The correct answer is A. Because of the newly developed biometric technology, the FBI was able to quickly identify two suspects is best describes the relationship between the Boston Marathon
What is biometric technology?
After the Boston Marathon bombing in 2013, the FBI was able to use biometric technology to quickly identify the two suspects, Tamerlan and Dzhokhar Tsarnaev. Biometric analysis was used to match images of the suspects captured by surveillance cameras with images in the FBI's biometric database. This helped the FBI to quickly identify the suspects and bring them to justice.
What is FBI?
The FBI stands for the Federal Bureau of Investigation. It is a law enforcement agency of the United States government that is primarily responsible for investigating and enforcing federal laws.
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The diagram below shows a sled moving along a smooth, frictionless track.
The sections 2 and 4 of the track will the sled experience an unbalanced force which is frictionless surface.
As we see from the diagram the track is a frictionless surface where the sled will move. In section 1 and 3, the sled will experience a balanced force because the gravitational force pulling the sled down is equal to the normal force of the track pushing the sled up. While in section 2 and 4, however, the sled will experience an unbalanced force because the gravitational force pulling the sled down will be greater than the normal force of the track pushing the sled up. This will cause the sled to accelerate and move faster. Hence section 2 and 4 will experience an unbalanced force.
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wo 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed. Ball B stops. Which statement correctly describes the change in momentum of the two balls? a. Delta PB = Delta PA b. |Delta PB| = |Delta PA| c. |Delta PB| > |Delta PA| d. |Delta PB| < |Delta PA|e. Delta PB > Delta PA
The change in momentum of ball B is greater than the change in momentum of ball A (|Delta P_{B}| < |Delta P_{A}|) when two 0.20-kg balls, moving at 4 m/s east, strike a wall. Ball A bounces backwards at the same speed, while ball B stops.
When the two balls strike the wall, they experience a change in momentum due to the impulse of the wall.
The initial momentum of the system (two balls and the wall) is:
P_{initial}= m_{A}v_{A} + m_{B}v_{B}
After the collision, ball A bounces backwards with the same speed, so its final momentum is:
P_{A} = -m_{A}*v_{A}
Ball B stops, so its final momentum is:
P_{B} = 0
The total final momentum of the system is:
P_{final} = P_{A} + P_{B} = -m_{A}*v_{A}
The change in momentum of ball A is:
Delta P_{A} = P_{A} - m_{A}v_{A} = -2m_{A}*v_{A}
The change in momentum of ball B is:
Delta P_{B} = P_{B} - m_{B}v_{B} = -m_{B}v_{B}
Therefore, |Delta P_{B}| < |Delta P_{A}|, which means that option (d) is the correct answer.
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A ball is attached to the end of a string it swung at a vertical circle of three of 0.33M what is the minimum velocity that the ball must have to make it around the circle
Answer:
To make it around the circle, the tension in the string must provide the necessary centripetal force to keep the ball moving in a circle. At the top of the circle, the tension in the string must provide all the force to keep the ball moving in a circle. At the bottom of the circle, the tension in the string must provide the centripetal force in addition to the force of gravity.
We can use the centripetal force formula to solve for the minimum velocity: F_c = m * a_c
where F_c is the centripetal force, m is the mass of the ball, and a_c is the centripetal acceleration.
At the top of the circle, the centripetal force is equal to the tension in the string: F_c = T
where T is the tension in the string.
At the bottom of the circle, the centripetal force is equal to the sum of the tension in the string and the force of gravity:
F_c = T + mg
where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2), and T is the tension in the string.
The centripetal acceleration is given by: a_c = v^2 / r
where v is the velocity of the ball and r is the radius of the circle.
Since the circle has a radius of 0.33 m, we can substitute this into the equation for a_c: a_c = v^2 / 0.33
Combining these equations, we get:
At the top of the circle: T = m * v^2 / 0.33
At the bottom of the circle: T + mg = m * v^2 / 0.33
We can solve for the minimum velocity by using these two equations to eliminate the tension in the string: m * v^2 / 0.33 + mg = m * v^2 / 0.33
Simplifying this equation, we get: v = sqrt(0.33 * g)
Plugging in the values, we get: v = sqrt(0.33 * 9.8) = 1.81 m/s
Therefore, the minimum velocity that the ball must have to make it around the circle is 1.81 m/s
Reflection, refraction, and the formation of images by mirrors and lenses has been successful described by the A) wave model of light. B) ray model of light. C) particle model of light. D) none of the given answers
The correct answer is B). Reflection, refraction, and the formation of images by mirrors and lenses has been successful described by the Ray Model of Light.
