You spaceship has a snazzy lounge called Ten-Forward that needs a new spacecouch. Sadly the couch you bought is too long and won't fit into your car when it is stationary. The couch has a length Lc = 14.0 m and mass m = 49 kg, and your shuttlecraft has a length of L = 9.0 m How fast would you need to run, in terms of the speed of light c, in order to get the couch to fit inside the length of the shuttlecraft?
Answer:
v = speed
c = speed of light
using the equation
L = Lc Sqrt( 1 - (v/c)2)
9 = 14 Sqrt( 1 - (v/c)2)
v/c = 0.765
v = 0.765 c
A refrigerator has a coefficient of performance equal to 4.00. The refrigerator takes in 110 J of energy from a cold reservoir in each cycle. (a) Find the work required in each cycle. J (b) Find the energy expelled to the hot reservoir. J
Answer:
The correct answer is:
(a) 27.5 Joules
(b) 141.5 Joules
Explanation:
Given:
Energy,
[tex]Q_c = 110 \ J[/tex]
Coefficient of performance refrigerator,
[tex]Cop(refrig)=4[/tex]
(a)
As we know,
⇒ [tex]Cop(refrig) = \frac{Q_c}{Work}[/tex]
or,
⇒ [tex]Work=\frac{Q_c}{Cop(refrig)}[/tex]
[tex]=\frac{110}{4}[/tex]
[tex]=27.5 \ Joules[/tex]
(b)
⇒ [tex]Heat \ expelled = Heat \ removed +Work \ done[/tex]
or,
⇒ [tex]Q_h = Q_c+Work[/tex]
[tex]=114+27.5[/tex]
[tex]=141.5 \ Joules[/tex]
Which circuit element is of special importance in AC circuits?
A. Resistor
B. Ammeter
C. Battery
D. Capacitor
Answer:
Explanation:capacitor
Answer:
Ammeter
Explanation:
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1 A thing ring has a mass of 6kg and a radius of 20cm. calculate the rotational inertia.
Answer:
2400kgm²
Explanation:
Rotational inertia=mass x radius²
0
-
ZOOLS
6) The mass of a motorcycle is 250 kg. What is?
A) Its weight on Earth in Newtons?
B) Its weight on the moon (in Newtons)?
ges
C) The mass of your motorcycle on the moon?
Answer:
Explanation:
Weight is actually a force. A force can change depending on its location. A mass remains constant no matter where it is.
A)
F = m * a
m = 250 kg
a = 9.81 m/s^2
F = 250 * 9.81 = 2452.5 N
B)
The acceleration due to gravity on the moon is roughly 1/6 what it is on earth. You can check its value in your notes.
a = 9.81 + (1/6) = 1.635
m = 250
F = 250 * 1.635
F = 408.75
C)
The mass is the same anywhere in the universe.
250 kg
Determine the magnitude as well as direction of the electric field at point A, shown in the above figure. Given the value of k = 8.99 × 1012N/C.
Answer:
Electric field at A = 9.28 x 10¹² N/C
Explanation:
Given:
K = 8.99 x 10¹² N/C
Missing information:
Length = 11 cm = 11 x 10⁻² m
q = 12.5 C
Find:
Electric field at A
Computation:
Electric field = Kq / r²
Electric field at A = [(8.99 x 10¹²)(12.5)] / [11 x 10⁻²]²
Electric field at A = 9.28 x 10¹² N/C
A river is 87. meters wide and its current flows northward at 6 meters per second. A boat is launched with a velocity of 1.0 meters per second eastward from the west bank of the river. Determine the magnitude and direction of the boat’s resultant velocity as it crosses the river.
Answer:
explained
Explanation:
If a person rows a boat across a rapidly flowing river and tries to head directly for the other shore, the boat instead moves diagonally relative to the shore, as in Figure 1. The boat does not move in the direction in which it is pointed. The reason, of course, is that the river carries the boat downstream. Similarly, if a small airplane flies overhead in a strong crosswind, you can sometimes see that the plane is not moving in the direction in which it is pointed, as illustrated in Figure 2. The plane is moving straight ahead relative to the air, but the movement of the air mass relative to the ground carries it sideways.
