The product of 3 radians, 1 revolution, 60 minutes, and 1 hour is 21600π rad [tex]min^2[/tex] hr.
To find the product, we need to multiply the given values together. Let's break it down step by step:
First, let's convert the given values to a common unit.
1 revolution (rev) is equal to 2π radians (rad). So, 1 rev can be written as 2π rad.
Next, we have 60 minutes (min). Since there are 60 minutes in an hour, we can convert 60 minutes to 1 hour by dividing it by 60. This gives us 1 hour (hr).
Now, let's multiply the values together:
3 rad * 1 rev = 3 rad * 2π rad (since 1 rev = 2π rad)
= 6π rad
Next, we'll multiply by 60 min:
6π rad * 60 min = 360π rad min
Lastly, we'll multiply by 1 hr:
360π rad min * 1 hr = 360π rad min * 1 hr * 60 min (since 1 hr = 60 min)
= 21600π rad [tex]min^2[/tex] hr
Please note that π represents the mathematical constant pi, which is approximately equal to 3.14159.
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A person pushes on a box in the East direction with 8
N of force, another person pushes on the same box
south with 20 N of force. What force (magnitude and
direction) would a third person need to push on the
crate so that the box is in equilibrium?
Magnitude of the third
vector is
Direction of third
vector is
✓ [Choose ]
46.40 N
28.00 N
21.54 N
21.8° South of East
21,8° North of West
68.2° South of East
68.2° North of West
Answer:
In order for the box to be in equilibrium, the third person's force should be equal but opposite in direction to the resultant force of the two forces already acting on the box.
First, let's calculate the resultant force acting on the box. The box is being pushed with 8 N to the east and 20 N to the south. Since these forces are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant force:
Magnitude = sqrt((8 N)^2 + (20 N)^2)
= sqrt(64 N^2 + 400 N^2)
= sqrt(464 N^2)
= 21.54 N
The direction of the resultant force can be calculated using trigonometry. Specifically, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.
tan(θ) = Opposite/Adjacent
tan(θ) = 20 N / 8 N
θ = atan(20/8)
θ = 68.2°
The direction of the force is therefore 68.2° South of East (since we have taken East as the base direction and South as the angle direction).
The third person should therefore apply a force of 21.54 N in the direction exactly opposite to 68.2° South of East, which is 68.2° North of West.
So, the correct choices are:
Magnitude of the third vector is 21.54 N.
Direction of third vector is 68.2° North of West.
The coherence length for Na light is 2.945×10-2 m.The wavelength of Na light is 5890 Å. Calculate %0D%0A– (i) Number of oscillations corresponding to the coherence length (ii) Coherence time.
An eraser rests on a clipboard that is tilted at an angle
of 23° with the ground. The eraser is not sliding down
the clipboard. What is the minimum coefficient of
static friction, needed for this to be the case?
0.26
O 042
O Not enough information to tell
O 0.16
The eraser on the tilted clipboard needs a minimum static friction coefficient of 0.3907. No option matches; The correct answer is (O) Not enough information to tell.
In this problem, we are given that an eraser rests on a clipboard that is tilted at an angle of 23° with the ground. Also, the eraser is not sliding down the clipboard. We need to find the minimum coefficient of static friction required to hold the eraser in its place.The coefficient of static friction is given by the formula:f_s = (μ_s)N, where f_s is the force of static friction, μ_s is the coefficient of static friction and N is the normal force acting on the object. In this case, the normal force acting on the eraser is equal to its weight. Thus, the normal force acting on the eraser is given by: N = mg, where m is the mass of the eraser and g is the acceleration due to gravity. Substituting the values of N and θ in the above equation, we get f_s = mg sin θThus, the minimum coefficient of static friction needed to hold the eraser in place is given by:μ_s = f_s / N = (mg sin θ) / (mg) = sin θ = sin 23° = 0.3907 (approx.)Therefore, the minimum coefficient of static friction needed for the eraser to stay in its place is 0.3907. The closest option given is 0.26, which is not equal to the value obtained in the calculation. Hence, the correct answer is option (O) Not enough information to tell.For more questions on static friction
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what is the reading of the spring balance.