Reflection, refraction, and the formation of images by mirrors and lenses can be explained using the Ray Model of Light, which states that light travels in straight lines, called rays.
As an electromagnetic wave, light travels in straight lines along narrow beams of light, which are referred to as rays. Despite the fact that reflection or refraction can alter its path, light always moves in a straight line.
When light rays reflect off a surface or pass through a lens, the angle of reflection or refraction can be calculated using geometry and the law of reflection/refraction.
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#1)
A 500 Hz triangular wave with a peak amplitude of 50 V is applied to
the vertical deflecting plates of a CRO. A 1 kHz saw tooth wave with a
peak amplitude of 100 V is applied to the horizontal deflecting plates.
The CRO has a vertical deflection sensitivity of 0. 1 cm/V and a
horizontal deflection sensitivity of 0. 02 cm/V. Assuming that the two
inputs are synchronized, determine the waveform displayed on the
screen?
[2 Marks]
The CRO (Cathode Ray Oscilloscope) will display a triangular wave that is vertically stretched and horizontally compressed.
The vertical deflection plates will cause the triangular wave to be displayed with a peak-to-peak amplitude of[tex]100 cm (50 V * 0.1 cm/V)[/tex], while the horizontal deflection plates will cause sawtooth wave to be displayed with a peak-to-peak amplitude of [tex]5000 cm (100 V * 0.02 cm/V).[/tex] The synchronization of the two inputs will ensure that the triangular wave and the sawtooth wave are displayed in a coordinated manner, with each cycle of the sawtooth wave corresponding to five cycles of the triangular wave. The resulting display will show a pattern of diagonal lines that gradually rise and then quickly drop back to the starting position, with each line representing a cycle of the sawtooth wave.
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a hydrostatic transmission has pump volumtric efficiency 91 %, a pump mechanical efficiency of 93 %, a motor mechanical efficiency of 95%, and a motor volumetric efficiency of 91%. what is the overall efficiency of the hst (in percent)?
The hydrostatic transmission's overall efficiency in percent can be calculated using the given information as follows:
Given that:
Volumtric efficiency of the pump = 91%Mechanical efficiency of the pump = 93%Mechanical efficiency of the motor = 95%Volumetric efficiency of the motor = 91%Formula for calculating overall efficiency of HST is given as:
Overall efficiency of HST = pump volumetric efficiency × pump mechanical efficiency × motor mechanical efficiency × motor volumetric efficiencySubstituting the given values in the above formula, we get:
Overall efficiency of HST = 0.91 × 0.93 × 0.95 × 0.91 = 0.7460585 = 74.61%
Therefore, the overall efficiency of the hydrostatic transmission is 74.61% (rounded to two decimal places).
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A slingshot sends a stone vertically upward from a height of 20 feet above a pool of
water. The starting speed of the stone is 90 feet per second. Its distance in feet, d.
above the water is given by the equation:
d-20+90t-16t^2, where t is the time in seconds after the launch.
Drag statements to the table to show what each coordinate labeled on the graph
represents in this problem situation.
the height of the stone when it is launched
the time when the stone hits the water
the time when the stone is launched the maximum height of the stone
the time when the stone reaches its maximum height
Coordinate
A
the height of the stone when it hits the water
What the Coordinate Represents
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
DRAG AND DROP
Coordinate , A - the height of the stone when it hits the water. A slingshot sends a stone vertically upward from a height of 20 feet above a pool of water.
What the Coordinate Represents?The coordinate A represents the height of the stone when it hits the water. When the stone hits the water, its height above the water surface is zero.
So, we can set the expression for the stone's height equal to zero and solve for t to find the time when the stone hits the water. The height of the stone when it is launched is given as 20 feet, which is a fixed value in this problem.
The time when the stone is launched is also a fixed value, which is zero. The maximum height of the stone is the highest point the stone reaches above its initial height of 20 feet. The time when the stone reaches its maximum height is the time at which the vertical velocity of the stone becomes zero.
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as you found in part a, your weight will be greater than normal when the elevator is moving upward with increasing speed. for what other motion would your weight also be greater than your normal weight?
Answer:
1) F = M a accelerating forward would cause a seeming increase weight.
