A frame of reference is essential when describing motion because it provides a standard or point of comparison that helps us understand and analyze the movement of an object. It allows us to determine the position, velocity, and acceleration of an object relative to a fixed point or system.
Establishing a Standard: A frame of reference provides a fixed point or system against which the motion of an object is observed. It establishes a standard against which we can measure and compare the position, velocity, and acceleration of the object. Without a frame of reference, it would be challenging to determine the exact motion of an object and understand its relative change in position.Relativity of Motion: The concept of relativity is central to understanding motion. An object's motion is always described relative to something else, whether it's the ground, another object, or an observer. Different frames of reference can yield different observations of the same motion. By defining a specific frame of reference, we can establish consistency and compare different objects or events in a meaningful way.Quantifying Motion: A frame of reference allows us to quantify motion using mathematical equations. For example, the velocity of an object is determined by its change in position over time relative to the chosen frame of reference. By defining a frame of reference, we can apply mathematical formulas and analyze the motion using concepts such as speed, acceleration, and displacement.Communication and Analysis: A frame of reference provides a common language and system for communicating and analyzing motion. It allows scientists, engineers, and researchers to share and interpret data consistently. By using a standardized frame of reference, we can compare results, conduct experiments, and make predictions based on a shared understanding of motion.For more such questions on motion, click on:
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Which statement is false regarding seismic waves? HELP FAST
A.P waves are longitudinal.
B.S waves are transverse.
C.P waves only move through solids.
D.S waves only move through solids.
16. Sodium ions bond with chlorine ions to form
table salt, NaCl. Explain why one sodium ion
bonds with one chlorine ion
The volumetric discharge at the start of a baseflow recession
was 830 m^3/s; after 60 days the volumetric discharge declined to
550 m^3/s. What is the total volume of baseflow discharge after 100
days
The total volume of baseflow discharge after 100 days would be 690 [tex]m^{3}/s[/tex] * 40 days = 27,600 [tex]m^{3}[/tex].
To calculate the total volume of baseflow discharge after 100 days, we can use the concept of the area under the curve.
Assuming a linear decline in volumetric discharge over time, we can use the average discharge during the 60-day period (830 + 550) / 2 = 690 [tex]m^{3}/s[/tex] as an approximation.
The total volume of baseflow discharge can be obtained by multiplying the average discharge by the duration. In this case, the duration is 100 - 60 = 40 days. So, the total volume of baseflow discharge after 100 days would be 690 [tex]m^{3}/s[/tex] * 40 days = 27,600 [tex]m^{3}[/tex].
This calculation assumes a linear decline in discharge, which may not precisely reflect the actual baseflow recession behavior. However, it provides a rough estimate of the total volume of baseflow discharge over the given time period.
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a partice set into motion within a circle ofradiusm 14 cm having 33.3 if the particle starts on the positive x axis at time --
A particle is set in motion within a circle of radius 14 cm having 33.3. If the particle starts on the positive x-axis at time 0, it will take less than 100 words to explain the position of the particle at a later time.
A particle is set in motion within a circle of radius 14 cm, having an angle of 33.3. The particle starts on the positive x-axis at time 0, so its initial angle is 0°. As the particle moves around the circle, its position changes, but its distance from the center remains constant at 14 cm.
If the particle moves through an angle of 33.3°, it will be at a certain position on the circle. After the particle moves through an angle of 33.3°, its final angle will be 33.3°. To find its position on the circle, we can use trigonometry. We know that the radius of the circle is 14 cm, and we know the angle the particle has moved through.
Therefore, we can use the sine and cosine functions to find the x- and y-coordinates of the particle's position on the circle.
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why do some ceiling lights do not have an earth wire?
Answer: Answer Below
Answer below
Explanation:
Some appliances - such as vacuum cleaners and electric drills - do not have an earth wire. This is because they have plastic casings, or they have been designed so that the live wire cannot touch the casing. ... These appliances have double insulation.
Some of the ceiling lights do not have an Earth wire due to the presence of insulations in plastic casings.
The given problem is based on the concept and fundamentals of insulation. An insulation is a material that is used when we need to prevent the heating due to electrical overloading or the heat transfer.