A boat is trying to cross a river. Due to the velocity of river the path traveled by boat is diagonal. The velocity of boat v boat is in positive y direction. The velocity of river v river is in positive x direction. The resultant diagonal velocity v total which makes an angle of theta with the horizontal x axis is towards north east direction.
Figure 1. A boat trying to head straight across a river will actually move diagonally relative to the shore as shown. Its total velocity (solid arrow) relative to the shore is the sum of its velocity relative to the river plus the velocity of the river relative to the shore.
An airplane is trying to fly straight north with velocity v sub p. Due to wind velocity v sub w in south west direction making an angle theta with the horizontal axis, the plane’s total velocity is thirty eight point 0 meters per seconds oriented twenty degrees west of north.
Figure 2. An airplane heading straight north is instead carried to the west and slowed down by wind. The plane does not move relative to the ground in the direction it points; rather, it moves in the direction of its total velocity (solid arrow).
In each of these situations, an object has a velocity relative to a medium (such as a river) and that medium has a velocity relative to an observer on solid ground. The velocity of the object relative to the observer is the sum of these velocity vectors, as indicated in Figure 1 and Figure 2. These situations are only two of many in which it is useful to add velocities. In this module, we first re-examine how to add velocities and then consider certain aspects of what relative velocity means.
How do we add velocities? Velocity is a vector (it has both magnitude and direction); the rules of vector addition discussed in Chapter 3.2 Vector Addition and Subtraction: Graphical Methods and Chapter 3.3 Vector Addition and Subtraction: Analytical Methods apply to the addition of velocities, just as they do for any other vectors. In one-dimensional motion, the addition of velocities is simple—they add like ordinary numbers. For example, if a field hockey player is moving at 5 m/s
straight toward the goal and drives the ball in the same direction with a velocity of 30 m/s
relative to her body, then the velocity of the ball is 35 m/s
relative to the stationary, profusely sweating goalkeeper standing in front of the goal.
In two-dimensional motion, either graphical or analytical techniques can be used to add velocities. We will concentrate on analytical techniques. The following equations give the relationships between the magnitude and direction of velocity (
The figure shows components of velocity v in horizontal vx and in vertical y axis v y. The angle between the velocity vector v and the horizontal axis is theta.
Figure 3. The velocity, v, of an object traveling at an angle θ to the horizontal axis is the sum of component vectors and
These equations are valid for any vectors and are adapted specifically for velocity. The first two equations are used to find the components of a velocity when its magnitude and direction are known. The last two are used to find the magnitude and direction of velocity when its components are known.
an alternating voltage of 100V, 50HZ Is Applied across an impedance of (20-j30) calculate the resistance, the capacitance, current, the phase angle between current and voltage
The resistance R = 20 Ω
The capacitance C = 106.1 μF
The current, I is 2.773 A at 56.31°.
The phase angle of the between the current and the voltage is 56.31° leading.
Since the impedance Z = 20 - j30 Ω, the resistance, R is the real part of the impedance. So R = ReZ = 20 Ω
So, the resistance R = 20 Ω
To find the capacitance, we need first to find the reactance of the capacitor X. Since the impedance Z = 20 - j30, the reactance of the capacitor X. is the imaginary part of the impedance. So X = ImZ = 30 Ω.
Now the reactance of the capacitor X = 1/ωC where ω = angular frequency of the circuit = 2πf where f = frequency of the circuit = 50 Hz and C = capacitance
So, C = 1/ωX = 1/2πfX
Substituting the values of the variables into the equation, we have
C = 1/2πfX
C = 1/(2π × 50 Hz × 30 Ω)
C = 1/3000π
C = 1/9424.778
C = 1.061 × 10⁻⁴ F
C = 106.1 × 10⁻⁶ F
C = 106.1 μF
So, the capacitance is 106.1 μF
The current I = V/Z where V = voltage = 100 V at 0° and Z = impedance.
The magnitude of Z = √(20² + (-30)²)
= √(400 + 900)
= √1300
= 36.06 Ω
and its angle Φ = tan⁻¹(ImZ/ReZ)
= tan⁻¹(-30/20)
= tan⁻¹(-1.5) = -56.31°
So, V = 100 ∠ 0° and Z = 36.06 ∠ -56.31°
So, the current, I = V/Z = (100 ∠ 0°)/36.06 ∠ -56.31°
= 100/36.06 ∠(0° - (-56.31° ))
= 2.773 ∠ 56.31° A
So, the current is 2.773 A at 56.31°.