2) F = m v^2 / R a person moving in a circular arc would have an apparent component of weight towards the center of rotation (in addition to his normal vertical component of weight).
calculate the fluid force on one side of a 5ft by 5ft square plate if the plate is at the bottom of a pool filled with water to a depth of 8ft and, a. lying flat on its 5ft by 5ft face. b. resting vertically on a 5 ft edge c. resting on a 5 ft edge and tilted at 45 degrees to the bottom of the pool.
The fluid force on one side of the 5ft by 5ft plate lying flat on its 5ft by 5ft face, we can use the equation F = ρghA and the F = 1,945,000 N.
What is the fluid force?Since the plate is at the bottom of the pool and the pool is filled with water to a depth of 8ft, h = 8ft and the area of the plate A = 5ft × 5ft = 25ft².
There F is the fluid force, ρ is the density of the fluid, g is the acceleration due to gravity, h is the depth of the fluid, and A is the area of the plate.
Therefore, the fluid force on one side of the plate is:
F = ρghA = 1000kg/m³ × 9.81m/s² × 8ft × 25ft² = 1,945,000 N.
To calculate the fluid force on one side of the plate resting vertically on a 5 ft edge, we can use the same equation as above but with an area equal to the length of the plate multiplied by the depth of the pool (8ft):
F = ρghA = 1000kg/m³ × 9.81m/s² × 8ft × 5ft = 392,000 N.
To calculate the fluid force on one side of the plate resting on a 5ft edge and tilted at 45 degrees to the bottom of the pool, we can use the same equation as above but with an area equal to the length of the plate multiplied by the depth of the pool multiplied by the cosine of the angle of the plate:
F = ρghA = 1000kg/m³ × 9.81m/s² × 8ft × 5ft × cos(45) = 283,200 N.
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If the resulting trajectory of the charged particle is a circle, what is ⍵, the angular frequency of the circular
motion?
Express ⍵ in terms of g, m, and Bo.
The angular frequency of circular motion is given by the expression:
ω = [tex]\sqrt{qB/m}[/tex]
If the resulting trajectory of the charged particle is a circle, the angular frequency (ω) of the circular motion can be expressed in terms of g, m, and Bo as follows:
ω = [tex]\sqrt{qB/m}[/tex]
where q is the charge of the particle, B is the magnetic field strength, and m is the mass of the particle.
This formula is known as the cyclotron frequency equation.
The circular motion occurs because the magnetic force (F = qvB) on the charged particle is perpendicular to its velocity (v) and results in a centripetal force that keeps the particle in a circular path with a constant speed.
The angular frequency (ω) represents the rate at which the particle completes a full revolution (2π radians) around the center of the circular path per unit of time.
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if two tiny identical spheres attract each other with a force of 2.0 nn when they are 29 cm apart, what is the mass of each sphere? express your answer with the appropriate units.
The mass of each sphere with the appropriate units are the 0.6 kg by the two tiny identical spheres attract each other with a force of 2.0 nn when they are 29 cm apart.
Let's consider the following scenario: Two tiny identical spheres attract each other with a force of 2.0 nn when they are 29 cm apart. The mass of each sphere is what we need to calculate. The formula for calculating the mass of each sphere. F = Gm1m2 / r²Where:F = Force. G = Gravitational constantm1 and m2 = the masses of the object sr = the distance between the objects.
Substitute the given values: Force (F) = 2.0 nn. Distance (r) = 29 cm = 0.29 m. Gravitational constant (G) = 6.67 × 10-11 N.m²/kg²Find the mass of each sphere.m1 = m2 = m. Multiply the entire equation by ][tex]r² / G:m² = F × r² / G = (2.0 nn) × (0.29 m)² / 6.67 × 10-11 N.m²/kg²= 0.6 kg.[/tex]
Therefore, each sphere's mass is 0.6 kg.
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What ionic compound would bond in a 1 to 2 ratio?
An ionic compound that would bond in a 1:2 ratio would be one in which the cation has a charge of 2+ and the anion has a charge of 1-. This is because the total charge of the compound must be neutral.
An ionic compound is a type of chemical compound that is formed through the transfer of electrons between atoms. In an ionic compound, one or more positively charged ions (known as cations) are attracted to one or more negatively charged ions (known as anions) to form a stable structure. The cations and anions are held together by electrostatic forces known as ionic bonds.
