Answer:
Explanation:
Charge on uranium ion = charge of a single electron
= 1.6 x 10⁻¹⁹ C
charge on doubly ionised iron atom = charge of 2 electron
= 2 x 1.6 x 10⁻¹⁹ C = 3.2 x 10⁻¹⁹ C
Let the required distance from uranium ion be d .
force on electron at distance d from uranium ion
= 9 x 10⁹ x 1.6 x 10⁻¹⁹ / r²
force on electron at distance 61.10 x 10⁻⁹ - r from iron ion
= 9 x 10⁹ x 3.2 x 10⁻¹⁹ / (61.10 x 10⁻⁹ - r )²
For equilibrium ,
9 x 10⁹ x 1.6 x 10⁻¹⁹ / r² = 9 x 10⁹ x 3.2 x 10⁻¹⁹ / (61.10 x 10⁻⁹ - r )²
2 d² = (61.10 x 10⁻⁹ - r )²
1.414 r = 61.10 x 10⁻⁹ - r
2.414 r = 61.10 x 10⁻⁹
r = 25.31 nm .
(a) The distance from the uranium atom at which an electron will be in equilibrium is [tex]2.04 \times 10^{-8} \ m[/tex]
(b) The magnitude of the force on the electron from the uranium ion is [tex]3.46 \times 10^ 6 \ N[/tex]
The given parameters:
distance between the iron and the uranium, d = 61.1 nmcharge of uranium ion, q₁ = 1.6 x 10⁻¹⁹ Ccharge of doubly ionized atom, q₂ = 2q₁ = 3.2 x 10⁻¹⁹ CThe force on the electron due to uranium ion at distance r is calculated as follows;
[tex]F _1 = \frac{Kq_1^2}{r^2} \\\\F_1 = \frac{9\times 10^9 \times (1.6\times 10^{-19})^2}{r^2} \\\\F_1 = \frac{2.3 \times 10^{-28}}{r^2}[/tex]
The force on the electron due to uranium ion at distance less than 61.10 nm.
R = 61.10 nm - r
[tex]F_2 = \frac{9\times 10^9 \times (3.2 \times 10^{-19})^2}{(61.1 \times 10^{-9} \ - \ r)^2} \\\\\F_2 = \frac{9.216 \times 10^{-28}}{(61.1 \times 10^{-9} \ - \ r)^2}[/tex]
At equilibrium, the force between the electron and ions will be equal.
[tex]\frac{9.216 \times 10^{-28}}{(61.1 \times 10^{-9} \ - \ r)^2}= \frac{2.3 \times 10^{-28}}{r^2}\\\\\frac{4}{(61.1 \times 10^{-9} \ - \ r)^2} = \frac{1}{r^2} \\\\4r^2 = (61.1 \times 10^{-9} \ - \ r)^2\\\\2^2r^2 = (61.1 \times 10^{-9} \ - \ r)^2\\\\2r = 61.1 \times 10^{-9} \ - \ r\\\\3r = 61.1 \times 10^{-9} \\\\r = \frac{61.1 \times 10^{-9}}{3} \\\\r = 2.04 \times 10^{-8} \ m[/tex]
The magnitude of the force on the electron from the uranium ion is calculated as follows;
[tex]F = \frac{kq_1^2}{r^2} \\\\F = \frac{9\times 10^9 \times 1.6\times 10^{-19}}{(2.04 \times 10^{-8})^2} \\\\F= 3.46 \times 10^6 \ N[/tex]
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Which describes the reaction of a substance to form one or more new substances?
a physical change
a chemical change
a change of state
You are walking down a straight path in a park and notice there is another person walking some distance ahead of you. The distance between the two of you remains the same, so you deduce that you are walking at the same speed of 1.17 m/s. Suddenly, you notice a wallet on the ground. You pick it up and realize it belongs to the person in front of you. To catch up, you start running at a speed of 2.75 m/s. It takes you 10.5 s to catch up and deliver the lost wallet. How far ahead of you was this person when you started running
Answer:
16.6 m
Explanation:
Let d be the distance the other person is ahead of you. Since the other person is walking at a speed, v = 1.17 m/s, after picking the wallet, the other person moves a distance , vt in time, t = 10.5 s, the total distance covered by you till catch up is D = d + vt.