Insulation helps to keep the temperature of desired place under the controlled situation. It provides the protection against the heat in summer and cold in winter. Some appliances - such as vacuum cleaners and electric drills - do not have an earth wire. This is because they have plastic casings, or they have been designed so that the live wire cannot touch the casing. These appliances have double insulation.
Thus, we can conclude that some of the ceiling lights do not have an Earth wire due to the presence of insulations in plastic casings .
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In a solution, the solvent is...
a chef fills 50ml container with 43.5 g of cooking oil. what is the density of the oil?
Answer:
0.87 g per ml
Explanation:
D=M/V
43.5/50=0.87
What is the attractive or repulsive force between two ferromagnetic objects is called?
consider a uniformly charged spherical volume of radius r which contains a total charge q. find the electric field and the electrostatic potential at all points in the space.
A uniformly charged spherical volume of radius r with total charge q has electric field E = q / (4πεr²) and electrostatic potential difference VAB = - ∫AB E.dl.
A uniformly charged spherical volume of radius r containing a total charge q has an electric field and electrostatic potential at all points in space. The electric field intensity can be determined by applying Gauss's law. The Gaussian surface considered should have spherical symmetry similar to the sphere being considered. The Gaussian surface is placed such that the total charge enclosed is q.Let's calculate the electric field intensity E. The electric field intensity E at a point within a spherical surface is given by E = q / (4πεr²), where q is the total charge enclosed within the sphere, ε is the permittivity of the medium, and r is the radius of the sphere.The electrostatic potential difference between two points A and B is given by the equation: VAB = - ∫AB E.dl. We can use the above equation to determine the electrostatic potential at all points in the space. Here, dl is the differential length along the path between points A and B and E is the electric field at that point in the direction of dl. The electric field has a negative sign, as the electric field lines always flow from positive to negative potential points in the opposite direction.For more questions on electric field
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how does thermal energy relate to temperature during condensation
Answer:
"This process, which is the opposite of vaporization, is called condensation. As a gas condenses to a liquid, it releases the thermal energy it absorbed to become a gas. During this process, the temperature of the substance does not change. The decrease in energy changes the arrangement of particles."
Condensation is a phase transition where the temperature remains constant but the thermal energy will change.
What is condensation?Condensation is a phase transition that can be described as the process through which the physical state of the matter changes from the gaseous phase into the liquid phase. For example, condensation takes place when water vapour changes into liquid water. When the water vapours in the air come in contact with a cold surface, they condense and become water droplets.
Condensation process by which water vapour is changed into liquid water. Any gas can be condensed or liquified at high pressure and low temperature.
During the phase transition, the temperature remains constant therefore during the condensation the temperature is constant and the heat energy of the molecules will change. Because when the gas molecules release the energy to get slow down then they clump together and become liquid.
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6. If you you apply a force of 30 N to the left to and object and your friend applies a force of 20 N
to the right. What is the net force on the object?
Answer:it’s 10N
Explanation:So 30N is going left and 20N is going right so you would subtract it because they are going opposite ways if they where going the same why then you would add them.
If you are applying a force of 30 N and your friend is applying a force of 20 N in opposite directions, the net force will be 10 N.
What is action reaction Force?Newton postulated that anytime objects A and B come into contact, they exert forces on one another. These two forces—also known as the action and reaction forces—are covered by Newton's third law of motion. The official formulation of Newton's third law is as follows: Every action has a corresponding and opposing reaction.
According to Newton's Third Law, forces always work in pairs. Think about what it illustrates when a boy plays with a dog's toy. The kid exerts force on the dog's toy, while the dog's toy exerts force on the boy. These two forces work together to form a pair.
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Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 × 1026 kg and the rings have an average radius of 100,000 km. (G = 6.67 × 10-11 N · m2/kg2)
The orbital speed of an ice cube in Saturn's rings is approximately 194 million m/s, calculated using the formula for orbital speed.
The orbital speed of an ice cube in the rings of Saturn can be calculated using the formula for the orbital speed of a satellite:
[tex]\begin{equation}v = \sqrt{\frac{GM}{r}}[/tex]
where v is the orbital speed, G is the gravitational constant, M is the mass of Saturn, and r is the average radius of the rings.