Ionic compounds typically have high melting and boiling points, are usually crystalline solids at room temperature, and are often soluble in water. They can conduct electricity when dissolved in water or when melted, but not when in a solid state. Ionic compounds have a wide range of applications, including as building blocks for ceramics, in the production of batteries, and as components of various chemical processes. Examples of common ionic compounds include sodium chloride (table salt), calcium carbonate (chalk), and potassium iodide (used in medicine).
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A pendulum has length / and a bob of mass m. Which of the following is true of the linear momentum of the bob as it swings through the lowest point? a. It remains constant because momentum is always conserved. b. It increases in magnitude and changes direction. c. It decreases in magnitude and does not change direction. d. It is converted to angular momentum. e. It is converted to kinetic energy.
The following is true of the linear momentum of the bob as it swings through the lowest point that it increases in magnitude and changes direction.
What is linear momentum ?Momentum (more specifically linear momentum or translational momentum) is defined in Newtonian mechanics as the product of an object's mass and velocity. It is a vector quantity with magnitude and direction. If m is the mass of an object and v is its velocity (also a vector quantity), then p = m * v. The kilogram meter per second (kgm/s) is the unit of momentum measurement in the International System of Units (SI), which is equivalent to the newton-second. According to Newton's second law of motion, the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but it is a conserved quantity in any inertial frame, which means that if a closed system
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A child sits on the floor and twirls a 0.100 kg ball connected to a 1.0 m string in a horizontal cirlce along the floor with a speed of 2.0 m/s. What forces are acting on the floor? All of the above A. Only gravity force and tension B. Tension C. Force due to gravity weight D. normal force
The forces acting on the floor when a child twirls a 0.100 kg ball connected to a 1.0 m string in a horizontal circle along the floor with a speed of 2.0 m/s are: A. Only gravity force and tension.
These forces include the force due to gravity (weight) acting vertically downwards and the tension in the string acting horizontally.
The formula for centripetal acceleration is: a = v²/r
where - a is the centripetal acceleration
- v is the velocity
- r is the radius of the circle
The force of tension is the force that arises when an object is pulled or stretched by a rope or cable that is connected to it. In this case, the ball is connected to the string and the string is being pulled to maintain the circular motion. Therefore, the force of tension is present.
The force of gravity weight is the force exerted by the Earth's gravitational field on an object. It is calculated using the formula: W = mg
where - W is the weight of the object
- m is the mass of the object
- g is the acceleration due to gravity (9.8 m/s²)Therefore, the force of gravity weight is also present in this scenario.
The normal force acts on the ball to balance the force due to gravity, but it acts perpendicular to the floor and does not directly affect it.
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Which of the following values are needed to solve for the heat capacity of a heated unknown solid when it is placed in a coffee cup calorimeter? Select all that apply.
A. The initial temperature of the water
B. The initial temperature of the solid
C. The mass of the solid
D. The mass of the water in the cup
E. The final temperature of the system
The initial temperature of the solid, the mass of the solid, the mass of the water in the cup, and the final temperature of the system are needed to solve for the heat capacity of a heated unknown solid when it is placed in a coffee cup calorimeter.
The heat capacity is the amount of heat required to raise the temperature of a system by one degree Celsius (or one Kelvin). When an unknown solid is heated and placed in a coffee cup calorimeter, the following values are needed to calculate its heat capacity: Initial temperature of the solid, Mass of the solid, Mass of the water in the cup, Final temperature of the system.
The calorimeter is used to measure the amount of heat gained or lost by the system (the solid and the water in the cup) during the process. The change in temperature of the system is used to calculate the heat gained or lost by the solid.
Therefore, the initial temperature of the solid, the mass of the solid, the mass of the water in the cup, and the final temperature of the system are needed to solve for the heat capacity of the heated unknown solid.
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Which of the following statements describes a method by which signaling via TGF-beta and BMP receptors is decreased ? I SMAD-mediated expression of a protein that acts in the nucleus to block SMAD-dependent signaling II SMAD-mediated expression of a SMAD that cannot be phosphorylated by a TGF-beta/BMP receptor complex. III SMAD-mediated histone acetylation of genes whose expression are regulated by SMADs. IV SMAD-dependent phosphorylation of the cytoplasmic receptor tails of type-I TGF-beta/BMP receptors. O I, II and III O I, II, III and IV III and IV I only Olandi O I and II
The following statements describes a method by which signaling via TGF-beta and BMP receptors is decreased is SMAD-mediated expression of a protein that acts in the nucleus to block SMAD-dependent signaling. The correct option is I.