Since the current is 2.773 A at 56.31°, the phase angle of the between the current and the voltage is 56.31° leading.
So, the phase angle of the between the current and the voltage is 56.31° leading.
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A resistor is submerged in an insulated container of water. A voltage of 12 V is applied to the resistor resulting in a current of 1.2 A. If this voltage and current are maintained for 5 minutes, how much electrical energy is dissipated by the resistor
Explanation:
Given:
[tex]\Delta t = 5\:\text{min} = 300\:\text{s}[/tex]
[tex]V = 12 V[/tex]
[tex]I = 1.2 A[/tex]
Recall that power P is given by
[tex]P = VI[/tex]
so the amount of energy dissipated [tex]\Delta E[/tex] is given by
[tex]\Delta E = VI\Delta t = (12\:\text{V})(1.2\:\text{A})(300\:\text{s})[/tex]
[tex]\:\:\:\:\:\:\:= 4320\:\text{W} = 4.32\:\text{kW}[/tex]
The voltage in an EBW operation is 45 kV. The beam current is 50 milliamp. The electron beam is focused on a circular area that is 0.50 mm in diameter. The heat transfer factor is 0.87. Calculate the average power density in the area in watt/mm2.
Answer:
[tex]P_d=6203.223062W/mm^2[/tex]
Explanation:
From the question we are told that:
Voltage [tex]V=45kV[/tex]
Current [tex]I=50mAmp[/tex]
Diameter [tex]d=0.50mm[/tex]
Heat transfer factor [tex]\mu= 0.87.[/tex]
Generally the equation for Power developed is mathematically given by
[tex]P=VI\\\\P=45*10^3*50*10^{-3}[/tex]
[tex]P=2.250[/tex]
Therefore
Power in area
[tex]P_a=1400*0.87[/tex]
[tex]P_a=1218watt[/tex]
Power Density
[tex]P_d=\frac{P_a}{Area}[/tex]
[tex]P_d=\frac{1218}{\pi(0.5^2/4)}[/tex]
[tex]P_d=6203.223062W/mm^2[/tex]
A wheel is rotating freely at angular speed 530 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and with 9 times the rotational inertia of the first, is suddenly coupled to the same shaft. (a) What is the angular speed of the resultant combination of the shaft and two wheels
Answer: [tex]53\ rev/min[/tex]
Explanation:
Given
angular speed of wheel is [tex]\omega_1 =530\ rev/min[/tex]
Another wheel of 9 times the rotational inertia is coupled with initial wheel
Suppose the initial wheel has moment of inertia as I
Coupled disc has [tex]9I[/tex] as rotational inertia
Conserving angular momentum,
[tex]\Rightarrow I\omega_1=(I+9I)\omega_2\\\\\Rightarrow \omega_2=\dfrac{I}{10I}\times 530\\\\\Rightarrow \omega_2=53\ rev/min[/tex]
A diffraction grating has 6000 lines per centimeter ruled on it. What is the angular separation (in degrees) between the second and the third orders on the same side of the central bright fringe when the grating is illuminated with a beam of light of wavelength 500 nm
Explanation:
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The angular separation (in degrees) between the second and the third orders on the same side of the central bright fringe if the wavelength is 500 nm and A diffraction grating has 6000 lines per centimeter ruled on it, is 27.29°.
What is diffraction?Waves spreading outward around obstructions are known as diffraction. Sound, electromagnetic radiation like light, X-rays, and gamma rays, as well as very small moving particles like atoms, neutrons, and electrons that exhibit wavelike qualities all exhibit diffraction.