Also, you moves with a speed of v' = 2.75 m/s in time t = 10.5 s as you pick up the wallet, you covers a distance d' = v't at catch up.
At catch up, D = d'
d + vt = v't
d = v't - vt
d = (v' - v)t
Substituting the values of the variables into d, we have
d = (2.75 m/s - 1.17 m/s)10.5 s
d = (1.58 m/s)10.5 s
d = 16.59 m
d ≅ 16.6 m
So, the other person was 16.6 m ahead of you when you started running.
In the absence of friction, if a force acting on a moving object stops acting, the object will
Answer:
Keep on moving
Explanation:
Newton's first law states "that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force."
An object has a kinetic energy of 14 J and a mass of 17 kg , how fast is the object
moving?
Kim was adopted as a baby and raised by loving parents in an enriched environment. Studies have shown that ________
Answer:
Kim was adopted as a baby and raised by loving parents in an enriched environment. Studies have shown that the correlation between IQ
( intelligence quotient) scores of adopted children and those of their biologically unrelated family members reduce to zero as they grow into adulthood.
Explanation:
Kim was adopted as a baby and raised by loving parents in an enriched environment. Studies have shown that the correlation between IQ
( intelligence quotient) scores of adopted children and those of their biologically unrelated family members reduce to zero as they grow into adulthood.
Also, a loving environment is equally important for a child's upbringing.
A person with a mass of 60 kg stands on a scale in an elevator. What will the scale read (apparent weight or normal force) when the elevator is accelerating downward at 1 m/s2?
Answer:
660 N
Explanation:
From the question,
When an Elevator moves downward,
R = m(g+a).................. Equation 1
Where R = apparent weight of the person, m = mass of the person, g = accleration due to gravity, a = acceleration of the elevator
Given: m = 60 kg, g = 10 m/s², a = 1 m/s²
Substitute these values into equation 1
R = 60(10+1)
R = 60(11)
R = 660 N.
Hence the apparent weight of the person is 660 N
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The Left and right forces acting on this cart are
A. balanced
B. super-positioned
C. unbalanced
D. counter-balanced
Answer:
B. Super-Positioned
Explanation:
A 680 nm laser illuminates a double slit apparatus with a slit separation distance of 7.83 μm. On the viewing screen, you measure the distance from the central bright fringe to the 2nd bright fringe to be 88.2 cm. How far away (in meters) is the viewing screen from the double slits?
Answer:
L = 5.08 10⁻¹ m = 50.8 cm
Explanation:
In a double slit experiment for constructive interference is given by
d sin θ = m λ
let's use trigonometry to find a relationship with the distance
tan θ = y / L
these experiments are very small angles
tan θ = [tex]\frac{sin \ \theta}{cos \ \theta}[/tex] = sin θ
when substituting
sin θ = y / L
substituting in the first equation
d y / L = m λ
L = [tex]\frac{d \ y}{m \ \lambda}[/tex]
let's calculate
L = [tex]\frac{ 0.783 \ 10^{-6} \ 88.2 \ 10^{-2} }{2 \ 680 \ 10^{-9}}[/tex]
L = 5.08 10⁻¹ m
The distance of viewing screen from the double slits will be L = 5.08 *10⁻¹ m = 50.8 cm
What is constructive interference?
This position, where the resulting wave is larger than either of the two original, is called constructive interference.
In a double slit experiment for constructive interference is given by
d sin θ = m λ
let's use trigonometry to find a relationship with the distance
[tex]tan\theta=\dfrac {y}{L}[/tex]
these experiments are very small angles
tan θ = = sin θ
when substituting
[tex]sin\theta = \dfrac{y}{l}[/tex]
substituting in the first equation
[tex]\dfrac{dy}{L}=m\lambda[/tex]
[tex]L=\dfrac{dy}{L\lambda}[/tex]
let's calculate
[tex]L=\frac{0.783\times 10^{-6}\times 88.2\times 10^{-2}}{2.680\times 10^{-9}}[/tex]
L = 5.08 10⁻¹ m
Hence the distance of viewing screen from the double slits will be L = 5.08 10⁻¹ m = 50.8 cm
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If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, what is the angle between the two vectors?