Assume that the surface is a perfect smooth surface, and the whole system is moving to the left with constant acceleration.
If the system is moving to the left with a constant acceleration and the surface is perfectly smooth, the reading on the spring balance would be zero.
How do we know?The spring balance measures the force exerted on it, which in this case would be the force due to gravity acting on the object.
However, since the surface is smooth and there is no friction, there would be no additional force acting on the object, resulting in zero net force and therefore zero reading on the spring balance.
We observe that only in these particular circumstances would the reading on the spring balance be zero.
The reading on the spring balance would be different if there were additional forces operating on the object, such as friction or an outside force.
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What happens to a light ray when it incident at an angle greater than the critical angle?
When a light ray is incident at an angle greater than the critical angle, a phenomenon known as total internal reflection occurs.
Total internal reflection happens when light travels from a medium with a higher refractive index to a medium with a lower refractive index. In this scenario, instead of the light ray refracting and passing into the second medium, it reflects back into the first medium. The incident ray strikes the interface between the two media at an angle greater than the critical angle, which is the angle at which the refracted ray would have a 90-degree angle of incidence.
Due to the laws of reflection, the light ray bounces off the interface, staying within the first medium. It travels along a path parallel to the interface, effectively being reflected internally. No light escapes into the second medium.
Total internal reflection has various practical applications. It is employed in fiber optics, where light signals are transmitted over long distances by repeatedly bouncing off the internal walls of the fiber. It is also utilized in devices like prisms, binoculars, and reflective coatings, where controlling the reflection of light is crucial.
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A collision cart (3 kg) is moving at 3 m/s and collides with a 2 kg cart moving at -5 m/s. If the 2 kg cart is moving at 4.6 m/s after they collide, find the final velocity of the 3 kg cart.
We used the conservation of momentum to find the final velocity of a 3 kg collision cart that collided with a 2 kg cart. We found that the final velocity of the 3 kg cart is -6.07 m/s.
In this question, a collision cart of 3 kg is moving at 3 m/s and collides with a 2 kg cart that is moving at -5 m/s. After they collide, the 2 kg cart is moving at 4.6 m/s. We are to find the final velocity of the 3 kg cart. We can use the conservation of momentum to solve this problem. The conservation of momentum states that the total momentum of an isolated system remains constant if there are no external forces acting on the system. In this case, the two carts can be considered as an isolated system. The formula for momentum is given by: p = mv, where p is the momentum, m is the mass, and v is the velocity. Before the collision, the total momentum of the system is given by: p1 = m1v1 + m2v2, where m1 is the mass of the 3 kg cart, m2 is the mass of the 2 kg cart, v1 is the velocity of the 3 kg cart, and v2 is the velocity of the 2 kg cart.Substituting the given values, we get:For more questions on velocity
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A pair of forceps used to hold a thin plastic rod firmly is shown in (Figure 1). If the thumb and finger each squeeze with a force FT=FF= 16.0 N , what force do the forceps jaws exert on the plastic rod? Express your answer to three significant figures and include the appropriate units. F1 =
The four particles as connected by rods of negligible mass as fig below. if the origin is the canter of rectangle and the system rotates in the XY plane about the Z axis with an rad angular speed of 12. calculate S a) The moment of inertia of the system about Z axis and b) The rotational kinetic energy of the system 3.00 kg 2.00 kg y(m) 2.00 kg 6.00 m 4.00 kg ---x(m)
The moment of inertia of the system about the Z-axis is 245 kg m², and the rotational kinetic energy of the system is 21168 J.
The moment of inertia of a system about its axis of rotation is the sum of the products of the masses of its constituents and the square of their respective distances from the axis of rotation.
The radius of the rectangular plate is 6 m, and the distance of each particle from the center is half of the sides of the rectangle, which are 4 m and 3 m.
