The distance between the two charges is approximately 0.0134 meters.
The Coulomb force between two point charges is given by Coulomb's Law,
[tex]F = \dfrac{k Q_1 Q_2}{r^2}[/tex]
where k is Coulomb's constant, Q1 and Q2 are the magnitudes of the two charges, and r is the distance between them.
Q1 = +8 x 10^-6C, Q2 = -5 x 10^-6C, and F = 0.2 N.
k = 9 x 10^9 N m^2/C^2.
Substituting these values into Coulomb's Law,
[tex]0.2 N = \dfrac{9 \times 10^9 \times 8 \times 10^{-6} \times -5 \times 10^{-6}}{ r^2}[/tex]
Multiplying both sides by r^2, we get:
r^2 = (3.6 x 10^-5 N) / 0.2
r^2 = 1.8 x 10^-4 m^2
r ≈ 0.0134 m
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In which collision(s) is kinetic energy conserved?
A.Elastic
B.Inelastic
C.Perfectly inelastic
Answer:
Explanation:
A elastic
in the vector diagram below, the magnitude of A is 15m, the magnitde of B is 18m and the magnitude of C is 6m. Find the resultant vector using component method. Angle A = 35 Angle B = 30 Angle C = 50.
Answer:
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
Explanation:
A force of 227 N is spread over an area of 3 m². What is the pressure?
Answer:
Explanation:
p=227/3=75.66Pascal
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Pressure is defined as : Force per unit Area
[tex]\qquad \sf \dashrightarrow \: p = \dfrac{force}{area} [/tex]
[tex]\qquad \sf \dashrightarrow \: p = \dfrac{227}{3} [/tex]
[tex]\qquad \sf \dashrightarrow \: p \approx75.67 \: \: pascals[/tex]
[ note : to get pressure in pascals, force and area should be in S.I unit, it's given in S.I unit in given question, but if not you can make conversion first and then solve ]
Order the three phases of bromine by distance between bromine particles, from least to greatest.
The three phases of bromine are: liquid, gas, and solid. To order these phases based on the distance between bromine particles, from least to greatest.
We need to consider how the intermolecular forces change as the temperature and pressure change.
In the solid phase, bromine molecules are packed tightly together, with the minimum distance between particles. This is because the intermolecular forces, including London dispersion forces and dipole-dipole forces, are strong enough to hold the particles in a fixed position.
In the liquid phase, the bromine molecules are further apart than in the solid phase, but still close enough to experience intermolecular forces. The temperature of the liquid is high enough to overcome the attractive forces and cause the particles to move about more freely, but not enough to separate the particles completely.
In the gas phase, the bromine molecules are separated by the greatest distance, with no strong intermolecular forces to hold them in place. The high temperature of the gas causes the particles to move rapidly, colliding with each other but not sticking together.
Therefore, the order of the three phases based on the distance between bromine particles is solid < liquid < gas.
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Water has a specific heat of 4184 Jkg⋅∘C. How much energy is needed to increase the temperature of a kilogram of water5∘C?
The specific heat capacity of water is 4184 and it needs 20920J energy to increase the temperature of a kilogram of water 5 degree celcius.
The amount of heat required to raise the temperature of one gramme of a substance by one degree Celsius. Specific heat is usually measured in calories or joules per gramme per Celsius degree. Water, for example, has a specific heat of 1 calorie (or 4.186 joules) per gramme per Celsius degree.
A substance's specific heat capacity is the amount of heat energy required to raise the temperature of a unit mass of that substance by 1oC. (or 1K). The SI unit of measurement is joule per kilogramme per kelvin (Jkg-1K-1).
By using the equation:-
Q= mCΔmCΔTT
(where, Q= energy, m= mass of the sample, C= specific heat of the sample and delta T is the change in temperature).
