Answer:
Impulse = Δp = 2.45 kg m/s
Explanation:
Impulse = change in momentum = final momentum - initial momentum
The initial momentum of the ball before hitting the ground is given by:
m * v_i = 0.14 kg * -9 m/s = -1.26 kg m/s
The final momentum of the ball after bouncing back is given by:
m * v_f = 0.14 kg * 8.5 m/s = 1.19 kg m/s
So the change in momentum is:
Δp = v_f - v_i = 1.19 kg m/s - (-1.26 kg m/s) = 2.45 kg m/s
Impulse = Δp = 2.45 kg m/s
let us focus on one of the spheres after the charge has been placed on the system. which combination of analysis models below correctly describes one of the spheres in this situation and will be of most use to us for solving this problem
The combination of analysis models that correctly describes one of the spheres in this situation and will be most useful for solving the problem depends on the specific details and requirements of the problem at hand.
Some commonly used models for analyzing charged spheres include the electric field generated by a point charge, Coulomb's law, and the method of images. The choice of the most appropriate model will depend on the specific conditions and requirements of the problem, such as the distribution of charge on the spheres and the distance between them. Charge is a fundamental property of matter that refers to the amount of electrical energy in a system. It is measured in units of Coulombs and can be positive, negative or neutral. Charge can interact with other charges through the electric force, which is described by Coulomb's Law. This interaction can result in a number of phenomena, including attraction, repulsion, and the transfer of electrical energy from one object to another. Understanding charge and its interactions is crucial for many fields, including physics, engineering, and chemistry, and has many practical applications, such as in electronics, power generation and storage, and in medical imaging technologies
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fill in the blank. research questions about the time course of cognition are better addressed using methods like___, whereas questions about the anatomy of cognition are better addressed using methods like___.
research questions about the time course of cognition are better addressed using methods like ERPs, whereas questions about the anatomy of cognition are better addressed using methods like fMRI.
What is ERPs and fMRI?The primary goal of an ERP system is to improve organisational efficiency by managing and improving how corporate resources are used.These systems are of three types, on-premises, cloud-based, and hybrid. It depends on the organization adopting ERP software to choose a suitable type for its business needs and operations to improve its productivity.
The fMRI magnet converts tissues into a visualizable state, and radio frequency pulses offer the signalling information required to distinguish them. The computer assembles the information from the radio frequency pulses into a manner that anyone who can read a weather map will recognise.
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114 Find two elements of R4 which belong to the span of the following vectors. Find an element of Rtwhich does nOt belong to their span. (Hint: Compute Ithe sum of the entries of each of the given vectors | Xi=lEI X [S_Um} 24 X=[}-2-2]'
The span of a set of vectors is the set of all linear combinations of those vectors. In this case, the set of vectors is:
X1 = [1, 2, 3, 4]
X2 = [2, 4, 6, 8]
Two elements in R4 that belong to the span of these vectors are:
a1X1 + a2X2 = [a1 + 2a2, 2a1 + 4a2, 3a1 + 6a2, 4a1 + 8a2]
So for example, if we choose a1 = 1 and a2 = -1, we get:
a1X1 + a2X2 = [1 - 2(-1), 2(1) - 4(-1), 3(1) - 6(-1), 4(1) - 8(-1)] = [3, 0, 9, -3]
Another example is if we choose a1 = 2 and a2 = -2, we get:
a1X1 + a2X2 = [2 - 2(-2), 2(2) - 4(-2), 3(2) - 6(-2), 4(2) - 8(-2)] = [6, 0, 18, -6]
To find an element of R4 that does not belong to the span of these vectors, we need to find a vector in R4 that cannot be expressed as a linear combination of X1 and X2. For example, the vector [1, 1, 1, 1] cannot be expressed as a linear combination of X1 and X2, so it does not belong to their span.
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A satellite of mass 2,000 kg is in an elliptical orbit about the Earth. When the satellite reaches point A, which is the closest point to the Earth, its orbital radius is 1.2x10'm and its orbital velocity is 7.1x 103 m/s. (Me = 6x1024 kg and Re = 6.4x10 m) a. Determine the total mechanical energy of the satellite at point A, assuming that the gravitational potential energy is zero at an infinite distance from the Earth. b. Determine the angular momentum of the satellite at point A. c. What is the minimum speed of the satellite at point A in order to escape from Earth? When the satellite reaches point B, which is the furthest point from the Earth, its orbital radius is 3.6x107m. d. Determine the speed of the satellite at point B.
