The ratio of F₂ : F₁ is 1 : 2
Newton's gravitation law states that the force of attraction between two objects can be formulated as follows:
F= Gm₁m₂/r²
F = Gravitational Force ( Newton )
G = Gravitation Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )
m = Object's Mass ( kg )
R = Distance Between Objects ( m )
Gravitational force on planet 1 = F₁
Gravitation force on planet 2 = F₂
mass of planet 1 = m₁
mass of planet 2 = m₂ = 2m₁
distance between planet 1 and star = R₁
distance between planet 2 and star = R₂ = 2R₁
ratio of force = F₂ : F₁ = ?
F₂ : F₁ = GMm₁/r₁² : GMm₂/r₂²
F₂ : F₁ = m₁/r₁² : m₂/r₂²
F₂ : F₁ = 2m₁/(2r₁)² : m₁/r₁²
F₂ : F₁ = (2/4) : 1
F₂ : F₁ = (1/2) : 1
F₂ : F₁ = 1 : 2
Therefore, the ratio of gravitation forces F₂ : F₁ is 1 : 2.
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Fillet Welds
Design a welded connection for an MC 9 ×23.9 of A572 Grade 50 steel connected to a 3⁄8-inch-thick gusset plate. The gusset plate is A36 steel. Show your results on a sketch, complete with dimensions.
a. Use LRFD. b. Use ASD.
The minimum weld size is 3/16 inch (based on the gusset plate thickness). Maximum size = 0.400- 1/16 0.338 in., or 5/16 in to the nearest 1/16 in.
LRFD solution,
P = 1.2D+1.6L 1.2(48)+ 1.6(120) = 249. 6 kips
Try w = 3/16 in.,
OR, 1.392 x 3 sixteenths = 4.176 kips/in.
The base metal shear yield strength (gusset plate controls) is 0.6F, t=0.6(36)
Shear rupture strength is 0.45F₁ = 0.45(58)() = 9.788 kips/in..
The weld strength of 4.176 kips/in. governs. Both longitudinal and transverse welds will be used. To determine the required length of the longitudinal welds, investigate the two options specified in AISC J2.4(c). First, assuming the same strength for both the longitudinal and transverse welds,
Total required length of weld= 249.6 4.176 59. 77 in.
length of longitudinal welds = 59.77-9.00 = 25.39 in.
For the second option, the strength of the longitudinal welds is 0.85(4.176) 3.550 kips/in.
and the strength of the transverse weld is 1.5(4.176) 6.264 kips/in.
The load to be carried by the longitudinal welds is
249.6-9(6.264) = 193.2 kips so the required length of the longitudinal welds is 193.2 2(3.550) 27.21 in.
To minimize the length of the connection, use the maximum weld size permitted. Use W 5/16 in.
PR. 1.392 x 5 sixteenths 6.96 kips/in
First, assuming the same strength for both the longitudinal and transverse welds,
249.6
total required length of weld= = 35.86 in.
6.96
length of longitudinal welds = 35.86-9.00 13. 43 in. 2
For the second option, the strength of the longitudinal welds is
0.85(6.96) 5.916 kips/in.
and the strength of the transverse weld is
1.5(6.96) 10.44 kips/in.
The load to be carried by the longitudinal welds is
249.6-9(10.44) = 155. 6 kips
so the required length of the longitudinal welds is
155.6/ 2(5.916) =13. 15 in.
The second option requires slightly shorter longitudinal welds. Try a 9-inch transverse weld and two 13½-inch longitudinal welds. Check the block shear strength of the gusset plate.
Agy Any 2x (13.5) 10. 13 in.2
Ant= (9) = 3.375 in.2
R = 0.6FA+Ubs FuAnt 0.6(58) (10.13)+ 1.0(58) (3.375) 548. 3 kips with an upper limit of 0.6FyAg+UbsFuAnt 0.6(36) (10.13)+1.0(58) (3.375) 414. 6 kips (controls) The design strength is OR, 0.75(414.6) 311 kips > 249.6 kips.
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shown from above in (figure 1) is one corner of a rectangular box filled with water. a laser beam starts 10 cm from side a of the container and enters the water at position x. you can ignore the thin walls of the container.
The minimum length required is 17.91 m when a laser beam starts 10 cm from side a of the container and enters the water at position x.
The output laser consists of a number of very closely spaced, discrete frequency components (very narrow spectral lines) covering a moderately broad spectral range. The discrete components are called laser modes and the spectral range they occupy is approximately the fluorescent line width of atomic transition giving rise to the laser output.
Laser oscillations occur, when the wave within the cavity replicate itself after two reflections so that the electric fields add in phase. In other words, the mirrors form a resonant cavity and standing wave patterns are setup.