[tex]Q= 1kg*4184J*(5-0)= 20920J.[/tex]
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5. On some highways, exit signs are numbered according to the number of kilometres the
exit is from the place where the highway originated. If you are driving south and pass
exit 35 at 2:15 pm and then you pass exit 116 at 3:09 pm, what is your velocity in m
Answer:
We can start by using the formula:velocity = distance/timeFirst, we need to calculate the distance traveled in kilometers.
To do this, we can subtract the exit numbers:
116 km - 35 km = 81 km
Next, we need to convert the time difference from hours and minutes to hours:
3:09 pm - 2:15 pm = 0.9 hours
Now we can use the formula to find the velocity:
velocity = 81 km / 0.9 hours
velocity ≈ 90 km/h
Finally, we can convert this velocity to meters per second by multiplying by 1000/3600:
velocity = 90 km/h x 1000 m/km / 3600 s/h
velocity ≈ 25 m/s
Therefore, your velocity is approximately 25 m/s.
Explanation:
using only the electrical specifications, determine how deep the external underground secondary service conduits are installed.
However, typically, electrical codes require that buried secondary service conduits be installed at a minimum depth of 18 inches (45.7 cm) below the surface. In some cases, local codes may require a deeper depth, such as 24 inches (60.9 cm) or more, depending on factors such as soil type, climate, and intended use of the conduit.
It is also important to note that other factors, such as the type and size of conduit, the type of wiring used, and the intended electrical load, may also affect the required burial depth. Therefore, it is essential to consult with local building codes and a licensed electrician or electrical engineer to determine the appropriate depth for installing external underground secondary service conduits.
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3.1 Displacement, Velocity, and Acceleration
A turtle's velocity changes from v₁ = 1.0 mm/s at 0 = 0° to v₂ - 1.2 mm/s at 0= 20°. What is the change in the turtle's velocity?
The change in velocity of the turtle from 1 mm/s at angle 0° to motion at a velocity of 1.2 mm/s at an angle 20° is -0.51 mm/s.
What is Velocity?Velocity is defined as the directional motion of an object, as indicated by the rate of change of position as observed from a particular frame of reference and measured by a particular standard of time.
Velocity is the vector quantity as it has both magnitude as well as direction. It is expressed as
Velocity= Displacement/ Time Taken
It's SI unit is meter/second. Other units commonly used are ft./s, miles per hour km/h etc.
Here, initial velocity of turtle = 1 mm/s at 0°
u = u cosθ = 1 mm/s cos 0 = 1 mm/s
final velocity = v cos 20 = 1.2 m/s cos 20 = 0.48 mm/s.
then, change in velocity = 0.48 mm/s - 1 mm/s = - 0.51 mm/s.
Therefore, the change in velocity of the turtle is - 0.51 mm/s.
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Question 6 of 10
When making a winter coat, you should pick a fabric that has which
characteristic?
A. Heavyweight
OB. Warm
C. Resistant to wear
D. All of the above
Answer: Warm
Explanation:
need help with this bad boy
The tension force T1 in the horizontal direction is mg sinθ, for the angle of zero, the tension force becomes zero. The tension force T2 is mgcosθ, for an angle of 30.1 the force is 63 N.
What is tension force?Tension force is a kind of force acting on object if it experience a force from a suspended mass on it. It is a vector quantity and having both direction and magnitude.
The horizontal tension force = mg sin θ
and the vertical or diagonal tension = mg cos θ
given mass suspended m = 25.5 kg.
Then, horizontal tension force T1 = 25.5 kg ×9.8 m/s²× sin 0 = 0
(sin 0 = 0)
The tension force T2 = mg cos θ
T2 = 25.5 kg ×9.8 m/s²× cos 30.1 = 63 N.
Therefore, tension force on cable 1 is zero and that on cable 2 is 63 N.
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define henry and its dimnsions
Answer:
The henry (symbolized H) is the International System of Units (SI) derived unit of electrical inductance. Reduced to base SI units, one henry is the equivalent of one kilogram meter squared per second squared per ampere squared (kg m2 s-2 A-2).