Answer:
26.57 degrees
Explanation:
Let the two vectors be a and b
The dot product of two vectors is expressed as;
a.b = |a||b|cosθ
The cross product is expressed as;
a×b = |a||b|sinθ
If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors, then;
|a×b| = 1/2|a.b|
|a||b|sinθ = 1/2|a||b|cosθ
sinθ = 1/2cosθ
2sinθ = cosθ
sinθ/cosθ = 1/2
tanθ = 1/2
θ = arctan(1/2)
θ = 26.57 degrees
Hence the angle between the two vectors is 26.57 degrees
The solid has a mass of 180 g. What is the density of the solid? Show your work. Be sure to use correct units of measurement. HELP NEEDED ASAP!!!!
Answer:
1.2 g/cm³
Explanation:
From the question given above, the following data were obtained:
Mass of solid = 180 g
Length (L) of solid = 10 cm
Width (W) of solid = 5 cm
Height (H) of solid = 3 cm
Density of solid =?
Next, we shall determine the volume of the solid. This can be obtained as follow:
Length (L) of solid = 10 cm
Width (W) of solid = 5 cm
Height (H) of solid = 3 cm
Volume (V) of solid =?
V = L× W × H
V = 10 × 5 × 3
V = 150 cm³
Finally, we shall determine the density of the solid. This can be obtained as follow:
Mass of solid = 180 g
Volume of solid = 150 cm³
Density of solid =?
Density = mass / volume
Density = 180 g / 150 cm³
Density of solid = 1.2 g/cm³
What is the Radiation left over from the big bang called?
Answer:
The Big Bang theory predicts that the early universe was a very hot place and that as it expands, the gas within it cools. Thus the universe should be filled with radiation that is literally the remnant heat left over from the Big Bang, called the “cosmic microwave background", or CMB.
Explanation:
The Big Bang theory suggest that the universe in early stage was at very hot place and which can be expanded, the gas within it cools. It is in an infinite universe and it has no edge.
What is big bang theory ?The Big Bang theory is a cosmological model which explain the existence of the observable universe from the earliest periods to the large-scale evolution.
The model describes the mechanism behind the universe expansion from an initial state of high density and temperature, it is very important concept as a lot of research is going on in this field to find out exactly how the universe began billions of years ago.
The universe began to cool down in order to allow the formation of particles become atoms after its initial phase of expansion, Primordial elements such as Hydrogen, Helium, and Lithium are condensed through gravity are formed early stars and galaxies.
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what is transactive memory
Here is a copy+pasted definition...
Transactive memory is a psychological hypothesis first proposed by Daniel Wegner in 1985 as a response to earlier theories of "group mind" such as groupthink.[1] A transactive memory system is a mechanism through which groups collectively encode, store, and retrieve knowledge. Transactive memory was initially studied in couples and families where individuals had close relationships but was later extended to teams, larger groups, and organizations to explain how they develop a "group mind",[1] a memory system that is more complex and potentially more effective than that of any of its individual constituents. A transactive memory system includes memory stored in each individual, the interactions between memory within the individuals, as well as the processes that update this memory. Transactive memory, then, is the shared store of knowledge.
In simple terms...
A transactive memory is a psychological hypothesis. It is a system in the brain which allows human's to encode, store, or get information.
For example...
let's say I learn 5 colors when I'm younger. My "transactive memory" will store it and will allow my brain to "retrieve" the information to allow me to remember colors I previously "stored".
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Suppose that the voltage across the resistor is held constant at 40 volts. If the resistance is steadily decreasing at a rate of 0.2 ohms per second, at what rate is the current changing at the moment that the resistor reaches 5 ohms?
Answer:
The current is increasing at a rate of 0.32 ampere per second.