Therefore, using the parallel axis theorem, we get the moment of inertia of the system about the Z-axis as shown below.
[tex]Iz = ICM + MR^{2}[/tex]
(1)We can obtain the moment of inertia of the rectangle about its center as: [tex]ICM = (1/12) ML^{2}[/tex]
(2) where M is the mass of the rectangle, and L is the length of the rectangle.
Substituting values, we get: ICM = [tex](1/12) $\times$ 3.00 $\times$ (4^{2} + 6^{2} )[/tex]
ICM = [tex]5 kg m^{2}[/tex]
Using the parallel axis theorem, the moment of inertia of the four particles about the center of the rectangle is:
[tex]IP = 4 $\times$ [(1/12) $\times$ 2.00 $\times$ (4^{2} + 3^{2})] + 2.00 $\times$ (3^{2}) + 4.00 $\times$ (4^{2})IP = 97 kg m^{2}[/tex]
The moment of inertia of the system about Z-axis is: [tex]Iz = ICM + MR^{2} Iz = 5 kg m^{2} + 3.00 kg $\times$ (6^{2} ) + 4 $\times$ [(4^{2}+ 3^{2} )/4] Iz = 245 kg m^{2}[/tex]
The kinetic energy of a rotating body is given as:[tex]K.E. = (1/2) I\omega^{2}[/tex] where I is the moment of inertia of the system, and ω is the angular velocity of the system.
The rotational kinetic energy of the system is:[tex]K.E. = (1/2) I\omega^{2} K.E. = (1/2) $\times$ 245 $\times$ (12)^{2} K.E. = 21168 J[/tex]
2)[tex]I\omega^{2} K.E. = (1/2) $\times$ 245 $\times$ (12)^{2} K.E. = 21168 J[/tex]
Therefore, the moment of inertia of the system about the Z-axis is 245 kg m², and the rotational kinetic energy of the system is 21168 J.
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A hockey player (80 kg) is skating at 7.5 m/s and collides with another player (75 kg) moving at 0.5 m/s. If the collision is completely inelastic, calculate the final velocity of the pair of hockey players.
13
The final velocity of the pair of hockey players is 4.12 m/s.
In an inelastic collision, the two objects stick together and move as a single unit after the collision. To calculate the final velocity of the pair of hockey players, we can apply the principle of conservation of momentum.
The initial momentum of the system is given by the sum of the individual momenta of the players before the collision. The momentum (p) of an object is defined as the product of its mass (m) and velocity (v): p = m * v.
For the first player, with a mass of 80 kg and initial velocity of 7.5 m/s, the initial momentum is 80 kg * 7.5 m/s = 600 kg·m/s. For the second player, with a mass of 75 kg and initial velocity of 0.5 m/s, the initial momentum is 75 kg * 0.5 m/s = 37.5 kg·m/s.
The total initial momentum of the system is the sum of these individual momenta: 600 kg·m/s + 37.5 kg·m/s = 637.5 kg·m/s.
Since the collision is completely inelastic, the two players stick together and move as a single unit after the collision. Therefore, the final velocity of the pair of hockey players is determined by dividing the total initial momentum by the total mass of the system: final velocity = total initial momentum / total mass.
The total mass of the system is 80 kg + 75 kg = 155 kg. Dividing the initial momentum (637.5 kg·m/s) by the total mass (155 kg), we find the final velocity of the pair of hockey players to be approximately 4.12 m/s.
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Assuming all of the spring’s energy is transferred to the 3.0 kilogram calculate the speed v1 of the 3.0 kilogram block immediately after it is propelled by the spring
The speed (v1) of the 3.0-kilogram block immediately after being propelled by the spring can be calculated by equating the initial potential energy stored in the spring to the kinetic energy of the block. The formula for kinetic energy is given by KE = 1/2 * m * [tex]v^2[/tex], where m is the mass of the object and v is its velocity.
Therefore, using this formula, we can find the speed (v1) as follows:
1. Determine the potential energy stored in the spring using the formula for potential energy: PE = 1/2 * k * [tex]x^2[/tex], where k is the spring constant and x is the displacement from the equilibrium position. As the question does not provide these values, we cannot determine the potential energy directly.