A satellite of mass 2,000 kg is in an elliptical orbit about the Earth. When the satellite reaches point A, which is the closest point to the Earth, its orbital radius is 1.2x10'm and its orbital velocity is 7.1x 103 m/s. (Me = 6x1024 kg and Re = 6.4x10 m). So, the total mechanical energy of the satellite at point A is -0.6x10^13 J, assuming that the gravitational potential energy is zero at an infinite distance from the Earth.
The total mechanical energy (E) of an object in orbit is given by the equation E = kinetic energy (K) + potential energy (U).
At point A, the kinetic energy (K) is given by the equation K = (1/2)mv^2, where m is the mass of the satellite (2,000 kg) and v is its velocity (7.1x10^3 m/s).
The potential energy (U) is given by the equation U = -GMe/r, where G is the gravitational constant (6.67x10^-11 Nm^2/kg^2), Me is the mass of the Earth (6x10^24 kg), and r is the distance of the satellite from the Earth (1.2x10^6 m).
Substituting the values into the equations and solving, we get:
K = (1/2)(2,000 kg)(7.1x10^3 m/s)^2 = 3.0x10^13 J
U = -(6.67x10^-11 Nm^2/kg^2)(6x10^24 kg)/(1.2x10^6 m) = -3.6x10^13 J
E = K + U = 3.0x10^13 J + (-3.6x10^13 J) = -0.6x10^13 J
So, the total mechanical energy of the satellite at point A is -0.6x10^13 J, assuming that the gravitational potential energy is zero at an infinite distance from the Earth.
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If a ball is thrown in the air with a velocity 50 ft/s, its height in feet t seconds later is given by y = 50t − 16t^2.
(a) Find the average velocity for the time period beginning when t = 2 and lasting
0.5 second
0.1 second
0.05 second
0.01 second
The average velocity for the time period beginning when t = 2s and lasting 0.5s is 39.625ft/s, 0.1s is 15.6ft/s, 0.05s is 14.8ft/s, 0.01s is 16ft/s
Given the initial velocity of the ball (u) = 50ft/s
The motion is given as: [tex]y = 50t - 16t^2[/tex] where y is the height of the ball.
We can see that it is similar to [tex]y = ut + 1/2at^2[/tex] such that 1/2a = 16 then a = 32m/s2
The initial time when the ball is thrown in air (t1) = 2s
The total distance a particle has travelled divided by the total amount of time it has taken to travel that distance is the definition of an object's average velocity. So, let the height h1 be covered in t1s and h2 be covered in t2s such that average velocity (v) = h2-h1/t2-t2
(a) Initially, t1 = 2s and t2 = 2+0.5s = 2.5s where [tex]y = 50t - 16t^2[/tex]
Then h1 = 50 x 2 - 16 x 2x2 = 36ft
h2 = 50 x 2.5 - 16 x (2.5)x2.5 = 115.25
V = 115.25 - 36/2.5-2 = 79.25/2 = 39.625ft/s
(b) Let t2 = 0.1 + 2 = 2.1s then,
h2 = 50 x 2.1 - 16 x (2.1)x2.1 = 34.44ft
V = 34.44 - 36/0.1 = -1.56/0.1 = -15.6ft/s
(c) Let t2 = 0.05 + 2 = 2.05s then,
h2 = 50 x 2.05 - 16 x (2.05)x2.05 = 35.26ft
V = 35.26 - 36/ 0.05 = -0.74/0.05 = -14.8ft/s
(d) Let t2 = 0.01 + 2 = 2.01s then,
h2 = 50 x 2.01 - 16 x (2.01)x2.01 = 35.84ft
V = 35.84 - 36/ 0.01 = -0.16 /0.01 = -16ft/s
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newton's law with friction (force on angle) determine the acceleration of the system depicted below.