Given:
The number of lines = 6000 per cm,
The Wavelength, λ = 500 nm = 500 × 10 ⁻⁹ m
Calculate the diffraction grating,
[tex]d = 1 / no\ of\ lines[/tex]
d = 10⁻² / 6000 m,
Calculate the second-order maxima angle and third-order maxima angle by the formula given below,
[tex]dsin\theta_1 = n_1 \lambda[/tex]
[tex]sin\theta_1 = n_1\lambda / d[/tex]
[tex]\theta _1 = sin^{-1}[2\times 500\times 10 ^{-9}/10^{-2}\times 6000][/tex]
θ₁ = sin⁻¹(0.6)
θ₁ = 36.87°
Similarly, for θ₂,
θ₂ = sin⁻¹(3 × 500 × 10 ⁻⁹ / 10⁻² × 6000)
θ₂ = sin⁻¹(0.9)
θ₂ = 64.16°
Calculate the separation as follows,
θ₂ - θ₁ = 64.16° - 36.87°
θ₂ - θ₁ = 27.29°
Therefore, the angular separation (in degrees) between the second and the third orders on the same side of the central bright fringe if the wavelength is 500 nm and A diffraction grating has 6000 lines per centimeter ruled on it, is 27.29°.
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You place a 55.0 kg box on a track that makes an angle of 28.0 degrees with the horizontal. The coefficient of static friction between the box and the inclined plane is 0.680. a) Determine the static frictional force which holds the box in place. b) You slowly raise one end of the track, slowly increasing the incline of the angle. Determine the maximum angle that the incline can make with the horizontal so that the box just remains at rest. Ms 680 u Fgsin 281 Ffg Mgm r 680 55 4 8
Answer:
[tex]\theta=34 \textdegree[/tex]
Explanation:
From the question we are told that:
Mass [tex]m=55kg[/tex]
Angle [tex]\theta =28.0[/tex]
Coefficient of static friction [tex]\alpha =0.680[/tex]
Generally, the equation for Newtons second Law is mathematically given by
For
[tex]\sum_y=0[/tex]
[tex]N=mgcos \theta[/tex]
for
[tex]\sum_x=0[/tex]
[tex]F_{s}=mgsin\theta[/tex]
Where
[tex]F_{s}=\alpha*N\\\\F_{s}=\alpha*m*gcos \theta[/tex]
[tex]F_{s}=0.68*55*9.8*cos 28[/tex]
[tex]F_{s}=323.62N[/tex]
Therefore
[tex]\alpha mgcos \theta=mg sin \theta[/tex]
[tex]\theta=tan^{-1}(0.68)[/tex]
[tex]\theta=34 \textdegree[/tex]
(a) The static frictional force which holds the box in place is 323.62 N.
(b) The maximum angle that the incline can make with the horizontal is 34.2⁰.
Net forceThe net force applied to keep the box at rest must be zero in order for the box to remain in equilibrium position. Apply Newton's second law of motion to determine the net force.
∑F = 0
Static frictional forceThe static frictional force is calculated as follows;
Fs = μFncosθ
Fs = 0.68 x (55 x 9.8) x cos28
Fs = 323.62 N
Maximum angle the incline can makeFn(sinθ) - μFn(cosθ) = 0
mg(sinθ) - μmg(cosθ) = 0
μmg(cosθ) = mg(sinθ)
μ(cosθ) = (sinθ)
μ = sinθ/cosθ
μ = tanθ
θ = tan⁻¹(μ)
θ = tan⁻¹(0.68)
θ = 34.2⁰
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The speed of a sound wave
A. Depends on wavelength.
B. Depends on the medium.
C. Depends on amplitude.
D. None of the above.
Answer:
B) the medium
Explanation:
B. Depends on the medium.
A stationary horn emits a sound with a frequency of 228 Hz. A car is moving toward the horn on a straight road with constant speed. If the driver of the car hears the horn at a frequency of 246 Hz, then what is the speed of the car? Use 340 m/s for the speed of the sound
Answer: 26.84 m/s
Explanation:
Given
Original frequency of the horn [tex]f_o=228\ Hz[/tex]
Apparent frequency [tex]f'=246\ Hz[/tex]
Speed of sound is [tex]V=340\ m/s[/tex]
Doppler frequency is
[tex]\Rightarrow f'=f_o\left(\dfrac{v+v_o}{v-v_s}\right)[/tex]
Where,
[tex]v_o=\text{Velocity of the observer}\\v_s=\text{Velocity of the source}[/tex]
Insert values
[tex]\Rightarrow 246=228\left[\dfrac{340+v_o}{340-0}\right]\\\\\Rightarrow 366.84=340+v_o\\\Rightarrow v_o=26.8\ m/s[/tex]
Thus, the speed of the car is [tex]26.84\ m/s[/tex]
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What do scientists use to determine the temperature of a star?