Plugging in the values:
[tex]\begin{equation}v = \sqrt{(6.67 \times 10^{-11} \text{ N} \cdot \text{m}^2/\text{kg}^2) \cdot (5.68 \times 10^{26} \text{ kg}) / (100,000,000 \text{ m})}[/tex]
v ≈ √(3.76 × 10¹⁶ N · m²/kg)
v ≈ 1.94 × 10⁸ m/s
Therefore, the orbital speed of an ice cube in the rings of Saturn is approximately 1.94 × 10⁸ m/s.
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2. A seal swims at 10 m/s against an
ocean current of 2 m/s. How far will the
seal swim in 2 minutes?
Answer:
So 960m in 2min
Explanation:
10-2=8
so 8m/s
8m/s times 60=480 times two because it is two so 960
Why should you be physically active?
Answer:
You should be physically active because you need to exercise or you might become overweight/obese. Exercise helps burn off calories which cause obesity. It is also good for your heart and lungs it keeps them active and healthy.
in a circuit, a 10 uf capacitor and a 5 uf capacitor are connected in series, and the combination is connected in parallel with a 15 uf capacitor. if a potential difference of 20 v is applied across the entire circuit, what is the potential difference across each capacitor?
The potential difference across the 10μF capacitor is 6.67 V, the potential difference across the 5μF capacitor is 30 V, and the potential difference across the 6μF capacitor is 20 V (the same as the potential difference applied across the entire circuit).
When a 10μF capacitor and a 5μF capacitor are connected in series, their equivalent capacitance will be:1/C= 1/C+ 1/C=> 1/C= 1/10+ 1/5
=> 1/C= 3/10
=> C = 10/3 μF
When the combination of the above two capacitors is connected in parallel with a 15μF capacitor, the equivalent capacitance of the combination will be:
1/C= 1/10/3 + 1/15
=> 1/C= (1/10+ 1/15)/3
=> 1/C= 1/6
=> C = 6μF
When a potential difference of 20 V is applied across the entire circuit, the potential difference across each capacitor can be found using the formula for the charge of a capacitor, Q = CV.
The charge on the 10μF capacitor will be: Q = CV
=> Q = (10/3) × 10⁻⁶ × 20
=> Q = 2/3 × 10⁻⁴ C
The potential difference across the 10μF capacitor will be:
V= Q/C
=> V= (2/3 × 10⁻⁴)/10/3 × 10⁻⁶
=> V = 20 V/3 = 6.67 V
The charge on the 5μF capacitor will be: Q = CV
=> Q = 5 × 10⁻⁶ × 20
=> Q = 1 × 10⁻⁴ C
The potential difference across the 5μF capacitor will be: V= Q/C
=> V= (1 × 10⁻⁴)/10/3 × 10⁻⁶
=> V = 30 V
The charge on the 6μF capacitor will be:
Q = CV
=> Q = 6 × 10⁻⁶ × 20
=> Q = 1.2 × 10⁻⁴ C
The potential difference across the 6μF capacitor will be: V= Q/C
=> V= (1.2 × 10⁻⁴)/6 × 10⁻⁶
=> V = 20 V
Therefore, the potential difference across the 10μF capacitor is 6.67 V, the potential difference across the 5μF capacitor is 30 V, and the potential difference across the 6μF capacitor is 20 V (the same as the potential difference applied across the entire circuit).
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how speed and position affect the energy possess by an object?
Answer:
more speed means that an object has more energy, now if an object's place is something such as a hill, the potential energy will increase meaning an object will have more speed and acceleration. this is because you have the earth's gravity helping you out when the object goes downhill, giving it the higher potential energy
write an expression in terms of t to represent the angle's measure (counterclockwise from the 3 o'clock position) after any amount of time elapsed since the point started moving.
To represent the angle's measure counterclockwise from the 3 o'clock position after any amount of time, we can use the concept of angular velocity. Angular velocity is the rate at which an object rotates in radians per unit of time.
Let's assume that the angular velocity is represented by the symbol ω (omega) and time is represented by t.
The angular displacement, which represents the angle's measure counterclockwise from the 3 o'clock position, can be calculated using the formula:
Angular displacement = ω * t
In this case, since we want the angle's measure counterclockwise from the 3 o'clock position, the angular displacement will increase as time passes. The positive direction for the angle is counterclockwise.