Therefore, no acceleration will occur until the frictional force exceeds the Driving Force (F), which in this case is gravity. The equation would then indicate a negative acceleration, which would not actually occur. Friction is a reactive force rather than an active one.
What is the best method for resolving forces to compute acceleration including friction on horizontal and incline planes?When you resolve, set your axes to be perpendicular and parallel to the surface rather than necessary vertical and horizontal axes.
As the item on the surface neither sinks into it nor accelerates away from it, the forces perpendicular to the surface will add up to zero.
The total of the forces acting parallel to the surface may be used to calculate the acceleration using the formula F=ma.
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Calculate the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface if its mass is 1700 kg.A) 2014 NB) 2330 NC) 1755 ND) 2610 N
The correct option is D, the force of Earth's gravity on a spacecraft 2.00 Earth radii above the Earth's surface is 2610 N.
The force of Earth's gravity on a spacecraft can be calculated using the equation F = G * (m1 * m2) / r^2, Earth's surface is approximately 2 * 6,371,000 m = 12,742,000 m). Plugging in the values, we get:
F = 6.67 x 10^-11 Nm^2/kg^2 * (5.97 x 10^24 kg * 1700 kg) / (12,742,000 m)^2
F = 2610 N
Force is a term used in physics to describe the influence that causes an object to undergo a change in motion. It is a vector quantity, meaning it has both magnitude and direction. Force can cause an object to move, change its speed, or change its direction. It can also cause a stationary object to start moving. There are several types of forces, including gravitational forces, electrical forces, magnetic forces, and friction forces. Force can also be described as a push or a pull.
Force is an essential concept in physics as it helps us understand the behavior of objects and how they interact with each other. For example, the force of gravity keeps planets in orbit around the sun. The force of friction is what allows us to walk on the ground without slipping. The force of air resistance affects the motion of projectiles and affects the speed of vehicles.
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write the general antiderivative of the given rate of change function. (use c for the constant of integration.) the rate of change of dvd orders is given by s(m)
The general antiderivative of the rate of change function "the rate of change of DVD orders is given by s(m) = 600m + 5DVDs per month" is "DVD orders = 300m^2 + 5m + c", where c is the constant of integration.
The antiderivative of a function is the original function whose derivative is equal to the given rate of change function. To find the antiderivative of the rate of change function "the rate of change of DVD orders is given by s(m) = 600m + 5 DVDs per month", we need to integrate the function with respect to the independent variable m.
The antiderivative of the function s(m) = 600m is 300m^2 and the antiderivative of the constant 5 is 5m. Adding these two antiderivatives, we get the general antiderivative of the rate of change function:
DVD orders = 300m^2 + 5m + c
where c is the constant of integration and represents the arbitrary offset from the original function. To find the value of c, additional information or boundary conditions are required. This antiderivative represents the total number of DVD orders as a function of the number of months since the beginning of the year.
Complete question:
Write the general antiderivative of the given rate of change function.
DVD Orders The rate of change of DVD orders is given by
s(m) = 600m + 5DVDs per month
where m is the number of months since the beginning of the year.
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An astronomer finds an object at a distance of 6.8 AU from theEarth. Which type of object is this likely to be?
A A comet in our solarsystem.
B A star in ourGalaxy.
C An artificial satelliteorbiting the Earth.
D A distant galaxy.
A sound source producing 1.40 kHz waves moves toward a stationary listener at one-half the speed of sound. What frequency will the listener hear? Now, suppose instead that the source is stationary and the listener moves toward the source at one-half the speed of sound. What frequency does the listener hear?
When the sound source is moving towards the stationary listener at one-half the speed of sound, the frequency heard by the listener will be 1.40 kHz.
When the source is stationary and the listener moves towards the source at one-half the speed of sound, the frequency heard by the listener will be 1.80 kHz. This is because the Doppler effect causes the frequency of a sound wave to increase as the source moves towards the listener and decrease as the source moves away from the listener.
Frequency is a measure of how often a wave or signal repeats itself over a given period of time. Frequency is usually measured in hertz (Hz), which means the number of cycles per second. Frequency is an important concept in physics, as it is used to describe waveforms such as sound, light, and radio signals.