In most high power applications for material processing or medical surgery, the laser is used as a mean for transferring the energy to the target. Thus there is no importance for the longitudinal laser modes.
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Colors seen on the cover of your physics book are due to color A) addition. B) subtraction. C) either of these D) neither of these.
Color subtraction produces the colours displayed on the cover of our physics book.
What is colour subtraction?
If the incident light and pigment colours are known, the colour subtraction approach can be a useful tool for predicting the ultimate colour appearance of an object. The complementary colour scheme can be used to identify the light colours that will be absorbed by a certain material. To identify the colours of reflected light (or transmitted light), subtract the incident light colours (if any are present). Thus, the colour appearance of the item may be predicted.
Color subtraction produces the colours displayed on the cover of our physics book.
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Parallel rays of monochromatic light with wavelength 573 nm illuminate two identical slits and produce an interference pattern on a screen that is 75.0 cm from the slits. The centers of the slits are 0.640 mm apart and the width of each slit is 0.434 mm.If the intensity at the center of the central maximum is 4.90×10−4 W/m2 , what is the intensity at a point on the screen that is 0.710 mm from the center of the central maximum?
Express your answer to three significant figures and include the appropriate units.
From three significant figures, the intensity at a point on the screen 0.830mm from the center of the central maximum is I = 8.64 × 10⁻⁶ W/m².
And the appropriate units are [tex]Watts/meter^{2}[/tex].
Monochromatic Light:
Single-wavelength light sources are known as monochromatic lights, where mono stands for only one and chroma for color. Monochromatic lights are defined as visible light that falls within a specific range of wavelengths. It has a wavelength that falls within a constrained wavelength range.
Given,
The wavelength of light; λ = 573 nm = 573 × 10⁻⁹ m
Distance of interference from slits; R = 75 cm = .75 m
Distance between the centers of slit; d = 0.640 mm = 0.00064 m
Width of each slit; a = 0.434 mm = 0.000434 m
Intensity at the central maxima; [tex]I_{o}[/tex] = 4.9 × 10⁻⁴ W/m²
Distance of intensity from the center of the central maximum; y = 0.710 mm = 0.00071 m
Let us first find the angle θ from the formula;
tanθ = y/R
tan θ = 0.00083/0.75
tan θ = 0.001107
θ = tan⁻¹0.001107
θ = 0.06343
θ is very small so
∅ = 2πdsinθ/λ
∅ = 7.7964 rad
Similarly, for the distance between the centers of the slit;
β = 2πasinθ/λ
β = 5.761 rad
For a position on the screen that is 0.830 millimeters from the center of the central maximum, the intensity is calculated as follows:
[tex]I =I_{0}(cos^{2} \frac{\phi}{2} ) [\frac{sin\frac{\beta }{2} }{\frac{\beta }2}} ]^{2}[/tex]
[tex]I=5*10^{-4}(cos^{2}(\frac{7.7964}{2} ) )[\frac{sin\frac{5.287}{2} }{\frac{5.287}{2}} ] ^{2}[/tex]
I = 8.6 × 10⁻⁶ W/m²
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A hockey puck attached to a horizontal spring oscillates on a
frictionless, horizontal surface. The spring has force constant 4.50 N/m and the oscillation period is 1.20 s. (a) What is the mass of the puck? (b) During an oscillation, the acceleration of the puck has maximum magnitude 1.20 m/s^2. What is the amplitude of the oscillation?
Answers:
(a) 0.164 kg
(b) 0.0438 m = 4.38 cm
(a) The mass of the puck is 0.16 kg
(b) The amplitude of the oscillation is 4.3 cm.
What is the mass of the puck?The mass of the puck is calculated by applying the formula for the period of the oscillation.
T = 2π √ ( m /k )
T / 2π = √ ( m /k )
T² / 4π² = m/k
m = k ( T² / 4π² )
where;
k is the spring constantT is the period of oscillationm is mass of the puckThe mass of the puck is calculated as;
m = 4.5 ( 1.2² / 4π²)
m = 0.16 kg
The amplitude of the oscillation is calculated as follows;
a = ω²A
where;
ω is the angular frequencyA is the amplitude a is the maximum accelerationω = √ ( k /m )
ω² = k / m
from this equation "a = ω²A" make amplitude "A" the subject of the formula.
A = a / ω²
A = (a) / (k / m)
A = ( 1.2 ) / ( 4.5 / 0.16)
A = (1.2) / ( 0.03556)
A = 0.043 m = 4.3 cm
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Given the following code snippet, what is considered an argument(s)?def mystery(num1, num2) :result = num1 ** num2return resultmystery(10, 2)
Result = num1 ** num2, return result, mystery(10, 2) 10, 2. You can provide a function more information by using an argument.