TGF-beta or transforming growth factor-beta is a peptide growth factor that belongs to the cytokine superfamily, it is a potent regulator of cellular proliferation, differentiation, and other physiological activities. It is found in many cells, including bone cells, and participates in the formation and maintenance of bone tissue, in addition to its role in immune function.
Bone morphogenetic proteins (BMPs) are part of the transforming growth factor-beta superfamily of proteins. BMPs are essential for embryonic development, and their primary function is to regulate bone formation. SMADs are proteins that transmit signals from the cell surface to the nucleus in response to a variety of extracellular signals, including transforming growth factor-beta (TGF-beta) and bone morphogenetic protein (BMP). The SMAD family of transcription factors is composed of several members, including receptor-regulated SMADs, common-partner SMADs, and inhibitory SMADs.
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Part GNow, using the results of Part F, find the total kinetic energy K of the system. Remember that both particles rotate about the y axis.
Express your answer in terms of m, ω, and r.
Answer:
K = (11*m*(ω*r)^2)/2
Explanation:
Not surprisingly, the formulas K = (1/2)*I*ω^2 and K = (1/2)*m*v^2 give the same result. They should, of course, since the rotational kinetic energy of a system of particles is simply the sum of the kinetic energies of the individual particles making up the system.
explain how angela can calculate the frictional torque applied to the wheel. state what apparatus is to be used.
Angela can calculate the frictional torque applied to the wheel by using a torque wrench. The torque wrench measures the amount of torque needed to rotate the wheel, which is equal to the frictional torque.
Calculating the frictional torque applied to a wheel.To calculate the frictional torque applied to a wheel, Angela can use a torque wrench. A torque wrench is a tool that is used to measure the amount of torque required to rotate the wheel.
When the wheel is turned with the torque wrench, the amount of torque needed to rotate it is equal to the frictional torque that the wheel is experiencing.
By measuring the torque required to rotate the wheel, Angela can calculate the frictional torque accurately.
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suppose two protostars form at the same time, one with a mass of 0.5 msun and the other with a mass of 15 msun . which of the following statements are true? A) The 10MSun protostar will have a smaller change in surface temperature during this phase than the 0.5MSun protostar.
B) The 10MSun protostar will reach the main sequence cooler and fainter than the 0.5MSun protostar.
C) The 10MSun star will end its main-sequence life before the 0.5MSun star even completes its protostar stage.
D) The 10MSun protostar will have a smaller change in luminosity during the sequence shown than the 0.5MSun protostar.
E) The 10MSun protostar will be much more luminous than the 0.5MSun protostar.
The statements that are true are:
B) The 10MSun protostar will reach the main sequence cooler and fainter than the 0.5MSun protostar.
E) The 10MSun protostar will be much more luminous than the 0.5MSun protostar.
To understand why, we need to know that a star's mass determines its temperature, luminosity, and lifespan. More massive stars are hotter, more luminous, and have shorter lifespans than less massive stars.
In this case, the 15MSun protostar is much more massive than the 0.5MSun protostar. Therefore, statement B is true because the 10MSun protostar is closer in mass to the 15MSun protostar, and therefore it will have a higher temperature during the protostar phase, making it cooler and fainter when it reaches the main sequence.
Statement E is true because more massive stars are more luminous than less massive stars. The 10MSun protostar is closer in mass to the 15MSun protostar, and therefore it will be much more luminous than the 0.5MSun protostar.
Hence b and e are correct option.
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find the height of the roller coaster using two different methods. round your answers to one decimal place.
If there were no friction and air resistance, an ideal coaster could go down and up hills at the same height eternally. If you want to round to one or two decimal places, look at the digit immediately decimal point.
Roller coasters can reach what heights?Almost always, the start of a roller coaster is a vertical plummet. The automobiles are propelled by a motor to a top of a steep hill, after which gravity takes over completely. Typical vertical fall could be anywhere between 50 and 80 metres high.
How are answers rounded to decimal places?When round a decimal value, there are a few guidelines to remember. To put it another way, it round previous digit down if the final digit is much less than 5. However, you just round the previous figure up if it is 5 or above. Thus, it round number up if 5, 6, 7, 8, or 9 come after the number we are about to round.