Frequency is also used to describe the properties of an object or system, such as its resonant frequency.
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fill in the blank. after thomson's work showed that atoms contain smaller charged particles called electrons, millikan conducted experiments on charged oil droplets. from these experiments millikan precisely determined the to___ratio of an electron.
After Thomson's work showed that atoms contain smaller charged particles called electrons, Millikan conducted experiments on charged oil droplets. From these experiments, Millikan precisely determined the mass-to-charge ratio of an electron.
In 1897, J. J. Thomson replаced the mаgnetic field with аn electric field in а cаthode rаy tube with аn improved vаcuum, аnd he showed thаt the cаthode rаys were аttrаcted to the positive plаte аnd repelled by the negаtive plаte. This confirmed thаt the cаthode rаys were composed of negаtively chаrged pаrticles. Thomson cаlled these pаrticles corpuscles, but they hаve come to be cаlled electrons, а nаme suggested by George Johnstone Stoney in 1891.
Thomson wаs аble to cаlculаte the mаss to chаrge rаtio, аnd the results of his experiments аnd cаlculаtions suggested thаt electrons were аbout 1/1000 the mаss of hydrogen аtoms, suggesting thаt аtoms аre composed of pаrticles smаller thаn the аtoms itself. Becаuse the results of his experiments were independent of the gаs in the tube, he concluded thаt аll substаnces contаin these sаme electrons.
In 1909, Robert Millikаn аnd Hаrvey Fletcher observed chаrged oil droplets fаlling between two electricаlly chаrged plаtes. Millikаn аssumed thаt this wаs the chаrge of аn electron, аnd from the mаss to chаrge rаtio determined by Thomson, the mаss of the electron wаs found to be аbout 1/1836 the mаss of а hydrogen аtom, confirming thаt аtoms аre composed of pаrticles much smаller thаn even the smаllest аtom.
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true/false. if the earth somehow got 3 times more mass than it has now, but stayed the same size, our weight would increase by a factor of 9.
F=GmMr2=kM, where G is your weight and m is the primordial mass of the earth. Where k=Gmr2 k = G m r 2, F = G m M r 2 Equals k M.
Has the mass of the Earth remained constant?Did you realize that the weight of the planet Earth is decreasing daily? In spite of the 40,000 tons of space dust that reach the surface of our planet every year, it is really becoming 50,000 tonnes lighter.
Does the planet's weight increase or decrease?The University of Guelph's Joanna O'Meara, a lecturer and associate head in the faculty of physics, argues why meteor showers actually cause the Earth to grow heavier. According to her, space dust, which includes meteor and asteroid debris, adds around 40,000 tonnes of weight to the earth each year.
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The hot glowing surfaces of stars emit energy in the form of electromagnetic radiation. It is a good approximation to assume that the emissivity e is equal to 1 for these surfaces.
A) Find the radius RRigel of the star Rigel, the bright blue star in the constellation Orion that radiates energy at a rate of 2.7×1031W and has a surface temperature of 11,000 K. Assume that the star is spherical. Use σ=5.67×10−8W/m2⋅K4 for the Stefan-Boltzmann constant and express your answer numerically in meters to two significant figures.
The radius the star Rigel, a bright blue star in the constellation Orion that radiates energy at a rate of 2.7 × 10³¹ W and has a surface temperature of 11,000 K. (Assume that the star is spherical) = 5,422.17 km
To determine the radius of the star, we can apply the Stefan-Boltzmann law to determine the star output power.
Rigel emits radiation at a rate of 2.7 x 10²³ Watts
The power per unit area, according to the Stefan-equation, Boltzmann's is:
j = σT⁴
Where,
σ = (2[tex]\pi[/tex]⁵K⁴) / 15c²h³
T = temperature
σ = 5.670 x 10⁻⁸ Wm⁻²K⁻⁴
Hence,
The surface area of the star:
A = P / j
P = power ⇒ 2.7 × 10³¹
A = ( 2.7 × 10³¹) / (5.670 x 10⁻⁸) (11.000⁴)
= 3.52 x 10²³
The area = 4[tex]\pi[/tex]r²
3.52 x 10²³ = 4[tex]\pi[/tex]r²
r² = 2.58 x 10²²
r = 5,422.17 km
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1. A) If the radius of a cylinder increases by a factor of 2.73, by what factor does the volume change? Assume that the height of the cylinder stays the same.