Therefore, the expression in terms of t to represent the angle's measure after any amount of time is:
the actual value of ω will depend on the specific situation or context in which the rotation is occurring.
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a bar magnet is pushed toward a loop of wire as shown in fig ure q30.7 . is there a current in the loop? if so, in which direction? if not, why not?
Yes, there is a current in the loop as the bar magnet is pushed towards a loop of wire. The direction of current is clockwise in the loop of wire.
Faraday's law of electromagnetic induction states that a time-varying magnetic field can induce an electromotive force (EMF) in a conductor. The relationship between a time-varying magnetic field and an EMF is described by Faraday's law as induced EMF = -dΦ/dt.
The magnetic field of the bar magnet and the movement of the bar magnet, as well as the loop of wire, all contribute to the induced EMF in the loop. As a result, an induced current is generated in the loop. The direction of this induced current is given by Lenz's law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it. In other words, the current direction in the loop of wire is clockwise to oppose the movement of the magnet towards the wire.
Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it. In other words, the current direction in the loop of wire is clockwise to oppose the movement of the magnet towards the wire.
When a bar magnet is pushed towards a loop of wire, a current is induced in the wire, as per Faraday's law of electromagnetic induction. The induced EMF in the loop is given by induced EMF = -dΦ/dt, where Φ is the magnetic flux. The direction of the induced current is given by Lenz's law, which states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it. Therefore, the direction of current in the loop of wire is clockwise to oppose the movement of the magnet towards the wire.
In conclusion, the bar magnet's magnetic field induces an EMF in the loop of wire, resulting in a current flow in the loop. The direction of the induced current in the loop of wire is clockwise, as per Lenz's law, to oppose the magnet's movement towards the wire.
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what produces a magnetic field? 1. a moving electric charge 2. a moving atom 3. a massive object at rest
A magnetic field is produced by a moving electric charge. When an electric charge moves, it creates a magnetic field in the space surrounding it. The direction and strength of the magnetic field depend on the direction and velocity of the moving electric charge.
The magnetic field produced by a moving electric charge can be visualized as a series of circular lines of force that are perpendicular to the direction of motion of the electric charge. The strength of the magnetic field decreases with distance from the moving charge.
Magnetic fields are also produced by magnets. Magnets are materials that have the property of magnetism. This property arises from the alignment of the magnetic moments of the atoms or molecules that make up the material. The alignment of the magnetic moments produces a magnetic field in the space surrounding the magnet.
The strength and direction of the magnetic field depend on the arrangement of the magnetic moments within the material. Magnets can produce a static magnetic field that is not dependent on the motion of electric charges. This field can be used to attract or repel other magnets or magnetic materials.
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9. sandy pulls the cord on her lawn mower. in order for the engine to start, the pulley must turn at 180 rpm. the pulley has a radius of 0.2 feet. how many radians per second must the pulley turn? how fast must sandy pull the chord in order for the lawn mower to start?
The angular speed in radians per second required by the pulley to turn is 18.8495559215 radians per second. The speed required to start the lawn mower by Sandy is 1130.
973355.The angular speed in radians per second required by the pulley to turn is given as:radians per second = revolutions per minute x 2π/60From the given data, revolutions per minute is 180 rpm. So we have:radians per second = 180 x 2π/60 radians per second = 3π radians per second radians per second = 9.42477796077 radians per secondBut the pulley has a radius of 0.2 feet.
Hence, the linear speed of the pulley in feet per second is given as:linear speed = radius x angular speed = 0.2 x 9.42477796077 = 1.88495559215 feet per secondThus, the angular speed in radians per second required by the pulley to turn is 18.8495559215 radians per second.The speed required to start the lawn mower by Sandy is given as:Speed = 2πr x revolutions per minute/60But radius, r = 0.2 feet and revolutions per minute = 180 rpm. Therefore, we have:Speed = 2π x 0.2 x 180/60Speed = 1130.973355Hence, the speed required to start the lawn mower by Sandy is 1130.973355.