Explanation:
The voltage of the resistor is modelled after Ohm's Law, which states that voltage is directly proportional to current:
[tex]V = i\cdot R[/tex] (1)
Where:
[tex]V[/tex] - Voltage, measured in volts.
[tex]i[/tex] - Current, measured in amperes.
[tex]R[/tex] - Resistance, measured in ohms.
An expression for the rate of change in voltage is found by Differential Calculus:
[tex]\frac{dV}{dt} = \frac{di}{dt}\cdot R +i\cdot \frac{dR}{dt}[/tex]
[tex]\frac{dV}{dt} = \frac{di}{dt}\cdot R + \frac{V}{R}\cdot \frac{dR}{dt}[/tex] (2)
Where:
[tex]\frac{dV}{dt}[/tex] - Rate of change in voltage, measured in volts per second.
[tex]\frac{di}{dt}[/tex] - Rate of change in current, measured in amperes per second.
[tex]\frac{dR}{dt}[/tex] - Rate of change in resistance, measured in ohms per second.
If we know that [tex]\frac{dV}{dt} = 0\,\frac{V}{s}[/tex], [tex]R = 5\,\Omega[/tex], [tex]V = 40\,\Omega[/tex] and [tex]\frac{dR}{dt} = -0.2\,\frac{\Omega}{s}[/tex], then the rate of change in current is:
[tex]5\cdot \frac{di}{dt}-1.6 = 0[/tex] (3)
[tex]\frac{di}{dt} = 0.32\,\frac{A}{s}[/tex]
The current is increasing at a rate of 0.32 ampere per second.
An alarm clock is dropped off the edge of a tall building. You, standing directly under it, hear a tone of 1350 Hz coming from the clock at the instant it hits the ground. Since you know the building is 25 m tall, you can find out what the frequency of the alarm would be if you had just held it in your hands. What would that frequency be
Answer:
the frequency clock would be 1262.85 Hz
Explanation:
Given data;
height of building h = 25 m
from the third equation of motion;
v² = u² + 2as
Since the Alarm clock falls with an acceleration equal to the acceleration due to gravity; a = g = 9.81 m/s²
initial velocity u = 0
so we substitute our values into the kinematic equation
v² = (0)² + 2 × 9.81 × 25
v² = 490.5
v = √490.5
v = 22.1472 m/s
Now, since the alarm clock is moving both I am stationary;
my velocity will be zero.
so Frequency of the alarm clock will be;
f' = [ (v - [tex]v_{s}[/tex] ) / ( v + [tex]v_{0}[/tex] ) ] × f
we know that; speed of sound is 343 m/s, so v = 343 m/s, [tex]v_{s}[/tex] is 22.1472 m/s, f is 1350 Hz, [tex]v_{0}[/tex] is 0 m/s
so we substitute the values into the equation
f' = [ (343 - 22.142 ) / ( 343 + 0 ) ] × 1350
f' = [ 320.858 / 343 ] × 1350
f' = 0.935446 × 1350
f' = 1262.85 Hz
Therefore, the frequency clock would be 1262.85 Hz
The source frequency or frequency of the alarm is 1,262.25 Hz.
The given parameters:
Observed frequency, Fo = 1350 HzHeight of the building, h = 25 mSpeed of sound, V = 343 m/sThe source velocity is calculated as follows;
[tex]v^2 = u^2 + 2gh\\\\ v^2 = 0 + 2gh\\\\ v = \sqrt{2gh} \\\\ v = \sqrt{2 \times 9.8 \times 25} \\\\ v = 22.14 \ m/s[/tex]
The source frequency or frequency of the alarm is calculated by applying Doppler effect as follows;
[tex]f_s = f_o (\frac{v- v_s}{v+ v_0} )\\\\ f_s = 1350 (\frac{343-22.14}{343} )\\\\ f_s = 1,262.25 \ Hz[/tex]
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Jada's husband puts on a Luther Vandross song every time they're going to be sexually intimate. Now when Jada is at a local bar and someone plays Luther Vandross songs she becomes sexually aroused. What is the conditioned stimulus
Answer:
The conditioned stimulus is the Luther Vandross
Explanation:
A conditioned stimulus is a stimulus that triggers a response in an organism that has been conditioned (or learned). In this case Jada's husband putting the song (conditioned stimulus) on every time they are sexually intimate has caused her response to the stimulus to be becoming aroused.