The new volume of the cylinder will increase by a factor of 7.453.
What is the volume of a cylinder?
The volume of a cylinder is calculated by applying the following equation as shown below.
V = πr²h
where;
r is the radius of the cylinderh is the height of the cylinderwhen the radius increases by a factor of 2.73, the new volume will become;
V = π(2.73r)²h
V = 7.453 πr²h
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consider the action of the biceps when carrying a load of 8 kg with the forearm making an angle of 20
When carrying a load of 8 kg with the forearm making an angle of 20, the biceps muscle must exert a force to hold the forearm and its load in place.
The amount of force the biceps must exert depends on the lever arm of the load, which is the perpendicular distance between the line of action of the force and the axis of rotation.
The lever arm of the load in this case is the distance between the line of action of the load and the axis of rotation of the elbow joint. With a lever arm of 8 kg and an angle of 20 degrees, the biceps must exert a force of 16.47 Newtons.
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mark climbs up onto the roof of his house to hang a new flood light above the garage. being afraid of heights, mark carefully looks over the edge and ponders a possible fall to the ground below. the top of the roof is 5 meters 5 meters above the ground below. if mark has a mass of 65 kg 65 kg , which of the following values is mark's gravitational potential energy? use g
This potential energy is known as gravitational potential energy. It is the gravitational field's potential energy that is released when two objects fall in close proximity to one another.
The short answer to the question of potential energyThe term "potential energy" refers to the energy that is conserved or stored in a material or object. The location, configuration, or status of the substance or object determines the stored energy.
Which potential energy is an example?Energy that has been stored is called potential energy. A battery, a stretched spring, and lifting an object are some examples. There are two major categories of energy: potential and kinetic.
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A circuit contains two resistors linked in parallel; each resistor has a resistance of 20 Ω . What is the circuit's total resistance?
The resultant resistance of the resistor combination is 10 Ω.
What is resistor?A resistor is an electrical component that controls or restricts how much electrical current can pass across a circuit in an electronic device. A specified voltage can be supplied via resistors to an active device like a transistor.
Resistance of each resistor is = 20 Ω
The resistors are connected parallelly.
Hence, the resultant resistance of the resistor combination = (20 ||20) Ω
= (20 × 20) ÷ (20 + 20) Ω
= 10 Ω.
Therefore, the resultant resistance of the resistor combination is 10 Ω.
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warm air over the beach rise while cooler dense air the ocean rushes in due to
Answer: Convection causes the warmer air over land to expand and rise, which in turn causes low air pressure over the land. The cooler air over the ocean rushes in to replace the warm air that just rose over land. This causes a sea breeze.
Explanation:
hope this helped ;) ! -middle schooler
Answer:
convection
Explanation:
heat rises up
What would the power (Watts) be for a speaker if it draws 3.0 Amps of current when connected to a 12.0 Volt source?
The power of Speaker can be calculated by
[tex]P=V.i\\P=(12).(3)\\P=36W[/tex]
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A man exerts a horizontal force of 145 N on a crate with a mass of 31.2 kg.
Answer:
Below
Explanation:
If you can't overcome the force of friction....the crate will not move
so friction force = 145 N
Coeff of friction = Ff / Normal force = 145 / (31.2 * 9.81) = .47
Which is the equation for a machine’s efficiency?(1 point)
The equation for a machine’s efficiency is = (output energy ÷ input energy) × 100%
What is efficiency ?Efficiency is the ability to achieve something or get a desired outcome without wasting resources, time, money, energy, or effort. In a broader sense, it is the capacity to carry out tasks effectively and efficiently.
It denotes the degree of performance that requires the fewest inputs to provide the greatest amount of output in more mathematical or scientific words.
Hence, mathematically, machine’s efficiency can be expressed as:
machine’s efficiency = (output energy ÷ input energy) × 100%
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The systematic ways in which our ethics are limited in ways we are not even aware of ourselves is called _______________
The systematic ways in which our ethics are limited in ways we are not even aware of ourselves is called implicit bias.