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an unknown gas is introduced into the aforementioned apparatus using the same tuning fork, and the first resonance occurs when the air column is 5.54 cm long. find the speed of sound in the gas.
The speed of sound in the gas will be less than 343 m/s as the frequency of the tuning fork in the gas will be less than its frequency in air.
In the given problem, an unknown gas is introduced into an apparatus where a tuning fork is used. And the first resonance occurs when the air column is 5.54 cm long. Now, we need to find the speed of sound in the gas.The speed of sound in the gas can be calculated as:v = 2LfHere, L is the length of the air column and f is the frequency of the tuning fork.For the first resonance, the length of the air column L = 5.54 cm or 0.0554 m. We need to find the frequency of the tuning fork, which we can get by finding the harmonic number of the first resonance.For the first resonance, n = 1So, the frequency of the tuning fork can be given as:f = n × v/2L = 1 × v/2L = v/2LNow, we need to find the value of v.We know that the speed of sound in air is 343 m/s. So, the frequency of the tuning fork in air is:f = v/2L = 343/2LWe also know that the frequency of the tuning fork is inversely proportional to the square root of the density of the medium. So, we can write:f_1/f_2 = √ρ_2/√ρ_1where f_1 and f_2 are the frequencies of the tuning fork in air and in the gas respectively, and ρ_1 and ρ_2 are the densities of air and the gas respectively.
Rearranging the above equation, we get:v = f_2/f_1 × √ρ_1/ρ_2 × 343Putting the values, we get:v = f_2/f_1 × √(1.2/ρ_2) × 343where the density of air at STP is 1.2 kg/m³.So, we need to find the frequency of the tuning fork in the gas. For this, we can use the formula:f_2 = f_1 × √ρ_1/ρ_2 × √(T_2/T_1)where T_1 and T_2 are the temperatures of air and the gas respectively. .
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There is a 28 resistance in the dryer. It is plugged into a 240 V circuit. How much current passes through the dryer?
[tex]\bf{ \underline{Given:- }}[/tex]
[tex] \sf{• \: There \: is \: a \: 28 \: resistance \: in \: the \: dryer. \: It \: is \: plugged \: into \: a \: 240 \: V \: circuit. }[/tex]
[tex] \\ [/tex]
[tex]\bf{ \underline{To \: Find :- }}[/tex]
[tex] \sf{• \: How \: much \: current \: passes \: through \: the \: dryer.}[/tex]
[tex] \\ [/tex]
[tex] \huge\bf{ \underline{ Solution :- }}[/tex]
[tex] \sf According \: to \: the \: question, [/tex]
[tex] \sf• \: Resistance \: (R) = 28 \: Ω[/tex]
[tex] \sf• \: Voltage \: (V) = 240 \: v[/tex]
[tex] \bf \red{ \bigstar{ \: Formula \: of \: Current \: (I) = \frac{V}{R}}}[/tex]
[tex] \rightarrow \sf I = \frac{240}{28} [/tex]
[tex] \rightarrow \sf I = 8.57[/tex]
[tex] \\ [/tex]
[tex] \bf \purple{Therefore, \: 8.57 \: Amps. \: current \: passes \: through \: the \: dryer.}[/tex]
What is the geodesic distance between Fulton County Airport and Toledo Express Airport?
The geodesic distance between Fulton County Airport and Toledo Express Airport is approximately 63.4 miles.
The geodesic distance is the shortest path between two points on a curved surface, such as the Earth. To calculate the geodesic distance between Fulton County Airport and Toledo Express Airport, we can use the coordinates of these locations.
Fulton County Airport is located in Wauseon, Ohio, with coordinates approximately 41.60°N latitude and 84.13°W longitude. Toledo Express Airport is situated in Swanton, Ohio, with coordinates approximately 41.59°N latitude and 83.81°W longitude.
Using these coordinates, we can employ the Haversine formula, which takes into account the Earth's radius, to calculate the geodesic distance. Applying the formula yields an approximate distance of 63.4 miles between the two airports.
It is important to note that this is an estimation and may vary slightly depending on the specific method and parameters used for calculation. The geodesic distance provides a measure of the shortest distance between the two airports, considering the curvature of the Earth's surface.
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Which of the following is NOT an example of a force?