write the formula of kinetic energy and explain the terms in that
Answer:
Formula of kinetic energy:
[tex]k.e = \frac{1}{2} m {v}^{2} [/tex]
Explanation:
k.e: kinetic energy (J)
m: mass (kg)
v: velocity (m/s)
kinetic energy equals one half of the multiplication between mass and velocity
A-10A twin-jet close-support airplane is approximately rectangular with a wingspan (the length perpendicular to the flow direction) of 17.5 m and a chord (the length parallel to the flow direction) of 3 m. The airplane is flying at standard sea level with a velocity of 200 m/s. If the flow is considered to be completely laminar, calculate the boundary layer thickness at the trailing edge and the total skin friction drag. Assume that the wing is approximated by a flat plate. Assume incompressible flow.
Solution :
Given :
Rectangular wingspan
Length,L = 17.5 m
Chord, c = 3 m
Free stream velocity of flow, [tex]$V_{\infty}$[/tex] = 200 m/s
Given that the flow is laminar.
[tex]$Re_L=\frac{\rho V L}{\mu _{\infty}}$[/tex]
[tex]$=\frac{1.225 \times 200 \times 3}{1.789 \times 10^{-5}}$[/tex]
[tex]$= 4.10 \times 10^7$[/tex]
So boundary layer thickness,
[tex]$\delta_{L} = \frac{5.2 L}{\sqrt{Re_L}}$[/tex]
[tex]$\delta_{L} = \frac{5.2 \times 3}{\sqrt{4.1 \times 10^7}}$[/tex]
= 0.0024 m
The dynamic pressure, [tex]$q_{\infty} =\frac{1}{2} \rho V^2_{\infty}$[/tex]
[tex]$ =\frac{1}{2} \times 1.225 \times 200^2$[/tex]
[tex]$=2.45 \times 10^4 \ N/m^2$[/tex]
The skin friction drag co-efficient is given by
[tex]$C_f = \frac{1.328}{\sqrt{Re_L}}$[/tex]
[tex]$=\frac{1.328}{\sqrt{4.1 \times 10^7}}$[/tex]
= 0.00021
[tex]$D_{skinfriction} = \frac{1}{2} \rho V^2_{\infty}S C_f$[/tex]
[tex]$=\frac{1}{2} \times 1.225 \times 200^2 \times 17.5 \times 3 \times 0.00021$[/tex]
= 270 N
Therefore the net drag = 270 x 2
= 540 N
2. Using a giant screw, a crew does 650 J of work to drill a hole into a rock.
The screw does 65 J of work. What is the efficiency of the screw? Show your
work. Hellpppp
Answer:
42,250
Explanation:
It goes inside=
Displacemt
It does work=
Work done
To find efficiency of jule we do=
Dicplacement × Work done
650 × 65
42,250
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A baseball strikes the catcher's glove with a horizontal velocity of 40 m/s. The mass of the baseball is 0.15 kg. The displacement of the baseball due to the deformation of the catcher's glove and the movement of the catcher's hand is 8 cm from the instant it first makes contact with the glove until it stops. a. How much kinetic energy does the baseball possess just before it strikes the glove
Answer:
the kinetic energy is 120 J
Explanation:
a. The computation of the kinetic energy before it strikes the glove is as follows:
As we know that
The Kinetic energy is
= 1 ÷ 2 × m × v^2
= 1 ÷ 2 × (0.15)(40^2)
= 120 J
Hence, the kinetic energy is 120 J
Which is the best example of the use of imagery in a sentence?
Answer:
Common Examples of Imagery
Taste: The familiar tang of his grandmother's cranberry sauce reminded him of his youth. Sound: The concert was so loud that her ears rang for days afterward. Sight: The sunset was the most gorgeous they'd ever seen; the clouds were edged with pink and gold.