What do the code snippet's arguments and parameters mean?The variables used to define a function are known as parameters. They are variables that will be used in the function body and are present in the function signature. When we call a function, arguments are the real values that are supplied to it.
Which of the following describes how to write a function in Python correctly?A function is defined in Python by using the def keyword, which is followed by the function's name, parentheses, and a colon. Make sure to indent with a tab or 4 spaces the following step, and then specify.
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(11.2) Describe the expanding steady state model. Describe an observation that would test the predictions of the perfect cosmological principle. Is the steady state model in conflict with present observations of the universe?
calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of with the horizontal (see below). he exerts a force of 500 n on the crate parallel to the ramp and moves at a constant speed. be certain to include the work he does on the crate and on his body to get up the ramp.
The work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of with the horizontal 3.14 x 103 J.
We know that
F = w x d
given
d =4 m
mass of man = 85 kg
force exerted by man on block = 500 N
resolving mg will give mgsin\large \theta and mgcos\large \theta
Ftotal = Fm + 500
Ftotal = mgsin\large \theta + 500 = 85x 9.8 x sin20 + 500 = 284.902 + 500 = 784.902 N
W = Ftotal x d = 784.902 x 4 = 3139.61 = 3.14 x 103 J
In physics, work is energy transferred to or from an object by applying a force along a displacement. In its simplest form, if the constant force is aligned with the direction of travel, it equals the product of the force and the distance traveled.
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identify the correct statement from the following. classical physics is valid for matter speeds larger than the speed of light classical physics is valid for object size smaller than microscopic objects classical physics is valid under weak gravitational fields all of these options none of these options
Classical Physics is normally concerned with matter and energy on the normal scale of observation, while modern physics is caring with the behavior of matter and energy under extreme conditions or on a very large or very small scale.
For example, atomic and nuclear physics studies matter on the tiny scale at which chemical elements can be identified. The physics of elementary particles is on an even smaller scale since it is concerned with the most basic units of matter.
Classical Physics is also known as high-energy physics because of the extremely high energies required to produce many types of particles in particle accelerators.
On this scale, regular, commonsense notions of space, time, matter, and energy are no longer valid.
Computational modeling is essential for quantum and relativistic physics.
Classic physics is considered the limit of quantum mechanics for a large number of particles.
On the other side, classic mechanics is derived from relativistic mechanics. Like, in most of the formulations from special relativity, a correction factor (v/c)**2 appears, where v is the velocity of the object and c is the speed of light.
For velocities much minute than that of light, one can neglect the terms with c2 and higher that appear.
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a particle moving in a straight line with constant acceleration has a velocity of 3 ms-1 at one instant, and 5 seconds later, it has a velocity of 23 ms-1. The value of t is
A particle has a velocity of 3 m/s at one instant and a velocity of 23 m/s after 5 seconds when it is travelling straight forward with constant acceleration, then t=5sec at a displacement of 65m.
Acceleration, which refers to the rate at which velocity varies over time in terms of both speed and direction, has a value of t of 5 seconds. A point or object going straight ahead is accelerated when it accelerates or decelerates. Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. The equation a = v/t denotes acceleration (a), which is the change in velocity (v) over the change in time (t).
Total distance (S) = 23-3 = 20
Here v=23, u=3, time = 5sec
acceleration a= (v-u)/t
a=(23-3)/5
a=(20/5)
a=4
Now S=ut+ (1/2 *a *[tex]t^{2}[/tex])
S = 3(5) + (1/2 * 4 * 25)
S= 15+50
S= 65
t= 5 sec (time doesn't change here only displacement changes).
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when you urinate, you increase pressure in your bladder to produce the flow. for an elephant, gravity does the work. an elephant urinates at a remarkable rate of 0.0060 m3 (a bit over a gallon and a half) per second. assume that the urine exits 1.0 m below the bladder and passes through the urethra, which we can model as a tube of diameter 8.0 cm and length 1.2 m. assume that urine has the same density as water, and that viscosity can be ignored for this flow.
A model as a tube of diameter 8.0 cm and length 1.2 m. assume that urine has the same density as water, the pressure is -9088 pa.
Calculation :
v = flowrate/area = 0.0060/π(0.04)² = 1.2 m/s
2). from Bernoulli's eqn ,
[tex]P_{bla}[/tex] - [tex]P_{atm}[/tex] = [tex]\frac{1}{2}Pv _{2} ^{2}[/tex] + [tex]\frac{1}{2}Pv _{1} ^{2}[/tex] - ρgh1
[tex]P_{bla}[/tex] - [tex]P_{atm}[/tex] = [tex]\frac{1}{2}Pv _{2} ^{2}[/tex] + 0 - ρgh1
ΔP = 1/2(1000)(1.19)² - (1000)(9.8)(1)
= 712.4 - 9800
= -9088 pa
Pressure (symbol: p or P) is the force normal to the surface of an object per unit area over which that force is distributed.