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How does the star formation in spirals compare to the star formation of elliptical galaxies?
The spiral galaxies are characterized by the arms winding out from a central nucleus while the elliptical galaxies are characterized by their lack of structure or a central bulge.
Star formation refers to the process by which dense areas within molecular clouds in interstellar space, typically lasting tens of millions of years, form newborn stars. It takes a long time for stars to form, and this process is not well understood.
In comparison to spiral galaxies, elliptical galaxies have low star formation.
Furthermore, elliptical galaxies are made up of stars with a wide range of ages, indicating that the star formation process was rapid and early on in their history.
Spiral galaxies have more gas and dust in their disks than elliptical galaxies, and these are the sites of intense star formation.
The arms are believed to be regions of higher density of stars and interstellar material, as well as more significant gravitational interactions among stars, gas, and dust than in the rest of the disk.
Thus, spiral galaxies are sites of ongoing star formation while elliptical galaxies are mainly populated by old and evolved stars that no longer form. Therefore, spiral galaxies have a higher rate of star formation than elliptical galaxies.
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Light of 630 nm wavelength illuminates two slits that are 0.25 mm apart. FIGURE EX33.5 shows the intensity pattern seen on a screen behind the slits. What is the distance to the screen?
The distance to the screen from the two slits is 4.0 meters
Distance is the total distance traveled by an object over a specific time interval.
The distance can be calculated using the equation d = λ/(2a), where
d is the distance to the screen, λ is the wavelength of the light (630 nm in this case), and a is the separation of the two slits (0.25 mm in this case).Plugging these values in, we get: d = 630 nm / (2 * 0.25 mm) = 4.0 m. The distance to the screen from the two slits is 4.0 meters, as seen in Figure EX33.5.
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When a ball bounces against a wall there will be large change in velocity in short period of time. This means the ____ is large, hence the net ___ must be proportionately large as well.
A change in velocity in short period of time means the acceleration is large, hence the net force must be proportionately large as well.
What is a force?A force is a physical quantity that induces a body to undergo an alteration in speed, direction of motion, or shape. A force can be classified as a push or a pull. When forces are equal, the forces are balanced and the object is not moving. Otherwise, if the forces are not equal, making it unbalanced will not give the object any movement.
The force that induces the change in the speed or direction of an object is referred to as a net force. The net force is equal to the product of the mass of the object and its acceleration. Newton (N) is the unit of measurement for force.
When a ball bounces against a wall, there will be a large change in velocity in a short period of time. This means the acceleration is large, hence the net force must be proportionately large as well.
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Help! The image characteristics are ____. (2 points)
A concave mirror is shown with curvature positioned at 8 on a ruler that goes from 0 to 14 centimeters. The object is located at 5, and the focal point is located at 6.5.
a
upright, virtual, and smaller
b
upright, real, and same size
c
inverted, virtual, and smaller
d
inverted, real, and same size
Which is correct?
if the total mass is m , find the moment of inertia about an axis through the center and perpendicular to the plane of the square. use the parallel-axis theorem. express your answer in terms of the variables m and a .
The moment of inertia of the square about an axis through the center and perpendicular to the plane of the square is I = m a²/3.
Step by step explnation:
The moment of inertia about an axis through the center and perpendicular to the plane of the square can be found using the parallel-axis theorem. The moment of inertia about the center of the square is [tex]I_c_m[/tex] = (m a²)/6.
Using the parallel-axis theorem, the moment of inertia about an axis through the center and perpendicular to the plane of the square is I = [tex]I_c_m[/tex] + m a² = ma²/3.
Thus, the moment of inertia of the square about an axis through the center and perpendicular to the plane of the square is I = m a²/3.
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A ball rolls across the floor, slowing down with constant acceleration of magnitude . The ball has positive velocity ???? after rolling a distance x across the floor.
Calculate the ball's initial speed ????0 if ????= 4.51 m/s2, ????=11.17 m/s, and x=2.66 m.
A ball rolls across the floor, slowing down with a constant acceleration of magnitude a = 4.51 m/s2.
The ball has positive velocity v after rolling a distance x = 2.66 m across the floor.
To calculate the ball's initial speed v0 if
v = 11.17 m/s.
The initial velocity of the ball, v0 =?
