greatly increases the surface area in contact and mechanical interlocking with any surface it touches. This results in high friction.The other options:• Wooden surface: Depends on the smoothness of the wood, can range from low to medium friction.
• Glass surface: Very smooth so it has low friction.
• Paper surface: Relatively smooth so friction would be low to medium depending on the paper type.
from lowest to highest friction it would be:Glass < Paper < Wooden < SandpaperSandpaper has the roughest surface, so it exhibits the highest friction among the given options.A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 320-g piece moves along the x-axis with a speed of 2. 00 m/s and a 355-g piece moves along the y-axis with a speed of 1. 50 m/s. The third piece has a mass of 100 g. In what direction does the third piece move? you can neglect any horizontal forces during the crash.
The third piece moves at an angle of 39.8° relative to the x-axis, which is in the northeast direction.
We can start the problem by using conservation of momentum. The momentum before the impact is zero since the plate is at rest, and the momentum after the impact is the sum of the momenta of the three pieces.
Since there are no horizontal forces during the crash, the total momentum is conserved in the x and y directions separately.
Let's call the velocity of the third piece v and assume it moves at an angle θ relative to the x-axis. Then we can write the following equations:
Initial momentum in x-direction = Final momentum in x-direction
0 = 0.32 kg * 2.00 m/s + 0.355 kg * 0 m/s + 0.1 kg * v cos(θ)
Initial momentum in y-direction = Final momentum in y-direction
0 = 0.32 kg * 0 m/s + 0.355 kg * 1.50 m/s + 0.1 kg * v sin(θ)
Simplifying these equations, we get:
0.64 = 0.1 v cos(θ)
0.535 = 0.1 v sin(θ)
We can divide the second equation by the first equation to get:
tan(θ) = 0.535/0.64 = 0.836
Taking the inverse tangent of both sides, we get:
θ = 39.8°
Therefore, the third piece moves at an angle of 39.8° relative to the x-axis, which is in the northeast direction.
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If I weigh 742. 32 N on Earth at a place where g = 9. 80 m/s2 and 5900. 91 N on the surface of another planet, what is the acceleration due to gravity on that planet?
The acceleration due to gravity on the surface of the other planet is approximately 77.98 m/s².
To find the acceleration due to gravity on another planet, we can use the formula:
Weight = Mass × Acceleration due to gravity
On Earth, your weight is given as 742.32 N, and the acceleration due to gravity is 9.80 m/s².
We can rearrange the formula to solve for mass:
Mass = Weight / Acceleration due to gravity
So, on Earth, your mass would be:
Mass on Earth = 742.32 N / 9.80 m/s²
Mass on Earth = 75.63 kg
Now, let's consider the surface of another planet where your weight is given as 5900.91 N.
We'll use the same formula and solve for the acceleration due to gravity on that planet:
5900.91 N = Mass × Acceleration due to gravity on the other planet
Substituting the value of mass we calculated earlier:
5900.91 N = 75.63 kg × Acceleration due to gravity on the other planet
Now, we can solve for the acceleration due to gravity on the other planet:
Acceleration due to gravity on the other planet = 5900.91 N / 75.63 kg
Acceleration due to gravity on the other planet ≈ 77.98 m/s²
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a guitar string 61 cm long vibrates with a standing wave that has three antinodes. part a which harmonic is this?
This standing wave corresponds to the third harmonic. The fundamental frequency of a guitar string is determined by the length of the string, which in this case is 61 cm.
When a standing wave is produced on the string, the nodes (points where the wave has zero displacement) and antinodes (points of maximum displacement) can be counted to determine the harmonic number. In this case, the number of antinodes is 3, which corresponds to the third harmonic.
The fundamental frequency of the string is determined by the equation f = 1/2L√T/m, where L is the length of the string, T is the tension, and m is the mass per unit length of the string. The third harmonic frequency is three times the fundamental frequency, which is calculated by multiplying the fundamental frequency by 3. Therefore, the third harmonic frequency of the guitar string is three times the fundamental frequency.
In addition, the wavelength of the third harmonic is one-third of the wavelength of the fundamental frequency. This is because the wavelength of a wave is inversely proportional to its frequency. The wavelength of the third harmonic is one-third of the wavelength of the fundamental frequency, and the distance between the antinodes is one-third of the wavelength. Therefore, the standing wave with three antinodes corresponds to the third harmonic.
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If the protons were not held together by the strong nuclear force, what would be their initial acceleration due to the electric force between them
Using Newton's second law, F = ma, and the known mass of a proton, 1.673 x [tex]10^{27}[/tex] kg, the initial acceleration of the protons would be approximately 1.38 x [tex]10^{1}[/tex] [tex]m/s^{2}[/tex].
If the protons were not held together by the strong nuclear force, they would experience an electric force due to their positive charges.
According to Coulomb's law, the electric force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Therefore, the initial acceleration of the protons would depend on their separation distance and the magnitude of their charges.
Assuming a separation distance of 1 angstrom ([tex]10^{-10}[/tex] m), the electric force between two protons with charges of 1.602 x [tex]10^{-19}[/tex] C would be approximately 2.31 x [tex]10^{-28}[/tex] N.
Using Newton's second law, F = ma, and the known mass of a proton, 1.673 x [tex]10^{-27}[/tex] kg, the initial acceleration of the protons would be approximately 1.38 x [tex]10^{1}[/tex] [tex]m/s^{2}[/tex].
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Given that a 4 cylinder, 4 stroke engine gave the following test results:
Shaft Speed N = 2600 rev/min
Torque arm R = 16 cm
Net Brake Load F = 220 N
Fuel consumption mf = 2 g/s
Calorific Value (CV) = 42 MJ/kg
Determine the following:
(a) Brake Power;
(b) Fuel Power;
(c) Brake Thermal Efficiency.
By increasing and decreasing the brake thermal efficiency, compare the impact this has on the shaft speed or net brake load
(a) Pb = 2π * N * T
(b) Pf = mf * CV
(c) Brake Thermal Efficiency (ηb) = (Pb / Pf) * 100%
To determine the brake power, fuel power, and brake thermal efficiency, we can use the following formulas:
(a) Brake Power (Pb):
Pb = 2π * N * T
Where N is the shaft speed in revolutions per minute (rpm) and T is the torque.
(b) Fuel Power (Pf):
Pf = mf * CV
Where mf is the fuel consumption rate in kilograms per second and CV is the calorific value of the fuel in joules per kilogram.
(c) Brake Thermal Efficiency (ηb):
ηb = (Pb / Pf) * 100%
Let's calculate these values using the given information:
(a) Brake Power:
Shaft Speed N = 2600 rev/min
Torque arm R = 16 cm = 0.16 m
The torque (T) can be calculated using the formula:
T = F * R
Brake Power (Pb) = 2π * N * T
(b) Fuel Power:
Fuel consumption mf = 2 g/s = 0.002 kg/s
Calorific Value (CV) = 42 MJ/kg = 42 × [tex]10^6[/tex] J/kg
Fuel Power (Pf) = mf * CV
(c) Brake Thermal Efficiency:
Brake Thermal Efficiency (ηb) = (Pb / Pf) * 100%
Let's substitute the given values into the equations and calculate the results.
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