"If your primary goal is to build strength and increase muscle mass, you could____
increase the amount of aerobic activity
expand the number of anaerobic activities per week
complete workout sets of high repetitions and low weight (example: 3 sets of 20 repetitions with 5lb or less)
If one's primary goal is to build strength and increase muscle mass, completing workout sets of high repetitions and low weight is correct that is the last option, as the aerobic activity would not increase the muscle.
What is the importance of the muscle-building exercise?Anaerobic activities should be prioritized because they force the muscles to work at high intensity for short periods of time; this type of training is typically done with heavy weights for fewer repetitions and sets and builds the muscles.
Hence, if one's primary goal is to build strength and increase muscle mass, completing workout sets of high repetitions and low weight is correct that is the last option, as the aerobic activity would not increase the muscle.
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Students are conducting an experiment. One student has kept 3 books and another student 6 books. They are using a ramp with same size and dimensions. They are measuring the distance travelled by the car. What they are trying to find out? Will you be able to predict the outcome and give conclusion for that experiment?
A student conducts an experiment to find the speed of a toy car that has been released from various heights on a ramp as it reaches the bottom of the ramp.
What are the outcomes of the experiment?The student may need to obtain more height measurements in order to confirm the accuracy of his experiment and thereby enhance it. By averaging all the heights, it is now possible to determine the height's accuracy.
The results show the speed of a toy car from different heights measurements and can be improved by doing different trials.
Therefore, students try to find out the speed of a toy car from different heights.
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Problem:
Ash throws a Pokéball at an upwards angle of 30° above the horizontal with a speed of 5m/s
trying to catch a shiny Castform. If the Castform is on the ground and hit, find how far away it
was, as well as the max height the ball reaches. Assume the acceleration of the gravity for the
planet they are on has a value of g=9.8m/s^2 and we can ignore air resistance.
Draw a well labeled diagram of the physical situation. Make sure the initial velocity is drawn as
a vector and the trajectory is drawn, showing the coordinate axes with directions. Label
accelerations and the point where the ball reaches max height.
Hints: break the initial velocity into x and y parts, solve the y parts of the problem to find the
time, then use the result to solve the y parts.
Answer:
Explanation:
Here is a step by step explanation of how to solve the problem:
Break the initial velocity into x and y components. The velocity of the Pokéball can be broken down into two components: the horizontal component (vix) and the vertical component (viy). The horizontal component remains constant throughout the motion and has a value of vix = vcosθ, where v is the magnitude of the velocity and θ is the angle of launch. The vertical component changes due to the acceleration of gravity and has a value of viy = vsinθ - gt, where t is time.
Solve for the time of flight. We want to find the time it takes for the Pokéball to reach its maximum height, so we need to set viy = 0 and solve for t:
0 = vsinθ - gt
gt = vsinθ
t = vsinθ / g
Calculate the maximum height. The maximum height is reached when the vertical component of velocity is equal to zero, so we can use the equation:
h = viy^2 / (2g)
h = (vsinθ)^2 / (2g)
Calculate the range. The range is the horizontal distance traveled by the Pokéball during its flight, and it can be found using the equation:
x = vix * t
x = vcosθ * (vsinθ / g)
Draw a well labeled diagram of the physical situation. Draw the coordinate axes, showing the directions, and label the initial velocity as a vector. Show the trajectory of the Pokéball, including the point where it reaches its maximum height, and label the acceleration due to gravity.
b) A hammer of weight 100 N falls freely on a nail from height 1.25 m. Find the impulse and average force of blow if impact last for 10-² S.
Answer:
Explanation:
When the hammer hits the nail it transfers this energy to the nail in order to move it 1cm (0.01m). A transfer of energy is known as "work done" and work done = force x distance. So, force = work done / distance = 25 / 0.01 = 2500N Answer: Average force = 2500 Newtons.