Implicit bias refers to the unconscious attitudes, beliefs, and stereotypes that influence our thoughts and actions in ways we are not even aware of. This type of bias is often a result of cultural and societal conditioning, and it can impact our decision-making processes and behavior even when we consciously believe that we are being fair and objective. Implicit bias can affect all aspects of our lives, from our personal relationships to our professional practices, and it is a significant factor in perpetuating discrimination and inequality. Understanding and recognizing implicit bias is crucial for promoting equality and fairness in society, and for developing more equitable and just ethical practices.
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Calculate the x-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.
A positive charge of magnitude Q1 = 0.45 nC is located at the origin. A negative charge Q2 = -9.5 nC is located on the positive x-axis at x = 6.5 cm from the origin. The point P is located y = 7.5 cm above charge Q2.
The x-component of the electric field at point P due to charge Q1 is 270 N/C.
The query asks what charge Q1 is responsible for the x component of the electric field vector at point P. In light of this, you disregard charge Q2's contribution.
Assume that point P contains a little positive charge. By definition, the strength of the electric field caused by charge Q1 at point P is:
E = [tex]\frac{kQ1}{d^{2} }[/tex] where k is the coulomb constant and d is the straight-line distance from Q1 to P.
The distance, d, is the hypotenuse of the triangle formed by the point P, charges Q1 and Q2. Therefore,
d = [tex]\sqrt{0.065^{2} } + \sqrt{0.075} ^{2}[/tex] = 0.099 m
Now, finding the electric field, we get:
E = 8.99 × [tex]10^{-9} Nm^{2} C^{-2}[/tex] × 0.45 × [tex]10^{-9}[/tex] / [tex]0.099^{2}[/tex] = 412 n/c
The x component of the electric field, [tex]E_{x}[/tex], would be:
412 × cos49° = 270 N/C.
The Electric field points away from positive charges (q > 0) and towards negative charges. In Maxwell's equations, the E-field is always a vector field with three dimensions. This indicates that it consists of three parts: an x, y, and z component that respectively determine the x, y, and z directions of the electric field.
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a block of mass m1 is at rest on a long frictionless table, one end of which is terminated in a wall. another block of mass m2 is placed between the first block and the wall and set in motion to the left with constant speed v2i. assuming that all collisions are completely elastic, find the value of m2 for which both blocks move with the same velocity after m2 has collided once with m1 and once with the wall. assume the wall to have infinite mass.
After a collision, the center of mass velocity of this system of two balls with masses m1 and m2 and velocities v1 and v2 is ( m1 v1 + m2 v2 ) / ( m1 + m2 ).
What is the momentum law of motion?Momentum is the force needed to stop an item moving at a certain speed in a given amount of time. It is calculated by multiplying an object's mass by its velocity. The sum of the individual momenta determines the overall momentum for any array of many objects.
p = m.v
p = Momentum
m = Mass
v = Velocity
For ball 1,
m = m1
v = v1
p1 = m1 v1
For ball 2,
m = m2
v = v2
p2 = m2 v2
Center of mass velocity = Total momentum / Total mass
Total momentum is = p1 + p2
Total mass is= m1 + m2
Center of mass velocity is= ( p1 + p2 ) / ( m1 + m2 )
Center of mass velocity is= ( m1 v1 + m2 v2 ) / ( m1 + m2 )
Therefore, center of mass velocity of this system of two balls is
Center of mass velocity = ( m1 v1 + m2 v2 ) / ( m1 + m2 ).
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It has been proposed to use uranium carbide (UC) for the initial fuel in certain types of breeder reactors, with the uranium enriched to 25 w/o. The density of UC is 13.6 g/cm3 . The molecular weight of U-235 and U-238 are 235.0439 and 238.0508 respectively. (a) What is the atomic weight of the uranium? (b) What is the atomic density of U-235?
(a) The atomic weight of uranium can be calculated as a weighted average of the atomic weights of the isotopes U-235 and U-238, taking into account their natural abundances. The atomic weight of uranium is approximately 238.03 g/mol.