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Imagin you have mixed together some sand and salt Based on the venn diagram this mixture would be placed where
Answer:
a
Explanation:
ajjkiikkkkkhglutfgkitfgghiiij
You and a friend each hold a lump of wet clay. Each lump has a mass of 30 grams. You each toss your lump of clay into the air, where the lumps collide and stick together. Just before the impact, the velocity of one lump was < 3, 3, -3 > m/s, and the velocity of the other lump was < -4, 0, -4 > m/s. What is the velocity of the stuck-together lump just after the collision
Answer:
[tex]<-0.5, 1.5, -3.5>\ \text{m/s}[/tex]
Explanation:
[tex]u_1[/tex] = Velocity of one lump = [tex]3x+3y-3z[/tex]
[tex]u_2[/tex] = Velocity of the other lump = [tex]-4x+0y-4z[/tex]
m = Mass of each lump = [tex]30\ \text{g}[/tex]
The collision is perfectly inelastic as the lumps stick to each other so we have the relation
[tex]mu_1+mu_2=(m+m)v\\\Rightarrow m(u_1+u_2)=2mv\\\Rightarrow v=\dfrac{u_1+u_2}{2}\\\Rightarrow v=\dfrac{3x+3y-3z-4x+0y-4z}{2}\\\Rightarrow v=-0.5x+1.5y-3.5z=<-0.5, 1.5, -3.5>\ \text{m/s}[/tex]
The velocity of the stuck-together lump just after the collision is [tex]<-0.5, 1.5, -3.5>\ \text{m/s}[/tex].
If a force acts constantly on a stationary object, the object will
Answer:
accelerate in the direction of the force
Explanation:
Three collisions are elastic and three are inelastic. Determine which collision type took place for each collision. Support your conclusion with the data and observations from the lab.
Using your data, how are you able to determine if conservation of momentum occurs in each collision?
Write a conclusion for this lab. Also, make sure to discuss the conservation of momentum and how it applies to collisions.
Answer:
Explanation:
If objects stick together, then a collision is inelastic. When objects don't stick together, If the kinetic energy is the same, then the collision is elastic.
Consider the balloon and air inside the flask to be a closed system. Use the First Law of Thermodynamics to explain what happened to the balloon as heat was added by the environment.
Consider the balloon and air inside the flask to be in a closed system. Using the First Law of Thermodynamics to explain what happened to the balloon as heat was added by the environment.
Balloon will burst, due to more heat and in another flask air gets heated.
What is the first law of thermodynamics ?"The first law of thermodynamics states that energy can neither be created nor destroyed, only altered in form. For any system, energy transfer is associated with mass crossing the control boundary, external work, or heat transfer across the boundary. These produce a change of stored energy within the control volume."
What is heat ?"Heat is the energy that is transferred from one body to another as the result of a difference in temperature. If two bodies at different temperatures are brought together, energy is transferred i.e, heat flows—from the hotter body to the colder."
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The resistivity of blood is related to its hematocrit, the volume fraction of red blood cells in the blood. A commonly used equation relating the hematocrit h to the blood resistivity rho (in Ω⋅m) is rho=1.32/(1−h)−0.79. In one experiment, blood filled a graduated cylinder with an inner diameter of 0.90 cm. The resistance of the blood between the 1.0 cm and 2.0 cm marks of the cylinder was measured to be 198 Ω.
Required:
What was the hematocrit for this blood?
Answer:
[tex]0.35598[/tex]
Explanation:
r = Radius = [tex]\dfrac{0.9}{2}=0.45\ \text{cm}[/tex]
R = Resistance = [tex]198\ \Omega[/tex]
A = Area = [tex]\pi r^2[/tex]
l = Length of blood in cylinder = 1 cm
h = Hematocrit of the blood
Resistivity is given by
[tex]\rho=\dfrac{1.32}{1-h}-0.79[/tex]
Resistance is given by
[tex]R=(\dfrac{1.32}{1-h}-0.79)\dfrac{l}{\pi r^2}\\\Rightarrow h=1-\dfrac{1.32}{\dfrac{R\pi r^2}{l}+0.79}\\\Rightarrow h=1-\dfrac{1.32}{\dfrac{198\times \pi\times (0.45\times 10^{-2})^2}{0.01}+0.79}\\\Rightarrow h=0.35598[/tex]
The hematocrit of the blood is [tex]0.35598[/tex].