2. However, we can assume that all the spring's energy is transferred to the 3.0-kilogram block, which means the potential energy of the spring is equal to the kinetic energy of the block. Thus, we can equate the two energies:
PE = KE
3. Substitute the formulas for potential energy and kinetic energy:
1/2 * k * [tex]x^2[/tex] = 1/2 * m * [tex]v1^2[/tex]
4. Rearrange the equation to solve for v1:
[tex]v1^2[/tex] = (k * [tex]x^2[/tex]) / m
5. Take the square root of both sides to find v1:
v1 = sqrt((k * [tex]x^2[/tex]) / m)
Please note that to provide an exact numerical value for v1, we would need specific values for the spring constant (k) and the displacement (x) of the spring from the equilibrium position.
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What is the correct definition of wave?
A. a pattern of motion that repeats in a cycle
B. a method of carrying matter from place to place
C. a pattern of increasing energy
D. any motion in two directions, such as up and down
what is the value of pi(8.104)^2 written with correct significant numbers
Answer:206.3
Explanation:
XYZ are 3 cities. a = 222 miles. b = 150 miles. Angle YXZ = 30. Angle YZX = 45. c = ___ miles
The length of side YZ (c) is approximately 119.13 miles.
How to calculate the lengthTo find the length of side c, we can use the Law of Cosines, which states:
c² = a² + b² - 2ab * cos(C)
Plugging in the given values:
a = 222 miles
b = 150 miles
C = 30 degrees
We need to convert the angle from degrees to radians to use it in the cosine function. The conversion is as follows:
θ (radians) = θ (degrees) * π / 180
C (radians) = 30 degrees * π / 180 = π / 6 radians
c² = 222² + 150² - 2 * 222 * 150 * cos(π / 6)
c² = 49284 + 22500 - 66600 * cos(π / 6)
c² = 49284 + 22500 - 66600 * (√3 / 2)
c² = 71784 - 66600 * (√3 / 2)
c² = 71784 - 66600 * 0.866
c² = 71784 - 57600
c² = 14184
c = √14184
c ≈ 119.13 miles (rounded to two decimal places)
Therefore, the length of side YZ (c) is approximately 119.13 miles.
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Assuming that all the numbers given are exact, what is John's position at a time of 4.53 s? Enter your answer to at least three significant digits.
The position of John at a time of 4.53 s is 20.8 m.
It is essential to know that the formula for position, velocity, and acceleration is given as:
[tex]$$x=x_0+v_0t+\frac{1}{2}at^2$$[/tex]
[tex]$$v=v_0+at$$[/tex]
[tex]$$v^2=v_0^2+2a(x-x_0)$$[/tex]
Here, x is the position, v is the velocity, t is the time elapsed, and a is the acceleration. John's position at a time of 4.53 s is given as follows:
Given,
[tex]$$x_0=0, v_0=4.6 m/s, t=4.53s, a=-9.8m/s^2$$[/tex]
From the above formula, we can calculate the position of John at a time of 4.53 s.Substitute all the values in the formula for position, and we get,
[tex]$$x=x_0+v_0t+\frac{1}{2}at^2$$[/tex]
[tex]$$x=0+(4.6)(4.53)+\frac{1}{2}(-9.8)(4.53)^2$$[/tex]
[tex]$$x=20.8 m$$[/tex]
Therefore, the position of John at a time of 4.53 s is 20.8 m.
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A ray of light makes an angle of 35 with a plane mirror ,what is the reflection
When a ray of light strikes a plane mirror, the angle of reflection is equal to the angle of incidence.
In this case, the ray of light makes an angle of 35 degrees with the plane mirror. Therefore, the angle of reflection will also be 35 degrees. To understand why this happens, we need to consider the properties of reflection. When light interacts with a smooth surface like a mirror, it follows the law of reflection.