O Inertia
O Friction
O Air resistance
O Gravity
A swimmer push water backwards.give reasons.
Answer:
According to newton's 3rd law of motion in each and every action there is an equal and opposite force. So if he push the water backwards then according to the above principle or law he will be able to move forward.
BlueBolt Bottlers has a bottle-filling process with a mean value of 64 ounces and a standard deviation of 8 ounces. a. Suppose that the upper and lower tolerance limits are 71 and 57 ounces, respectively. What is the process capability ratio? What would the standard deviation have to be in order for the process to meet the tolerance limits 99.7% of the time? b. Now suppose BlueBolt Bottlers makes some process improvements, thereby lowering the standard deviation of the process to 1.5 ounces, rather than 8 ounces. Using the data in part (a), and the new standard deviation, calculate the process capability ratio. Is the filling process able to meet the tolerance limits 99.7% of the time? Does the process provide Six Sigma quality levels? Explain.
In part (b), the filling process is unable to meet the tolerance limits 99.7% of the time, and it does not achieve Six Sigma quality levels.
a. To calculate the process capability ratio (Cp) in part (a), we use the formula:
Cp = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)
Given:
Mean = 64 ounces
Standard Deviation = 8 ounces
Upper Specification Limit = 71 ounces
Lower Specification Limit = 57 ounces
Cp = (71 - 57) / (6 * 8) = 14 / 48 = 0.2917 (rounded to four decimal places)
To determine the standard deviation required for the process to meet the tolerance limits 99.7% of the time, we use the Z-score corresponding to a 99.7% confidence level, which is approximately 3.
Z = (Upper Specification Limit - Mean) / Standard Deviation
Rearranging the formula, we can solve for the standard deviation:
Standard Deviation = (Upper Specification Limit - Mean) / Z
Standard Deviation = (71 - 64) / 3 = 7 / 3 = 2.3333 (rounded to four decimal places)
b. In part (b), with the improved process having a standard deviation of 1.5 ounces, we can recalculate the process capability ratio using the same formula:
Cp = (Upper Specification Limit - Lower Specification Limit) / (6 * Standard Deviation)
Using the same specification limits as before:
Cp = (71 - 57) / (6 * 1.5) = 14 / 9 = 1.5556 (rounded to four decimal places)
To determine if the filling process is able to meet the tolerance limits 99.7% of the time, we compare the new Cp value to the critical value of 2. Since Cp is less than 2, the process does not provide Six Sigma quality levels.
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6. find the work done by a 10 pound force acting in the direction <1,2> in moving an object 3 feet from (0,0) to (3,0).
The object moved from the point (0,0) to (3,0) by exerting a force of 10 pounds in the direction <1,2>. The work done in this process is calculated to be 30 foot-pounds.
To find the work done by a 10-pound force acting in the direction <1,2> in moving an object from (0,0) to (3,0), we need to calculate the dot product of the force vector and the displacement vector.
Force = 10 pounds
Direction vector = <1,2>
Displacement vector = (3-0)i + (0-0)j = 3i
The dot product of two vectors A = <a1, a2> and B = <b1, b2> is given by:
A · B = (a1 * b1) + (a2 * b2)
In this case, the force vector F = 10<1,2> and the displacement vector D = 3i. Therefore, the dot product of these vectors is:
F · D = (10 * 1) + (10 * 2)
F · D = 10 + 20
F · D = 30
The work done (W) is given by the equation:
W = F · D
Substituting the values we calculated:
W = 30
Since the given force was in pounds and the displacement was in feet, the work done is expressed in foot-pounds (ft-lb).
Therefore, the work done by the 10-pound force acting in the direction <1,2> in moving the object from (0,0) to (3,0) is 30 foot-pounds.
The dot product allows us to determine the work done by a force when it is applied in a particular direction. It measures the projection of the force vector onto the displacement vector, resulting in a scalar value representing the magnitude of work. In this case, the force and displacement vectors were given, allowing us to calculate the dot product and determine the work done.
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Two long parallel wires carry currents of 20 A and 5.0 A in opposite directions. The wires are separated by 0.20 m. What is the strength of the magnetic field midway between the two wires?