Various units are used to express pressure. Some of these are units of force divided by units of area. For example, the SI unit of pressure, Pascal (Pa), is 1 Newton per square meter (N/m2).
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a 450 g air-track glider attached to a spring with spring constant 8.00 n/m is sitting at rest on a frictionless air track. a 450 g glider is pushed toward it from the far end of the track at a speed of 150 cm/s . it collides with and sticks to the 450 g glider. What are the amplitude and period of the subsequent oscillations?
The amplitude and period of the subsequent oscillations 112.5 m/s
First the law of conservation of momentum,
(m1 + m2)*vf = m1*(vi)1 + m2*(vi)2
m1 = 450g
vi1 = 0
m2 = 450g
vi2 = 150 cm/s
(450 + 150)*vf = 0 + 450* 150
600*vf = 67500
vf = 112.5 cm/s = 112.5 m/s
An indicator of a periodic variable's change over a single period is its amplitude. When measured against a standard value, a non-periodic signal's amplitude is its magnitude. Amplitude has several definitions, all of which (listed below) depend on how much the extreme values of the variable deviate from one another. The amplitude of a periodic function is occasionally referred to as the phase in older writings. Peak amplitude is frequently employed in audio system measurements, telecommunications tests, and other applications where the measurand is a signal that oscillates above and below a reference value but is not sinusoidal. The greatest absolute value of the signal is this if the reference is zero; the mean value of the reference.
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4. If μs between a basketball shoe and a court is 0.56, and the normal reaction
force acting on the shoe is 350 N, how much horizontal force is required to
cause the shoe to slide?
mu sub s times N is the frictional force
which equals 196 N
so 196 newton force is required for the shoe to slide
Answer: 196 N
Explanation: The coefficient of static friction (μs) between two surfaces represents the maximum horizontal force that can be applied to an object before it begins to slide. The formula for calculating the required horizontal force to cause an object to slide is:
F = μs * N
where F is the required horizontal force, μs is the coefficient of static friction, and N is the normal reaction force acting on the object.
In this case, the required horizontal force to cause the basketball shoe to slide is:
F = 0.56 * 350 N
F = 196 N
So, a horizontal force of 196 N is required to cause the basketball shoe to slide on the court.
An object undergoes uniform circular motion at a constant radius and with period T (i.e., it makes one complete revolution around the circle in time T). As a result, the magnitude of the centripetal acceleration of the object is ac. Suppose now the motion is changed so that the period is T/2 but the radius is the same. What will be the new magnitude of the centripetal acceleration? a. a/2 b. 2ac c. 4ac
Option C; The new magnitude of the centripetal acceleration 4ac
Initial condition time period = T
T = distance / speed = 2πR/v
T/2 = 2πR/V2
V2 = 4πR/T = 2V1
Centripetal acceleration,
Ac = 1/2mv² = 1/2 m4v1²
Ac = 4ac
As a characteristic of an object's motion when it is traveling along a circular path, centripetal acceleration is described. Centripetal acceleration is the motion of an item in a circle with its acceleration vector pointing in its direction of motion. Centripetal accelerations result from centripetal forces. The centripetal force driving the motion is a result of their gravitational pull in the unique instance of the Earth's round motion around the Sun, or any satellite's circular motion around any celestial body.
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A sample of an ideal gas goes through the process shown in Figure . From A to B, the process is adiabatic; from B to C, it is isobaric with 345 kJ of energy entering the system by heat; from C to D, the process is isothermal; and from D to A, it is isobaric with 371 kJ of energy leaving the system by heat. Determine the difference in internal energy E int,B −E int.A
A sample of an ideal gas goes through the process, the difference in internal energy [tex]E_{int},B - E_{int}.A[/tex] is 4.29 × 10⁴ J.
To calculate the difference in internal energy (ΔE_int) between points B and A, we need to consider the energy changes in each segment of the process and apply the First Law of Thermodynamics, which states:
Δ[tex]E_{int[/tex] = Q - W
where Δ[tex]E_{int[/tex] is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
Let's calculate the changes in internal energy for each segment:
1. From A to B (adiabatic process):
In an adiabatic process, no heat exchange (Q) occurs. Therefore, Q = 0.
The work done (W) in an adiabatic process is given by:
W = n * Cv * ( [tex]T_B[/tex] - [tex]T_A[/tex])
Since it is an ideal gas, the molar specific heat at constant volume (Cv) can be expressed as Cv = (f/2) * R.