According to this law, the incident ray, the reflected ray, and the normal (a line perpendicular to the mirror's surface) all lie in the same plane. The angle of incidence is the angle between the incident ray and the normal, measured on the side of the normal where the light is coming from. In this case, the angle of incidence is 35 degrees.
According to the law of reflection, the angle of reflection is the angle between the reflected ray and the normal, also measured on the side of the normal where the light is coming from. Since the incident and reflected rays are on opposite sides of the normal, the angle of reflection is also 35 degrees.
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1)What is the pressure at point D in kPa ?
2)Temperature at point D
3)What is the net work done on the gas as it is taken through four cycles?
4)What is the internal energy of the gas when it is at point A?
5)What is the total change in internal energy of this gas during four complete cycles?
The answer is 1) The pressure at point D is 80 kPa. 2) The temperature at point D is 800 K. 3) The net work done on the gas over four cycles is zero. 4) The internal energy of the gas at point A is 100 J. 5) The total change in internal energy during four complete cycles is zero.
The total change in internal energy of this gas during four complete cycles is zero. The given diagram represents the Carnot cycle involving four stages. The four stages of the Carnot cycle are reversible and follow an ideal gas that is placed in a cylinder with a movable piston.Let's solve each question asked one by one.1) From the graph, it can be observed that the pressure at point D is 0.08 M Pa, which is equal to 80 kPa. Hence, the pressure at point D in kPa is 80 kPa.2) Temperature at point D The isotherm at point D is about 800 K. Hence, the temperature at point D is 800 K.3) The net work done on the gas as it is taken through four cycles is zero because the Carnot cycle is a cycle that has four stages. In each cycle, the net work done is the area enclosed by the cycle. Therefore, for a complete cycle, the net work done is zero because the area enclosed is a loop.4) The internal energy of the gas when it is at point A is 100 J because the internal energy of the gas is directly proportional to the temperature and volume. Here, at point A, the temperature is 500 K, and the volume is 2 m³, so the internal energy of the gas when it is at point A is 100 J.5) The Carnot cycle is a reversible cycle that is used to determine the efficiency of heat engines. It is a closed cycle that does not involve any net energy exchange with the surroundings. Therefore, the total change in internal energy of this gas during four complete cycles is zero since the initial and final states are the same. Hence, the total change in internal energy of this gas during four complete cycles is zero.For more questions on the Carnot cycle, click on:
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Identify the correct statement regarding the strength of chemical bonds. Strong bonds form with large atoms and weak bonds with small atoms. Weak bonds require less energy to form than strong bonds. Strong bonds occur with high temperature and weak bonds with low temperature. Weak bonds require more energy to form than strong bonds.
Option B is the right answer. The correct statement regarding the strength of chemical bonds is that weak bonds require less energy to form than strong bonds.
Bonds form when two atoms share, give, or take electrons.
The electrons in the valence shell or outermost energy level of an atom are used to create bonds.
When atoms interact and share electrons, they lower their potential energy.
The more tightly an atom's electrons are bound, the greater the energy required to break those bonds.
There are two types of bonds: strong and weak.
Strong bonds have a lower potential energy than weak bonds, and they require more energy to break.
As a result, strong bonds tend to be more difficult to break than weak bonds.
The type of bond between two atoms is determined by the difference in their electronegativities.
The strength of a bond is determined by the energy required to break it.
Bonds are considered strong when they have a higher bond energy than weak bonds, which have a lower bond energy.
This implies that more energy is required to break a strong bond than to break a weak bond.
Therefore, weak bonds require less energy to form than strong bonds.
To conclude, the correct statement regarding the strength of chemical bonds is that weak bonds require less energy to form than strong bonds.
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explain the term tenscopo
Answer: Here you go, i hope this kinda helps.
Explanation:Disambiguation is just a fancy way of saying "asking clarifying questions".
Watson Assistant replies to user's questions based on a confidence score.
Sometimes the customer's question could be interpreted in two or three different ways.