(1 of 5)
Drag the phase slider left and right to move the planet into and out of transit mode. The
normalized flux (relative amount of star light reaching an observer on Earth) when the
planet is off to the side (not transiting) is
while the normalized flux when the planet
is transiting is. (Hint: examine the plot at the top of the applet while you move the
phase slider. The number you are looking for is on the left of the plot.)
O 1.000, 0.990
O 0.990,1.000
O 1.00000, 0.99995
O 0.99995,1.00000
Drag the phase slider left and right to move the planet into and out of transit mode. The normalized flux (the relative amount of starlight reaching an observer on Earth) when the planet is off the side (not transiting) is 0.990 while the normalized flux when the planet is transiting is 1.000. Thus, the correct option for this question is B.
What is Normalized flux?Normalized flux may be characterized as a type of key methodology in spectral data mining. It is important for the efficiency and accuracy of the automatic processing of massive astronomical spectral data, information extraction, and sharing.
A transit occurs when a planet passes between a star and its observer. Transits within our solar system can be observed from Earth when Venus or Mercury travel. The frequency of the normalized flux when the planet is transiting is completely different from when the planet is off the side.
Therefore, the correct option for this question is B.
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Answer: 1.000,0.990 (correct)
Explanation:
1. What is the momentum of an 11 kg bowling ball rolling at 4 m/s?
Any moving object has momentum. The momentum of an 11 kg bowling ball rolling at 4 m/s is 44 kg m/s.
What is momentum?The momentum is defined as a quantity which is the product of the mass of the particles and its velocity. It is a vector quantity. It has both magnitude and direction. The rate of change of momentum is equal to the force acting on the particle.
The equation of the momentum is given as:
p = mν
= 11 kg × 4 m/s
= 44 kg m/s
Thus the momentum of the bowling ball is 44 kg m/s.
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A cement block accidentally falls from rest from the ledge of a 84.9-m-high building. When the block is 16.6 m above the ground, a man, 1.90 m tall, looks up and notices that the block is directly above him. How much time, at most, does the man have to get out of the way?
The man has at most 3.55 s to get out of the way.
What is kinematic equations?
Kinematics can be defined as a subfield of physics developed in classical mechanics that describes the motion of points, bodies and systems of bodies without considering the forces that cause them to move.
We can solve this problem using kinematic equations.
First, we can find the time it takes for the block to fall from a height of 84.9 m using the formula:
y = 1/2 * g * t^2
where
y is the distance fallen (84.9 m)g is the acceleration due to gravity (9.81 m/s^2) t is the timeRearranging this equation, we get:
t = sqrt(2y/g) = sqrt(2 * 84.9 m / 9.81 m/s^2) = 4.09 s (to two significant figures)
So the block will hit the ground after 4.09 s of falling.
Next, we can find the time it takes for the block to fall from a height of 16.6 m using the same formula:
t = sqrt(2y/g) = sqrt(2 * 16.6 m / 9.81 m/s^2) = 1.41 s (to two significant figures)
So the block will take 1.41 s to fall from a height of 16.6 m to the ground.
The man has to get out of the way before the block falls the remaining distance of (84.9 - 16.6) = 68.3 m. We can find the time it takes for the block to fall this distance using the same formula:
t = sqrt(2y/g) = sqrt(2 * 68.3 m / 9.81 m/s^2) = 3.55 s (to two significant figures)
Therefore, the man has at most 3.55 s to get out of the way.
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A 1500 kg car traveling east at 20 m/s collides with a moving 2500 kg truck moving 30 m/s west.. After they collide, the two interlock and move together. What was the final velocity of the truck? (Hint-momentum is a vector and direction matters, use + or - values as appropriate)* A. 11.25 m/s west B. 11.25 m/s east C. 32.6 m/s east D. 32.6 m/s west
Answer:
A
Explanation:
The final velocity of the truck can be calculated using the law of conservation of momentum. The law states that the total momentum of a closed system (the car and truck) remains constant unless an external force acts on the system.