The final velocity of the ball, v = 11.17 m/s
The acceleration of magnitude a = 4.51 m/s2
Distance travelled, x = 2.66 m
If an object has initial velocity v0, constant acceleration a, and travelled distance x, then its final velocity is given by:
v2 = v0² + 2ax
Here, the ball's initial velocity is v0, and its final velocity is v.
After substituting the given values, we have:
v2 = v0² + 2ax
=> (11.17)²
= v0² + 2(4.51)(2.66)
=> 124.57
= v0² + 25.39
=> v0² = 124.57 - 25.39
=> v0² = 99.18 => v0 = √99.18
=> v0 = 9.96 m/s
Hence, the initial velocity of the ball is v0 = 9.96 m/s.
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a truck collides with a car, and during the collision, the net force on each vehicle is essentially the force exerted by the other. suppose the mass of the car is 550 kg, the mass of the truck is 2200 kg, and the magnitude of the truck's acceleration is 10 m / s 2 10m/s 2 . find the magnitude of the car's acceleration.
Answer: The magnitude of the car's acceleration is 40m/s²
Explanation:
According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Therefore, the force exerted by the car on the truck is similar to the force exerted by the truck on the car in magnitude and opposite direction.
To begin, we must calculate the force exerted by the truck on the car. The force exerted by the truck on the car is given as:
F = maF = (mass of car) × (acceleration of car)
Now, we need to calculate the acceleration of the car.
a = F/m a = [(mass of truck) × (acceleration of truck)] / (mass of car)
Substituting the given values, we get:
a = [(2200 kg) × (10 m/s²)] / (550 kg) = 40 m/s²
Therefore, the magnitude of the car's acceleration is 40 m/s².
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An object with a mass of
1.23 kg
starts from rest at the origin. It then experiences a force as a function of time
F =A i^+(B−Ct) j^
, where A=0.234 N, B=1.15 N and C=0.345 N/s. What is the speed of this object at t=3.00 s ?
Velocity refers to measuring the speed and direction of change in the position of an object. The speed of the object at t = 3.00 s is v = 0.35 m/s.
At t = 3.00 s, the object with a mass of 1.23 kg will have a speed given by the equation v = sqrt(2*F/m), where F is the total force experienced by the object and m is its mass.
Substituting the values for F, A, B, C and m, we get:
[tex]v = sqrt(2.(0,234.i+(1,15 - 0,345.3)j^)/1,23)[/tex]
Simplifying, we get:
v = [tex]sqrt(2.(0,234.j+(-0,035)j)/1,23)[/tex]
Using the Pythagorean theorem, we can calculate the magnitude of the vector v:
v = [tex]sqrt ((0,234.0,234) + (-0,035.-0,035))/1,23)[/tex]
Therefore, the speed of the object at t = 3.00 s is v = 0.35 m/s.
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Module 25: AC Circuits Learn Question An inductor with inductance L is connected in series with an AC source that provides a sinusoidal voltage of v of t is equal to V times cosine of begin quantity omega times t end quantity, where V is the maximum voltage, omega is the angular frequency, and t is the time. If a second identical inductor is wired in series with the first inductor, what happens to the total inductive reactance, XL, of the circuit?
XL decreases by a factor of 2.
XL increases by a factor of 4.
XL decreases by a factor of 4.
XL increases by a factor of 2.
The total inductive reactance, XL, of the circuit increases by a factor of 2 when a second identical inductor is wired in series with the first inductor. Thus, option d is correct.
Inductive reactance is the opposition of an inductor to a change in current that produces a magnetic field. Inductive reactance is the inductive equivalent of resistive impedance.
It is measured in ohms and can be calculated using the following formula:
XL = 2πfL
where XL is the inductive reactance, f is the frequency of the applied voltage, and L is the inductance of the coil.
Since the two inductors are identical and the frequency of the AC source does not change, the total inductance of the circuit doubles, resulting in a factor of 2 increase in inductive reactance (XL). Thus, option d is correct.
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An object is_____ if its position changes relative to another object.
A. in motion
B. at reset
C. a frame of refence
D. magical
An object is "in motion" if its position changes relative to another object.
Motion is a fundamental concept in physics, which describes how objects move and change position over time. When we say that an object is in motion, we mean that it is changing its position with respect to some reference point or frame of reference.
A reference point is a fixed point in space that we use as a point of comparison to measure an object's position and motion. For example, when we say that a car is moving on a highway, we are using the highway as a frame of reference to measure the car's motion.
An item is considered to be "in motion" if its position in relation to another object changes.
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