For example, if you say you'd like to "book a table for 8", the assistant is able to ask a clarifying question:
Did you mean booking a table for 8PM, 8AM, or booking a table for 8 guests?
Watson Assistant will ask the question when its confidence score is divided between a few options to ensure that your customers get exactly the right service they need.
Calculate the quantity of heat energy which must be transferred to 2.25 kg of brass to raise its temperature from 20°C to 240°C if the specific heat of brass is 394 J/kgK.
The quantity of heat energy that must be transferred to 2.25 kg of brass to raise its temperature from 20 °C to 240 °C is 195030 J
How do i determine the quantity of heat energy?First, we shall list out the given parameters from the question. This is shown below:
Mass of brass (M) = 2.25 Kg Initial temperature of brass (T₁) = 20 °CFinal temperature of brass (T₂) = 240 °CChange in temperature of brass (ΔT) = 240 - 20 = 220 °CSpecific heat capacity of brass (C) = 394 J/kgKQuantity of heat energy (Q) =?The quantity of heat energy that must be transferred can be obtained as follow:
Q = MCΔT
= 2.25 × 394 × 220
= 195030 J
Thus, we can conclude quantity of heat energy that must be transferred is 195030 J
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Question 2 A Glindrical obiect has a Muss (M.. • 3.97g). Radiu (R= 5.0m), With a bucket of mass (m= 5.3rg) hanging from a string attached to a Cilindrical direct. Calculate the acceleration Calculate the tention in the String, where the diet is attalled. Calculate the distance it takes for the object to rotate downwards ,in 3.2 seconds.
What is the force of gravity between two objects with mass 15,000,000kg and 16,000,000kg respectively that are 14m apart?
The force of gravity between two objects with masses of 15,000,000kg and 16,000,000kg, separated by 14m, is approximately 1.04 x 10⁸ N.
Gravity is a force that pulls two objects towards each other. According to Newton's Law of Gravitation, the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between their centers of mass. Hence, the force of gravity between two objects with masses of 15,000,000kg and 16,000,000kg respectively that are 14m apart can be calculated using the formula F = Gm1m2/d², where F is the force of gravity, G is the gravitational constant (6.67430 × 10⁻¹¹ N m²/kg²), m1 and m2 are the masses of the objects, and d is the distance between them. Substituting the given values, we get:F = (6.67430 × 10⁻¹¹)(15,000,000)(16,000,000)/(14²)= 1.04 x 10⁸ N (approx)Therefore, the force of gravity between the two objects is approximately 1.04 x 10⁸ N.Summary: The force of gravity between two objects can be calculated using the formula F = Gm1m2/d², where F is the force of gravity, G is the gravitational constant, m1, and m2 are the masses of the objects, and d is the distance between them. Substituting the given values, we get that the force of gravity between two objects with mass 15,000,000kg and 16,000,000kg respectively that are 14m apart is approximately 1.04 x 10⁸ N.For more questions on the force of gravity
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What decibel level can cause hearing damage to begin?
A. 80
B. 10
C. 100
D. 60
The decibel level that can cause hearing damage to begin is 80.
The correct answer to the given question is option A.
According to the Occupational Safety and Health Administration (OSHA) standards. When sound intensity reaches 85 decibels or higher, it can cause permanent hearing loss or damage if not protected properly.
Decibels (dB) are the unit used to measure the loudness of sound. Sound is defined as a wave of pressure that arises when energy is transferred from one place to another. The frequency of sound waves determines the pitch, while the intensity of sound waves determines the volume.
Sound that is too loud can cause damage to the hair cells in the cochlea, which are responsible for converting sound vibrations into electrical signals that the brain can understand. The damage to the hair cells is irreversible, so it is essential to protect your ears from loud sounds.
OSHA standards define 85 decibels as the maximum exposure to sound levels that are safe for eight hours per day. If noise levels exceed 85 decibels, earplugs or earmuffs should be used to prevent hearing loss.
Therefore, it is crucial to be cautious with loud sounds and take necessary precautions to avoid hearing damage, such as using earplugs or earmuffs in noisy environments.