Let's call the final velocity of the system (car + truck) after the collision vf.
The initial momentum of the car before the collision is equal to m1 * v1 = 1500 kg * 20 m/s = 30000 kg m/s, where m1 is the mass of the car and v1 is its initial velocity.
The initial momentum of the truck before the collision is equal to m2 * v2 = 2500 kg * -30 m/s = -75000 kg m/s, where m2 is the mass of the truck and v2 is its initial velocity.
The total initial momentum of the system before the collision is equal to the sum of the initial momenta of the car and truck:
p_initial = m1 * v1 + m2 * v2 = 30000 kg m/s + (-75000 kg m/s) = -45000 kg m/s.
After the collision, the final momentum of the system is equal to the sum of the final momenta of the car and truck:
p_final = m1 * vf + m2 * vf = (1500 kg + 2500 kg) * vf = 4000 kg * vf.
Since the total momentum of the system is conserved, we can set the initial and final momenta equal to each other:
-45000 kg m/s = 4000 kg * vf
Finally, we can solve for the final velocity of the system (truck):
vf = -45000 kg m/s / 4000 kg = -11.25 m/s
Since the truck was moving west before the collision, the final velocity is 11.25 m/s west, so the answer is A. 11.25 m/s west.
Where on the physical activity pyramid do sedentary activities belong? a. A b. B c. C d. D please select the best answer from the choices provided.
In the physical activity pyramid, sedentary activities belong to Level D.
The Physical Activity Pyramid is a graphic representation of the different types of physical activities that are recommended for a healthy lifestyle.
The pyramid is divided into four levels, with the most important activities at the bottom and the least important at the top. The greatest and most significant activities for healthy everyday life are at the bottom and the least healthy activities at the top, which you should only perform occasionally.
Sedentary activities, which are activities that involve little or no physical movement, belong at the top of the pyramid, in Level D.
Level D is the smallest section of the pyramid, and it represents activities that should be limited in order to maintain good health.
Hence, option D is the correct choice.
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Can someone answer this question about Compton effect?
The Compton effect can be explained on the basis of the quantum theory of light and the wave theory of scattered radiation, hence option B is correct.
What is the Compton effect?The compton effect, photoelectric effect, and blackbody radiation are described by the quantum theory of light, while interference and diffraction are explained by the wave nature of light.
It causes X-rays and other powerful electromagnetic radiations to have longer wavelengths after being elastically dispersed by electrons.
Therefore, the compton effect, also known as Compton scattering, is the primary mechanism by which radiant energy is absorbed in the matter.
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The given question is incomplete, so the most probable complete question is,
Can someone answer this question about the Compton effect?
The Compton effect can be explained on the basis of __________
a) Wave nature of light
b) Quantum theory of light
c) Ray optics
d) Wave optics
How do you think scientists discovered that the flowering time of the field mustard had changed?.
Answer:
Explanation:
Because the scientists still had seeds from the pre-drought mustard plants collected in 1997, they were in a perfect position to find out whether the change in flowering time was really due to evolution. They grew pre-drought seeds alongside seeds collected from the exact same sites in 2004, after the drought.
There are many ways that scientists could have discovered that the flowering time of the field mustard had changed. One possible way is through direct observation and monitoring of the plant's growth and development over time. Another possible way is through the analysis of historical records or herbarium specimens.
What is mustard?Mustard is a plant species that belongs to the Brassicaceae family, which also includes other common plants such as broccoli, cabbage, and cauliflower. The mustard plant is characterized by its small yellow flowers, which grow on a tall stem with leaves that are either lobed or unlobed.