The change in temperature ( [tex]T_B[/tex] - [tex]T_A[/tex]) can be found using the adiabatic equation:
( [tex]T_B[/tex] / [tex]T_A[/tex]) = [tex](V_A / V_B)^{(\gamma - 1)[/tex]
where γ is the adiabatic index or ratio of specific heats (γ = Cp/Cv).
2. From B to C (isobaric process):
In an isobaric process, the change in internal energy is given by:
Δ[tex]E_{int[/tex] = Q - W
W = P * ΔV
where P is the constant pressure and ΔV is the change in volume.
3. From C to D (isothermal process):
In an isothermal process, the temperature remains constant. Therefore, Δ[tex]E_{int[/tex] = 0.
4. From D to A (isobaric process):
Similar to the B to C segment, the change in internal energy is given by:
Δ[tex]E_{int[/tex] = Q - W
Given that the heat added from B to C is 345 kJ, and the heat released from D to A is 371 kJ, we can now calculate the difference in internal energy (Δ[tex]E_{int[/tex]) between points B and A.
Thus, if we sum up all the changes in internal energy for each segment, we get the desired value of Δ[tex]E_{int[/tex] which is approximately 4.29 × 10^4 J.
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a metal with a work function of 1.2 ev is illuminated by visible light with the full range of wavelengths, which we take to be 400 nm to 700 nm. What is the maximum kinetic energy, in electron volts, of the photoelectrons?
The maximum kinetic energy, in electron volts of the photoelectrons, is K.Emax = 1.8ev.
Solution:
E = Wo + K.Emax
= 3.10ev = 1.3ev + K.Emax
= K.Emax = 1.8ev
Kinetic energy is the energy that an object has when it moves. If you want to accelerate an object you have to apply a force. To add strength, we need our work. When the work is done, the energy is transferred to the object and it moves at a new constant speed.
Kinetic energy is the kinetic energy observable as the motion of a body particle or group of particles. All moving objects use kinetic energy. A person walking throwing a baseball crumbs falling from a table and charged particles in an electric field are examples of kinetic energy.
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When the current in a long, straight air-filled solenoid is changing at the rate of 3000 A/S, the voltage across the solenoid is 0.600 V. The solenoid has 1200 turns and uniform cross-sectional area 35.0 mm? Assume that the magnetic field is uniform inside the solenoid and zero outside, so the inductance formula L MAN/ 2/1 for a solenoid with N turns, uniform cross-sectional area A, and length 1, applies Part A What is the magnitude B of the magnetic field in the interior of the solenoid when the current in the solenoid is 3.00 A? Express your answer with the approppriate units. μΑ ? B= Value Units Submit Request Answer
The magnitude of B in the interior of the solenoid is 5 * 10⁻⁷ A/m.
Given that,
Rate of change of current = 3000 A/s
EMF induced ε = 0.6 V
Number of turns N = 1200 turns
Cross-sectional area A = 35 mm² = 35 * 10⁻⁶ m²
Current i = 3 A
We know the relation, ε = L* dI/dt
Making L as subject, L = ε / ( dI/dt )
Substituting the values, we have
L = 0.6 / 3000 = 0.0002 H
We know the relation between N, i, B and L as
N* B = L *i
Making B as subject, we have
B = L *i/N = (0.0002 * 3)/1200 = 0.0000005 A/m = 5 * 10⁻⁷ A/m
Thus, magnetic field in the interior of the solenoid is 5 * 10⁻⁷ A/m.
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The diameter of the solar system is 10 light hours. A spaceship crosses the solar system in 15 hours, as measured on earth. How long, in hours, does the passage take according to passengers on the spaceship? Hint:c1 light hour per hour.Previous question
According to the spaceship's passengers, the journey took 11.2 hours.
How long would it take to travel to the solar system's outermost point?
In reality, most of interstellar space is located within our solar system. Voyager 1 will need around 300 years to get to the inner edge of the Oort Cloud, and perhaps another 30,000 years to travel past it. The star that is currently closest to our solar system is Alpha Centauri.
Calculation:The spacecraft will travel across in t = 15 hours.
Since this can be measured with a single clock at both locations, the time measured in S' frame is the correct time.
The velocity is :v = 10lh /15 h
v = 2/3 c
Because Δt° = Δς
Δς = Δt√1 - β²
Δς = (15h)√1 - (2/3)²
Δς = 11.2 h
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A thin plastic rod of length 2.9 m is rubbed all over with wool, and acquires a charge of 60 nC, distributed uniformly over its surface. Calculate the magnitude of the electric field due to the rod at a location 8 cm from the midpoint of the rod. Do the calculation two ways, first using the exact formula for a rod of any length, and second using the approximate formula for a long rod.