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Given that average speed is distance traveled divided by time, determine the values of m
and n
when the time it takes a beam of light to get from the Sun to the Earth (in s
) is written in scientific notation. Note: the speed of light is approximately 3.0 ×
108 m/s
.
The time a beam of light takes to travel from the sun to the Earth is 4.987 × 10²s. Therefore, m is equal to 4.987, and n is equal to 2.
The time it takes for a beam of light to get from the Sun to the Earth is determined by the formula:
Time = Distance / Speed of light;
Speed of light is 3.0 × 10⁸ m/s, and the distance from the sun to the Earth is 93,000,000 miles, which is equivalent to 1.496 × 10¹¹ meters.
The time it takes light to travel from the sun to Earth can be computed as follows:
Time = Distance / Speed of light
Time = (1.496 × 10¹¹ m) / (3.0 × 10⁸ m/s)
Time = (1.496 / 3.0) × 10³ s
Time = 0.4987 × 10³ s
Time = 4.987 × 10² s.
The time it takes for light to travel from the sun to the Earth is 4.987 × 10² s. Therefore, m is equal to 4.987, and n is equal to 2.
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A long, straight conveyor belt at a sushi restaurant carries sushi past customers with a constant velocity. If the sushi roll you want is 4.30 m to the right of you 11.0 s after exiting the little door at the beginning of the conveyor belt, and it is still 2.10 m to the right of you 10.0 s later, how far is the little door to the right of you?
Imagine a species of butterfly that comes in a variety of colors.
How can this type of diversity affect the population?
• A. The colors help the butterflies recognize and communicate with one another.
• B. The diversity means that fewer individuals will survive if the environment changes.
c. Some of the colors may help the individuals survive environmental changes.
• D. Some of the colors are more visible to predators than others.
A student pulls a rope attached to a crate of lab equipment with a force of 200N at an angle of 25° above the floor. Find the acceleration of the bar if it’s mass is 29kg and the µk between the box and the floor is .22
The acceleration of the crate is 4.13 m/[tex]s^2[/tex].
To find the acceleration of the crate, we need to analyze the forces acting on it and apply Newton's second law of motion.
Let's denote the acceleration as "a", the force applied by the student as "F", the mass of the crate as "m", and the coefficient of kinetic friction between the crate and the floor as "µk".
The force applied by the student can be broken down into two components: the horizontal component and the vertical component.
Horizontal component of the force (Fh) = F * cos(angle)
Vertical component of the force (Fv) = F * sin(angle)
In this case, the vertical component (Fv) does not affect the horizontal motion of the crate, so we'll focus on the horizontal forces.
The net horizontal force (F_net) acting on the crate is given by:
F_net = Fh - frictional force
The frictional force can be calculated as the product of the coefficient of kinetic friction (µk) and the normal force (N) exerted on the crate by the floor.
The normal force (N) is equal to the weight of the crate, which can be calculated as:
Weight = mass * gravity
Weight = m * g
Now, we can set up the equation for the net horizontal force:
F_net = Fh - µk * N
= Fh - µk * (m * g)
According to Newton's second law, the net force is equal to the mass of the object multiplied by its acceleration:
F_net = m * a
Equating the two equations for F_net, we have:
Fh - µk * (m * g) = m * a
Substituting the given values:
Fh = 200 N * cos(25°)
m = 29 kg
µk = 0.22
g = 9.8 m/[tex]s^{2}[/tex]
Fh ≈ 200 N * 0.9063 ≈ 181.26 N
Plugging these values into the equation, we can solve for the acceleration (a):
181.26 N - 0.22 * (29 kg * 9.8 m/[tex]s^{2}[/tex]) = 29 kg * a
181.26 N - 61.516 N = 29 kg * a
119.744 N = 29 kg * a
a ≈ 119.744 N / 29 kg ≈ 4.13 m/[tex]s^2[/tex]
Therefore, the acceleration of the crate is approximately 4.13 m/[tex]s^2[/tex].