Can a particle move in a direction of increasing electric potential, yet have its electric potential energy decrease? Explain
Answer:
Explanation:
Yes , it is possible .
When a negative charge moves towards a positive charge , it is moving in the direction of increasing electrical potential . In the whole process , its electrical potential energy decreases and its kinetic energy increases .
Actually the potential energy of a negative charge near a positive charge is negative and it is inversely proportional to distance .
V = - Qq / R , When R decreases , the negative value of potential increases . That means potential energy decreases .
A rocket, with a mass of 5100 kg, has an engine that provides a net upward force of 8.0 x 10^5 N. It starts from rest and reaches a maximum speed of 900 m/s. How long does it take to reach that maximum velocity?
Answer:
5.7375 seconds
Explanation:
The computation of the time required to reach that maximum velocity is shown below:
Given that
Mass = m = 5100 kg
Net upward force F = 8 × times 10^5 N
Initial speed = V_i = 0
Maximum speed = V = 900 m.s
Based on the above information
Impluse J = m(V - V_i)
= 5100 (900 - 0)
= 459 × 10^4 kg m.s
As we know that
J = FT
So
T = J ÷ F
= (459 × 10^4) ÷ (8 × 10^5)
= 5.7375 seconds
A 40.0-kg packing case is initially at rest on the floor of a 1500-kg pickup truck. The coefficient of static friction between the case and the truck floor is 0.30, and the coefficient of kinetic friction is 0.20. Before each acceleration given below, the truck is traveling due north at constant speed. Find the magnitude and direction of the friction force acting on the case
(a) when the truck accelerates at 2.20m/s22.20m/s 2 northward and
(b) when it accelerates at 3.40m/s23.40m/s 2 southward.
Answer:
Before providing an answer to the question, the values for acceleration given in questions A and B were written twice. So correction would go like this: For (a) when the truck accelerates at 2.20m/s2 northward, and for (b) when it accelerates at 3.40m/s2 southward.
The answer:
(a) 88N, northward.
(b) 78.4, southward.
Explanation:
(a) Maximum frictional force acting on the packing case= (coefficient of static friction) X (Normal force)
Normal force = mass X acceleration due to gravity
Maximum static frictional force acting on the packing case = (coefficient of static friction) X (mass of packing case X acceleration due to gravity)
Maximum static frictional force = (0.30) X (40.0-kg) X (9.8m/s 2) = 117.6N
While Reaction force acting on the packing case = (mass of packing case) x (acceleration generated by the pickup truck)
Reaction force acting on the case = (40.0-kg) X (2.20m/s2) = 88N
With these values, one can conclude that the packing case is at rest since the reaction force of the case acting in the opposite direction is lesser than the frictional force. Making the magnitude and direction of the friction force acting on the case still move northward, and the static frictional force acting on equals the reaction force.
The answer is 88N, northward.
(b) Here too, we need to still compare the reaction force with the value of the already determined Maximum static frictional force (117.6N) above. This is necessary to know the frictional force between the pickup truck"s floor and the packing case.
Reaction force acting on the case when acceleration is 3.40m/s2 = (40.0-kg) X (3.40m/s2) = 136 N
We can conclude that the reaction force (136 N) is greater than the maximum static frictional force (117.6N), suggesting that the packing case is in motion and the frictional force is no longer static.
This means a kinetic force is now acting on the pickup truck"s floor causing the packing case to also move. This kinetic force can be calculated as:
kinetic force = (coefficient of kinetic friction) X (mass of packing case X acceleration due to gravity)
= (0,20) X (40.0-kg) X (9.8m/s 2) = 78.4N
(It made me choose physics as the category, but the class is Astronomy)
The Earth's Escape velocity, the velocity needed to escape the Earth's
gravitational field, is