(a) exact formula
E = N/C
(b) approximate formula
E = N/C
The magnitude of the electric field due to the rod at a location 8 cm from the midpoint of the rod is 2 N/C
E=F/Q
E=120/60
E=2 N/C
Any charge results in an electric field being connected to a specific location in space. The value of E, also known as the electric field strength, electric field intensity, or just the electric field, expresses the magnitude and direction of the electric field. Without any specific knowledge of what caused the field, knowing the value of the electric field at a particular location is sufficient to predict what will happen to nearby electric charges. The electric force F, or Coulomb force, exerted per unit positive electric charge q at that location may be used to calculate the strength of an electric field, or E = F/q, if the second charge, or test, is positive.
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Special relativity would predict slow running, and General Relativity would predict fast running, of a clock at the top of a tower at the
equator
The running of a clock at the top of a tower at the equator would be predicted by special relativity to be slow, and by general relativity to be fast.
The equator, which separates Earth's Northern and Southern hemispheres, is a circle of latitude with a radius of around 40,075 kilometers (24,901 mi). Halfway between the North and South poles, at 0 degrees latitude, is a fictitious line. Any other roughly spherical celestial body can likewise be referred to by this name.
The equator of a spinning spheroid, such as a planet, is the parallel (circle of latitude) where latitude is defined to be 0° in astronomical (3D) spatial geometry. It is a fictitious line that divides the spheroid into its northern and southern hemispheres and runs parallel to its poles. It is, in other words, the point at which the spheroid intersects the plane that is perpendicular to its axis of rotation.
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The position of an object at any time t is given by: s(t) = x4 + 21x3 + 17x2 + 4x + 33 1. Determine the velocity of the object at any time t. 2. Does the object ever stop changing its position?
Given [tex]s(t) = t^{4} + 21t^{3} + 17t^{2} + 4t +33[/tex]
The velocity of the object at time t is [tex]v(t) = 4t^{3} + 63t^{2} + 34t + 4[/tex]
We know that, velocity is change in position with respect to time.
Therefore, [tex]v(t) = \frac{d[s(t)]}{dt}[/tex]
And it is given that [tex]s(t) = t^{4} + 21t^{3} + 17t^{2} + 4t +33[/tex]
So, differentiating above equation with respect to time t, we get
[tex]\\v(t) = \frac{d[s(t)]}{dt}\\\\ v(t) = \frac{d[t^{4} + 21t^{3} + 17t^{2} + 4t +33]}{dt} \\\\v(t) = 4t^{3} + 63t^{2} + 34t + 4[/tex]
For the second part of the equation, we need to find out if acceleration ever becomes zero. If acceleration is zero, it means the will stop changing it's position.
Now, we know that acceleration is change in velocity with respect to time.
Therefore, [tex]a(t) = \frac{d[v(t)]}{dt}[/tex]
[tex]a(t) = \frac{d[4t^{3} + 63t^{2} + 34t + 4]}{dt} \\\\a(t) = 12t^{2} + 126t +34[/tex]
Since acceleration becomes zero at two values of time t, therefore we can say that it will stop changing position.
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a car starts from rest at a stop sign. it accelerates at 4.3 m/s2 for 6.4 s , coasts for 2.2 s , and then slows down at a rate of 3.5 m/s2 for the next stop sign.
The sum stop signs of the car that accelerates at 4.3 m/s² for 6.4 s, coasts for 2.2 s, and then slows down at a rate of 3.5 m/s² = 216.118 m.
Velocity and accelerationVelocity is a vector quantity that shows how fast an object moves from one place to another. A vector quantity is a term that is intended for a quantity that has both value and direction, meaning that the determination of the value of that quantity is based on direction.
The equation is:
V = s/t
Acceleration is the rate of increase in speed in a certain time expressed in units of meters per second squared (m/s²).
The function of speed is to determine how fast an object goes at a certain distance and is measured based on a vector quantity. Conversely, acceleration serves to change the speed of an object that is moving.
The equation is:
α = v/t
The question is not complete, it should be:
How far apart are the stop signs?
We have,
Acceleration = 4.3 m/s²
t = 6.4 s
First, determine the distance (1)
It's start from rest, so v₀ = 0
s₁ = (v₀t)₁ + ½ (at)₁²
= 0 + ½ (4.3) (6.4)²
= 88.064 m
Next, the distance (2)
a₂ = 0 m/s²
s₂ = (v₀t)₂ + ½ (at)₂²
= 0 + 20.812
= 20.812 m
The last, the distance (3)
s₃ = (v₀t)₃ + ½ (at)₃²
= (27.52) (8.6) + ½ (-3.5) (8.6)²
= 107.242 m
So, the sum stop sign = 88.064 m + 20.812 m + 107.242 m
= 216.118 m
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g two point charges q1 = 2.30 nc and q2 = -6.10 nc are 0.100 m apart. point a is midway between them; point b is 0.0800 m from q1 and 0.0600 m from q2 (figure 1). take the electric potential to be zero at infinity.for related problemsolving tips and strategies, you may want to view a video tutor solution of potential and potential energy.