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A racing car has a uniform acceleration of 6 m/s2. In 10s it will cover:
two speakers create identical 240 Hz sound waves a person is 1.47 m from a speaker 1. what is the minimum distance to speaker 2 for there to be destructive interference at that spot? (Unit = M)
The minimum distance to speaker 2 for there to be destructive interference at that spot is 1.145 meters.
Destructive interference is said to happen when two waves with identical frequencies and amplitudes interfere with each other resulting in a wave with amplitude zero.
In order for us to calculate the minimum distance to speaker 2 for there to be destructive interference at that spot, we need to follow these steps:
Step 1: Find the wavelength of the sound waves wavelength, λ = speed of sound / frequency, f
The speed of sound is 343 m/s because the question doesn't give any value for it.
Therefore, λ = 343 / 240Hz = 1.43m
Step 2: Determine the distance from speaker 1 to the point of destructive interference
The distance from speaker 1 to the point of destructive interference, d = λ / 2 + kλ where k = 0, 1, 2, 3, ...
The smallest value for k is 0, so d = λ / 2 = 1.43 / 2 = 0.715m
Step 3: Calculate the distance from speaker 2 to the point of destructive interference
Since we want to know the minimum distance to speaker 2 for there to be destructive interference at that spot, we need to find the distance that is one-half wavelength more than the distance from speaker 1 to the point of destructive interference.d2 = d + λ / 2 = 0.715 + 1.43 / 2 = 1.145m
Therefore, the minimum distance to speaker 2 for there to be destructive interference at that spot is 1.145 meters.
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Q3: Force A, 12N acting horizontally to the right, force B, 20N acting. at 140° to force A; force C, 16N acting at 290° to force A. (Ans.: 3.06 kN, -45° to force A)
Answer:
To find the resultant force and its direction, we can use vector addition.
First, let's break down force B and force C into their horizontal and vertical components:
Horizontal component of force B:
Bx = 20N * cos(140°)
Vertical component of force B:
By = 20N * sin(140°)
Horizontal component of force C:
Cx = 16N * cos(290°)
Vertical component of force C:
Cy = 16N * sin(290°)
Now, let's add up the horizontal and vertical components of all the forces:
Horizontal component of resultant force:
Rx = Ax + Bx + Cx
Vertical component of resultant force:
Ry = Ay + By + Cy
To find the magnitude of the resultant force (R), we use the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)
To find the direction (θ) of the resultant force, we can use the inverse tangent function:
θ = atan(Ry / Rx)
Plugging in the given values:
Ax = 12N (horizontal component of force A)
Ay = 0N (vertical component of force A)
Bx = 20N * cos(140°)
By = 20N * sin(140°)
Cx = 16N * cos(290°)
Cy = 16N * sin(290°)
Now let's calculate the values:
Bx = 20N * cos(140°) ≈ -11.55 N
By = 20N * sin(140°) ≈ 9.56 N
Cx = 16N * cos(290°) ≈ 13.82 N
Cy = 16N * sin(290°) ≈ -5.45 N
Rx = 12N + (-11.55N) + 13.82N ≈ 14.27 N
Ry = 0N + 9.56N + (-5.45N) ≈ 4.11 N
R = sqrt(14.27^2 + 4.11^2) ≈ 14.98 N
θ = atan(4.11 / 14.27) ≈ -15.58°
The magnitude of the resultant force is approximately 14.98 N, and the direction is approximately -15.58° (or approximately -45° to force A).
Note: The negative sign indicates that the resultant force is in the opposite direction to force A.
2. A well 1000m deep at an angle of 45 degree, what is the true vertical depth of the well?
Answer: 707.11m
Explanation:
since the well is at 45 degrees, we can use trig ratios to figure out the vertical depth of the well as u can see image attached.
then since we are looking for the vertical depth and we have information on the hypotenuse we can say
sin45= [tex]\frac{verticle height}{1000}[/tex]
therefore, we can say.
1000sin(45) = vertical height
hence
vertical height = 707.11m