(b) To calculate the atomic density of U-235, we need to know the mass fraction (or weight fraction) of U-235 in uranium carbide fuel. Considering that uranium is enriched to 25 w/o U-235, the mass fraction of U-235 is 0.25. The atomic density of U-235 can then be calculated as follows:
atomic density = (mass fraction of U-235) * (UC density) / (atomic weight of U-235)
= (0.25) * (13.6 g/cm3) / (235.0439 g/mol)
= about 7.07 x 10^22 atoms/cm3
"Atomic" is a term that has many related but different meanings. In physics, "atom" refers to the smallest unit of an element that retains the chemical properties of that element. In computer science, "atomic" is used to describe an operation that is indivisible and cannot be stopped. This means that the operation was completed in its entirety or not at all.
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a 95kg halfback moving at 4.1 m/s on an apparent breakaway for a touchdownd what was their mutual speed
When a 95-kg halfback moving at 4.1 m/s is tackled from behind by an 85-kg cornerback running at 5.5 m/s in the same direction, their mutual speed immediately after the tackle is 1.96 m/s.
The mutual velocity of two colliding bodies is the velocity of the center of mass of the system after the collision. In an inelastic collision, the total momentum of the system is conserved, but the kinetic energy is decreased. The final velocity of the system can be calculated by dividing the total momentum by the total mass of the system.
In this case, the mutual velocity after the tackle is equal to the velocity of the center of mass of the system formed by the halfback and the cornerback. By using the equation for the center of mass velocity, the mutual velocity after the tackle can be calculated as follows:
v_cm = (m1 × v1 + m2 × v2) / (m1 + m2)
where v_cm is velocity of the center of mass (mutual velocity or mutual speed), m1 is the mass of the halfback, v1 is the initial velocity of the halfback, m2 is the mass of the cornerback, and v2 is the initial velocity of the cornerback.
v_cm = (95 kg × 4.1 m/s + 85 kg × 5.5 m/s) / (95 kg + 85 kg)
v_cm = 1.96 m/s
So the mutual speed immediately after the tackle was 1.96 m/s.
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Your question seems missing, but I suppose the question was:
"A 95-kg halfback moving at 4.1 m/s on an apparent breakaway for a touchdown is tackled from behind. When he was tackled by an 85-kg cornerback running at 5.5 m/s in the same direction, what was their mutual speed immediately after the tackle?"
an initially motionless test car is accelerated uniformly to 135 km/h in 7.88 s before striking a simulated deer. the car is in contact with the faux fawn for 0.755 s, after which the car is measured to be traveling at 71.0 km/h.a. What is the magnitude of the acceleration of the car before the collision?b. What is the magnitude of the average acceleration of the car during the collision?c. What is the magnitude of the average acceleration of the car during the entire test, from when the car first begins moving until the collision is over?
The magnitude of the acceleration of the car before the collision is 4.23[tex]\frac{m}{ (s ^ 2)}[/tex] and the magnitude of the average acceleration of the car during the collision is -16 [tex]\frac{m}{ (s ^ 2)}[/tex] and the magnitude of the average acceleration of the car during the entire test, from when the car first begins moving until the collision is over is 2.46[tex]\frac{m}{ (s ^ 2)}[/tex].
Velocity of car before collision is [tex]v_{1}[/tex] = 120km / h
Velocity of car after collision is, [tex]v_{2}[/tex] = 76.5km / h .
Time taken by a car before collision is, t =7.88:
Acceleration of car before collision is calculated as;
a = [tex]\frac{v-u}{t}[/tex]
a =[tex]\frac{120\times \frac{5}{18}-0 }{7.88}[/tex]
a = 4.23[tex]\frac{m}{ (s ^ 2)}[/tex]
Therefore magnitude of acceleration of a car before collision a = 4.23 [tex]\frac{m}{ (s ^ 2)}[/tex]
The average vehicle acceleration at the time of impact is computed as;
[tex]a_{avg}[/tex] = [tex]\frac{v-u}{t}[/tex]
[tex]a_{avg}[/tex] =[tex](120-76.5)\times \frac{5}{18}[/tex]
[tex]a_{avg}[/tex] =0.755 s
[tex]a_{avg}[/tex] =-16 [tex]\frac{m}{ (s ^ 2)}[/tex]
Here, a negative sign shows that the average acceleration is moving in the opposite direction from where the car is travelling.