Mustard has been cultivated for centuries for its seeds, which are used to produce mustard condiments, as well as for its leaves, which are used in salads and as a cooked vegetable. There are several different varieties of mustard, including white mustard (Sinapis alba), brown mustard (Brassica juncea), and black mustard (Brassica nigra).
Flowering timing refers to the time when a plant produces flowers, which is an important aspect of its life cycle. The timing of flowering can be influenced by several factors, including environmental conditions such as temperature, light, and water availability, as well as genetic factors.
Flowering timing is important for plant reproduction, as it determines when the plant will produce seeds. In many plant species, the timing of flowering is also influenced by environmental cues such as day length, which can trigger the plant to flower at specific times of the year.
Understanding flowering timing in plants is important for agriculture, as it can help farmers optimize crop yields by selecting the right varieties of plants for specific growing conditions and by manipulating environmental factors to promote optimal flowering. It is also an important area of research in plant biology, as scientists seek to understand the genetic and molecular mechanisms that control flowering timing in different plant species.
Here in the question,
There are several ways that scientists could have discovered that the flowering time of the field mustard had changed. One possible way is through direct observation and monitoring of the plant's growth and development over time.
For example, scientists may have regularly visited a field of mustard plants and recorded the timing of flowering for several years. By comparing the data from different years, they could have detected changes in the flowering time of the plants.
Another possible way is through the analysis of historical records or herbarium specimens. Herbarium specimens are dried and pressed plants that are stored in a collection for scientific study. By examining herbarium specimens collected from the same location over time, scientists could determine whether there had been any changes in the timing of flowering.
Additionally, researchers may have used satellite imagery to track changes in vegetation over time. By analyzing changes in the color and density of vegetation in a particular area, they could detect changes in the timing of flowering for different plant species, including field mustard.
Therefore, there are many different methods that scientists could have used to discover changes in the flowering time of field mustard, and it is likely that a combination of these methods was used to confirm the change.
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A truck moving across an ice road is spreading sand across the ice. The truck can be considered a closed, isolated system. Which of the following is true? A. The mass of the truck decreases with no change in the velocity of the truck B. The mass of the truck decreases while the velocity of the truck increases. C. The mass of the truck decreases while the velocity of the truck decreases. D.The mass of the truck remains the same while the velocity of the truck remains the same.
The mass of the truck decreases while the velocity of the truck increases. Option B
What is a closed system?A closed system is a system in which matter cannot enter or leave the system, but energy can be exchanged between the system and its surroundings. In other words, a closed system is isolated from its environment in terms of mass, but not in terms of energy.
Closed systems can be found in many different areas of science and engineering, including thermodynamics, mechanics, and engineering. For example, in thermodynamics, a closed system is a system in which heat can be transferred between the system and its surroundings, but no mass can be transferred. In mechanics, a closed system is a system in which the total momentum of the system remains constant, regardless of any external forces acting on the system.
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A student is playing with a magnetic compass near a bar magnet. At a range of 10 cm, they notice that the compass needle is pulled slightly towards the magnet. What would they see if the compass was moved to 8 cm?
A. The needle would not move from its original deflection.
B. The needle would be pushed in the opposite direction.
C. The needle would be pulled more towards the magnet.
D. The needle would return closer to its normal position.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
As the boy moves the bar magnet towards the magnetic compass, the needly is pulled slightly towards the bar magnet, so if he deduct the separation to 8 cm, most probably the needle would be pulled more towards the bar magnet.
Hence, the correct choice will be : (c)
Answer: c I think
Explanation I think its c
Two capacitors are connected in parallel across a 60 Hz supply. One of the capacitors is rated at 50 microfarads and has a current of 2.34 A through it.
Determine the capacitance of the second capacitor if the current through it is 0.40 A.
The capacitance of the second capacitor is 5.1 microfarads.
What is capacitance?Capacitance is the ability of an electrical component, such as a capacitor, to store an electrical charge. The amount of charge that can be stored is related to the capacitance, which is measured in Farads. The larger the capacitance, the more charge a capacitor can store.