The electric field is -641.25 volt, potential energy is -1.76x 10⁻³ J.
What is electric field ?
The term "electric field" or "electrostatic field" refers to the area surrounding an electric charge where stress or an electric force occur. A significant amount of tension might be produced in the area if the charge is of a big magnitude. The letter E is used to denote the electric field. Newtons per coulomb, or volts per metre, is the SI unit for the electric field.
What is potential energy ?
Potential energy is energy that is preserved or stored in a material or an item. The item or substance's position, organization, or condition determines the amount of stored energy. Consider it as energy with the "potential" to accomplish work.
Va = kq1/r1 + Kq2/r2
Va = 9 x 10/0.05 (2.3 x 10⁻⁹ – 6x 10⁹)
Va = -666 volt
Vb = 9x10⁹ (2.3x10⁻⁹/.08 – 6x10⁻⁹/.06)
Vb = -641.25 volt
Work done by electric field from b to a
W e = q(Vb-Va)
W e = 3x10⁻⁹ (-641.25+666)
W e = 74.25x10⁻⁹ J
W e = qEd = 30x 10⁻⁹x 3.2x10⁴x.63
W e = 6.05x10⁻⁴ J
W e = -qEd cos 45
W e = -30x10⁻⁹x3.2x10⁴x2.6 cos 45
W e = -1.76x 10⁻³ J
Therefore, electric field is -641.25 volt, potential energy is -1.76x 10⁻³ J.
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if the magnitude of the electric field due to the sphere at point p is ep, what is the magnitude of the field at point
The magnitude of the field at point is 1/4π∈od³ √q² d² + p²
E resulting from the dipole generated by charges at the very end.
Ex = Kp/d³ in x direction.
E due to the charge at center
Ey = Kq/d²
Net electric field is E = 1/4π∈od³ √q² d² + p²
"Distance. or quantity." is how magnitude. is simply. defined. It shows how an object moves when it is in motion, whether that movement is absolute, relative, or of a certain size. It serves as a way to describe something's size or scope. Magnitude is a term used in physics to describe either an amount or a distance. A force's strength is quantified by a number called its magnitude. Take a force of 10 N, for instance, in the direction of the east. The phrase "towards east" denotes a direction, and "10" represents the force's magnitude. The 'value' or 'amount' of any physical quantity is what is essentially meant by the term "magnitude." A automobile is travelling quicker than a bike, for instance, in terms of speed.
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The total horizontal distance traveled by the tennis ball during the entire time it is in the air is approximatelyA.23 m C.8.3 m B.17 m D.4.1 m.
The total horizontal distance traveled by the tennis ball during the entire time it is in the air is approximately: 23 m
What is horizontal distance?It is the line drawn horizontally from the viewer's eye. If an item is above the horizontal level, the angle of elevation is the angle created between the line of sight and horizontal level.
As we know,
H = [u(y)]²/2 g
or, H = (6.1)²/20
or, H = 1.86 m ≈ 1.9 m
Total max height = 1.9 m + 9.8 = 11 m
H = [u(y)]²/2g
or, 11 = [u(y)]²/20
or, u(y) = 14.832 m/s
u(x) = 7.6 m/sec
Now, R = u²sin 2θ/g
or, R = [2 u(x) u(y)] /g
or, R = [2×(7.6 )×( 14.832 )] / 10
or, R = 22.54 m
or, R = 23 m
Correct option: A
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colligative properties are those that depend on the identity and not the concentration of the solute those that depend on the concentration and not on the identity of the solute those that depend on the identity and the concentration of the solute those that do not depend on the amount or identity of the solute
Colligative properties are those of solutions that are influenced by the volume of a nonvolatile solute dissolved in a solution but not by the nature of the solute. The correct option to this question is both b and c
When solute molecules are dissolved in a certain solvent, solutions are created as homogenous mixtures. These solutions have special characteristics that could be referred to as collaborative qualities. These include melting point depression, osmotic pressure, rising boiling point, and reducing vapor pressure.
These solute molecules have an impact on vapor pressure, freezing point, and boiling points.
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Complete question :colligative
property depends on _____.
a. the identity of the solute
b. the concentration of the solution
c. the number of solute particles dissolved in the solution
d. both a and b
e. both b and c
15. Why are torque rods only really suitable for use in low Earth orbit?
The magnetic field is stronger.
The sensors are sensitive to gases.
The rotation is set at a fixed rate.
There is a limited amount of fuel.