[tex]a_{avg}[/tex] = [tex]\frac{v-u}{t}[/tex]
[tex]a_{avg}[/tex] =[tex]\frac{ (120-76.5)\times \frac{5}{18}}{0.755}[/tex]
[tex]a_{avg}[/tex] =-16[tex]\frac{m}{ (s ^ 2)}[/tex]
Here, the negative sign denotes that the average acceleration is occurring in the opposite direction to the motion of the car.
Therefore, the average acceleration of a car during collision is [tex]a_{avg}[/tex] =16 [tex]\frac{m}{ (s ^ 2)}[/tex]
and in direction opposite to the direction of car.
The average acceleration of the car during the test is calculated.
as,
[tex]a_{2}[/tex]=[tex]\frac{v-u}{t}[/tex] =[tex]76.5\times a_{2}[/tex]= [tex]\frac{76.5\times\frac{5}{18} }{7.88-0.75}[/tex]
[tex]a_{2}[/tex]=2.46[tex]\frac{m}{ (s ^ 2)}[/tex]
Therefore, the average acceleration of a car during entire test is a_{2} = 2.46[tex]\frac{m}{ (s ^ 2)}[/tex]
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true/false. two competing models attempt to explain the motions and changing brightness of the planets: ptolemy's geocentric model and copernicus' heliocentric model. sort the characteristics according to whether they are part of the geocentric model, the heliocentric model, or both solar system models.
The geocentric model is a solar system model that places the Earth at the center and explains the motion of the planets through circular paths. The heliocentric model, on the other hand, places the Sun at the center and explains the motion of the planets through orbit around the Sun. The changing brightness of the planets is explained by their varying distances from either the Earth (geocentric model) or the Sun (heliocentric model).
True, two competing models were created to explain the motions and changing brightness of the planets. These were Ptolemy's geocentric model and Copernicus' heliocentric model. The geocentric model, as its name suggests, places the Earth at the center of the solar system and the planets, including the Sun, orbit around it. The heliocentric model, on the other hand, places the Sun at the center of the solar system and the planets, including Earth, orbit around it.
In the geocentric model, the planets move in circular paths called epicycles, which are superimposed on larger circular paths called deferents. The changing brightness of the planets is explained by their varying distances from the Earth.
The heliocentric model explains the motion of the planets as the result of their orbit around the Sun. The changing brightness of the planets is also explained by their varying distances from the Sun.
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gaussian surfaces a and b enclose the same positive charge q. the area of gaussian surface a is three times larger than that of gaussian surface b. the electric flux through gaussian surface a is
In this case it will be equal to the flux of electric field through the Gaussian surface B as Flux through S(A) = Flux through S (B ) = Charge inside/ ∈₀
Gauss's law states that the net total electric charge inside a Gaussian surface equals the total electric flux. The electric flux will remain constant even if the Gaussian surface is three times bigger if both surfaces have an equal amount of total electric charge.
Now that we have an arbitrary charge distribution, we can determine the electric flux through any closed surface. We discovered that any electric field lines entering the surface at one point must necessarily exit at another point of the surface if a closed surface lacks any charge inside where an electric field line can terminate. Therefore, the electric flux will not exist if a closed surface has no charges inside the enclosed volume.
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A wheel of radius $a$ rolls along a horizontal straight line without slipping. Find parametric equations for the curve traced out by a point $P$ on a spoke of the wheel $b$ units from its center. As parameter, use the angle $\theta$ through which the wheel turns. The curve is called a trochoid, which is a cycloid when $b=a$
The position of point $P$ relative to the center of the wheel can be described as follows:
$x = a\theta - b\sin\theta$
$y = a - b\cos\theta$
$a$ is the radius of the wheel and $b$ is the distance of point $P$ from the center of the wheel. These equations define a trochoid. If $b = a$, then it becomes a cycloid.
About radiusThe radius is a circle is the line that connects the center point of the circle to a point on the circle. In a 3-dimensional sphere, the radius that connects the center of the ball to a point on the surface of the ball. The radius of a circle is half the diameter of the circle.
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