The total capacitance of two capacitors connected in parallel is equal to the sum of the individual capacitances. That is, C_total = C1 + C2.
We know the value of one of the capacitors, C1, to be 50 microfarads, and we know the current through it, I1, to be 2.34 A.
Since capacitance and current are inversely proportional, we can use this relationship to solve for the capacitance of the second capacitor, C2.
C2 = C1 * (I2 / I1)
where I2 is the current through the second capacitor, which we know to be 0.40 A.
Plugging in the values, we get:
C2 = 50 * (0.4 / 2.34)
C2 = 5.1 microfarads
Therefore, the capacitance of the second capacitor is 5.1 microfarads.
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excavation costs are based on the
A. amount of earth removed
B. depth of the frost line in the area
C. time involved multiplied by a standard rate
D. sophistication of the machinery necessary
Answer:
C
Explanation:
Excavation costs are generally based on the time involved multiplied by a standard rate.
hellppplpp me on this besties
The acceleration of the car is 2.5 m/s² to the right.
What is the acceleration of the car?The acceleration of the car is calculated by applying Newton's second law of motion as shown below.
F (net ) = ma
F - Ff = ma
where;
m is the mass of the cara is the acceleration of the carFf is the force of friction of the carF is the applied force of the car3400 N - 400 N = 1200a
3000 = 1200a
a = 3000 / 1200
a = 2.5 m/s² to the right
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What is the average distance from Sun in AU of an object with a planetary object with orbital period of 325 years?
Answer: So, the average distance from the Sun of a planetary object with an orbital period of 325 years is approximately 40.0 AU.
Explanation:
The average distance from the Sun (in astronomical units) of a planetary object with an orbital period of 325 years can be estimated using Kepler's Third Law of Planetary Motion. This law states that the square of the orbital period (T) of a planet is proportional to the cube of its average distance from the Sun (r):
T^2 = k * r^3
where k is a constant. We can rearrange this equation to solve for r:
r = (T^2 / k)^(1/3)
The value of k depends on the units used for T and r, so it is important to make sure that the units are consistent. If T is in years and r is in astronomical units (AU), then k has a value of approximately 4π^2.
Using this formula, we can estimate the average distance from the Sun of a planetary object with an orbital period of 325 years:
r = (325^2 / (4 * π^2))^(1/3)
r ≈ 40.0 AU
So, the average distance from the Sun of a planetary object with an orbital period of 325 years is approximately 40.0 AU.
A yoga instructor weighing 490 N sits, meditating, on a plane that is inclined 20.0° above the horizontal. Find the components of the weight forces that are parallel and perpendicular to the plane.
The vector components of the weight force parallel to the plane is 463.4 N, and the component perpendicular to the plane is 166.8 N upward.
What are the vector components?A quantity which has both magnitude and direction is termed as a vector quantity. It can be divided into two components in 2-dimensional plane: The vertical component and the horizontal component.
The weight force, which is equal to the force of gravity acting on the yoga instructor, has a magnitude of 490 N, which we can decompose into its vertical and horizontal components using trigonometry:
Vertical component = weight force x sin(20°)
= 490 N x sin(20°)
= 166.8 N (upward)
Horizontal component = weight force x cos(20°)
= 490 N x cos(20°)
= 463.4 N (parallel to the plane)
So the component of the weight force parallel to the plane is 463.4 N, and the component perpendicular to the plane is 166.8 N upward.
Learn more about the vector components, here:
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What is the mass of a car possessing 15,000 kg*m/s of momentum going a speed of 35 m/s?
A.525000 kg
B.428.6 kg
C.14965 kg
D.0.0023 kg
Answer: B is correct
Explanation: The mass of the car can be calculated using the equation: mass = momentum / velocity Therefore, the mass of the car is: mass = 15,000 kg*m/s / 35 m/s mass = 428.6 kg