Torque rods only really suitable for use in low Earth orbit due to the magnetic field is stronger option -1 is correct.
What is the process of a torque rod?By preventing the motor from rolling during the transfer of load, torque rods or torque roll restrictors reduce the effect of torque. The difficulties brought on by recovery functions are also addressed. They also stop vibration and noise from traveling from the motor block to the chassis, which limits motor roll.
Electromagnets used for attitude control on spacecraft are called torque rods. The spacecraft experiences a torque and changes in orientation when a current flows through the torque rod, creating a magnetic field that interacts with the geomagnetic field of the planet.
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which of the following sets of conditions is true for an exothermic reaction that is spontaneous at all temperatures?
An exothermic reaction that is spontaneous at any temperature meets the following criteria. ∆H < 0 , ∆S > 0 , ∆G < 0
This is because G = H - T S, and since -T S is always negative, if H is negative and S is positive, then G will always be negative.
Exothermic reactions (H0) characterize combustion. Due to the additional rise in the amount of gaseous species (net gain of one mole of gas, S > 0), this specific reaction entails an increase in entropy. As a result, the reaction is spontaneous (G0) at all temperatures. The sign of G will always be negative when H is negative and S is positive, and the reaction will always be spontaneous at all temperatures.
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complete question: Which of the following sets of conditions is true for an exothermic reaction that is spontaneous at all temperatures?
(a)∆H < 0 , ∆S < 0 , ∆G < 0
(b)∆H > 0 , ∆S < 0 , ∆G < 0
(c)∆H < 0 , ∆S < 0 , ∆G > 0
(d)∆H > 0 , ∆S < 0 , ∆G < 0
(e)∆H < 0 , ∆S > 0 , ∆G < 0
A kettle is rated as 2.3kW. A mass of 750g of water at 20oC is poured into the kettle.When the kettle is switched on, it takes 2.0 minutes for the H2O to start boiling. In a further 7.0 minutes, half of the mass of H2O is boiled away. Estimate for this water: The specific heat capacity, the specific latent heat of vaporization.
The specific heat capacity of water, Cw is 4.6 J/g/K
The specific latent heat of vaporization of water, Cv is 2576 J/K
What is the amount of energy used by the kettle?Electrical energy is defined as the product of electrical power in watts and time in seconds.
Mathematically;
Electrical energy = power * time
The amount of energy used by the kettle to boil the water is calculated below:
Energy used = 2.3 kW * 1000 W/kW * 2 * 60 s/min
Energy used = 276000 J
The specific heat capacity of water, Cw is determined as follows:
Energy = mass * Cw * temperature change
Cw = Energy / mass * temperature change
Cw = 276000 / 750 * (100°C - 20°C)
Cw = 4.6 J/g/K
The amount of energy used by the kettle to evaporate half the mass of the water is calculated below:
Energy = 2.3 kW * 1000 W/kW * 7 * 60 s/min
Energy used = 966000 J
The specific latent heat of vaporization of water, Cv is determined as follows:
Energy = mass * Cv
Cv = Energy / mass
Cv = 966000 / (750 * 0.5)
Cv = 2576 J/K
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Your camping buddy has an idea for a light to go inside your tent. He happens to have a powerful (and heavy!) horseshoe magnet that he bought at a surplus store. This magnet creates B = 0.15 T field between two pole tips 10 cm apart. His idea is to build a hand-cranked generator shown in Figure. He thinks you can make enough current to fully light a R = 1.0 ? lightbulb rated at 4.0W. That's not super bright, but it should be plenty of light for routine activities in the tent.
Crank 1.0 ?/4.0 w bulb
A. Find an expression for the induced current as a function of time if you turn the crank at frequency f. Assume that the semicircle has a radius of r = 5.0 cm and it is at its highest point at t = 0 s. Express your answer in terms of some or all of the variables B, R, r, f, t, and the constant ?.
B. With what frequency will you have to turn the crank for the maximum current to fully light the bulb?
C. Is this feasible? (Yes or no)
The equation for the induced current as a function of time when the crank is turned at frequency f is I = 2*pi*r2*B*Force(sin (2*pi*force*t))/R. You will need to turn the crank at a frequency of 540.54 Hz.
To completely illuminate the bulb requires the maximum current. Furthermore, this frequency is not practical. The current that results from electromagnetic induction is known as the induced current. The production of electric power relies heavily on electromagnetic induction. Several methods exist for producing this change, including altering the magnetic field's strength,
B, r, R, f, and t are words that describe induced current.
I = E/R = r2*B*2pi*force*sin(2*pi*force*t)/R
Max current Imax = 3.70*10-3 = Imax/3.70*10-3 P = I2/R
Imax = ((4)1/2)/2 AMP F = (2.3.70*10-3) = 540.54Hz
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