The strength of the magnetic field midway between two long parallel wires carrying currents of 20 A and 5.0 A in opposite directions and separated by 0.20 m is 3.75 × 10^−5 Tesla.
The magnetic field created by a long straight wire carrying current is given by Ampere's law. According to Ampere's law, the magnetic field at a point midway between the two wires is directly proportional to the currents in the wires and inversely proportional to the distance between them.
To calculate the magnetic field at the midpoint, we can use the formula:
B = (μ₀/2π) * (I₁ - I₂) / d,
where B is the magnetic field, μ₀ is the permeability of free space (4π × [tex]10^{-7}[/tex] T·m/A), I₁ and I₂ are the currents in the wires, and d is the distance between the wires.
Plugging in the given values, we have:
B = (4π × [tex]10^{-7}[/tex] T·m/A) * (20 A - 5.0 A) / 0.20 m
B = (4π × [tex]10^{-7}[/tex] T·m/A) * (15 A) / 0.20 m
B = (3π × [tex]10^{-6}[/tex] T·m/A) / 0.20 m
B = 3.75 ×[tex]10^{-5}[/tex] Tesla.
Therefore, the strength of the magnetic field midway between the two wires is 3.75 × [tex]10^{-5}[/tex] Tesla.
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a rocket fires its engines to launch straight up from rest with an upward acceleration of 5 m/s/s for 10 seconds. After this time, the engine shuts off and the rocket freely falls straight down back to the earth's surface. sketch a graph of the acceleration as a function of tome from t=0 seconds to t=10 seconds.
Assuming the acceleration is positive in the upward direction.
For the time, t=0 seconds to t=10 seconds, the acceleration of the rocket is 5 m/s^2 which is constant.
So, the required t acceleration time graph is a horizontal straight line from t=0 to t=10 seconds, as shown
a 32 g bullet is fired horizontally from a rifle at 380 m/s into a water bottle at pointblank range. the bullet travels completely through the 12 cm long bottle, located 2 m above the ground. (you may assume there is no change in the height of the bullet while travelling through the bottle.) it finally hits the ground at a point 3 m downrange from the point where it left the water. determine: a) the average force exerted by the water on the bullet. b) the total time elapsed from when the rifle is fired to when the bullet hits the ground.
The average force exerted by the water on the bullet can be calculated by using the formulaF= ma, where "F" is the force, "m" is the mass of the object and "a" is the acceleration of the object.The mass of the bullet is 32 g = 0.032 kg.
The acceleration of the bullet is given by the change in velocity which is 380 m/s (initial velocity) to 0 m/s (final velocity) in 12 cm = 0.12 m.The acceleration can be calculated using the formulaa = Δv / Δt = (0 - 380) / 0.12 = -3167 m/s².Now, we can find the force exerted by water on the bullet usingF = ma = (0.032 kg) x (-3167 m/s²) = -101.44 NTherefore, the average force exerted by the water on the bullet is 101.44 N (in the opposite direction of motion of the bullet).b) The total time elapsed from when the rifle is fired to when the bullet hits the ground can be found using the time of flight equation. Since the bullet is fired horizontally, there is no initial vertical velocity, so we can use the equationy = vit + (1/2)at²where y is the vertical distance (which is 2 m), vi is the initial velocity in the y direction (which is 0 m/s), a is the acceleration due to gravity (-9.8 m/s²) and t is the time taken to hit the ground.
Since the bullet hits the ground 3 m downrange from the point where it left the water, the horizontal velocity of the bullet (v) can be found using the formula v = d / twhere d is the horizontal distance travelled (which is 3 m) and t is the time taken to hit the ground.So, t = d / v = 3 m / (380 m/s) = 0.0079 sNow, using the time of flight equation:y = vit + (1/2)at²2 = 0 + (1/2)(-9.8)(t²)t² = 0.4082t = sqrt(0.4082) = 0.64 sTherefore, the total time elapsed from when the rifle is fired to when the bullet hits the ground is 0.64 s. (main answer).Explanation: The above calculations have been explained in detail in the answer section. The average force exerted by the water on the bullet is -101.44 N (in the opposite direction of motion of the bullet). The total time elapsed from when the rifle is fired to when the bullet hits the ground is 0.64 s.
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