Answer:
Measure the brightness of a star through two filters and compare the ratio of red to blue light. Compare to the spectra of computer models of stellar spectra of different temperature and develop an accurate color-temperature relation.
A mass is tired to spring and begins vibration periodically the distance between it's lowest position is 48cm what is the Amplitude of the vibration
Answer:
The amplitude of vibration of the spring is "24 cm"
The periodic vibrating body's motion follows a sinusoidal path. This sinusoidal path is illustrated in the attached picture.
From the picture, it can be clearly seen that the amplitude of the periodic vibration motion is the distance from its mean position to the highest point.
Since the distance of both the highest and the lowest points from the mean position is the same. Therefore, the distance between the lowest and the highest point must be equal to two times the amplitude of the wave.
Amplitude = 24 cm
a bullet is dropped from the same height when another bullet is fired horizontally. they will hit the ground
Answer:
it will drop simultaneously
One of the asteroids, Ida, looks like an elongated potato. Surprisingly it has a tiny (compared to Ida) spherical moon! This moon called Dactyl has a mass of 4.20 × 10^16 kg, and a radius of 1.57 × 10^4 meters, according to Wikipedia. Ida has a radius of 3.14 x 10^4 meters.
Find the acceleration of gravity on the surface of this little moon.
Answer:
g = 0.0114 m/s²
Explanation:
The value of acceleration due to gravity on the surface of the moon can be given by the following formula:
[tex]g = \frac{Gm}{r^2}[/tex]
where,
g = acceleration due to gravity on the surface of moon = ?
G = Universal Gravitational Constant = 6.67 x 10⁻¹¹ N.m²/kg²
m = mass of moon = 4.2 x 10¹⁶ kg
r = radius of moon = 1.57 x 10⁴ m
Therefore,
[tex]g= \frac{(6.67\ x\ 10^{-11}\ N.m^2/kg^2)(4.2\ x\ 10^{16}\ kg)}{(1.57\ x\ 10^4\ m)^2}[/tex]
g = 0.0114 m/s²
Vector a has a magnitude of 8 and makes an angle of 45 with positive x axis vector B has also the same magnitude of 8 units and direction along the
Answer:
prove that Sin^6 ϴ-cos^6ϴ=(2Sin^2ϴ-1)(cos^2ϴ+sin^4ϴ)
please sove step by step with language it is opt maths question
An oscillating particle has the equation x = 10cos(8πt +π ) (x in cm, t in s). The number of times the object passes through the equilibrium position in one second is
Answer:
x = A sin (wt + theta) where w = angular frequency - basic SHM equation
w = 8 pi = 2 pi f
f = 4 basic frequency
N = 8 number of times thru origin
Each cycle the particle will pass thru the origin +x and -x twice
Describe sound and record
Answer:
record is information created, received and maintained as evidence and information by an organization or person.in simpler terms it's a collection of of fields probably of different data types.
sound is however something loud or soft.which can be defined as vibrations that travel through the air or another medium.
I hope this helps
What are the multiple of meter ?
What are the sub multiple of meter?
Answer:
To cover a larger distance we use km(kilometre) , hm (hectometre) , and dac(decametre). These are called the multiples of Metre. For the distance is smaller , we use Dm (decimetre , cm(centimetre) and mm (millimetre) . These are called the submultiples of
A person runs up the stairs elevating his 102 kg body a vertical distance of 2.29 meters in a time of 1.32 seconds at a constant speed.
Determine the work done by the person climbing the stair case.
Answer:
Work done = 2289.084 Joules
Explanation:
Given the following data;
Mass = 102 Kg
Height = 2.29
Time = 1.32 seconds
We know that acceleration due to gravity, g = 9.8 m/s²
a. To find the work done by the person;
Here, work would be done in the form of gravitational potential energy.
Gravitational potential energy (GPE) is an energy possessed by an object or body due to its position above the earth.
Mathematically, gravitational potential energy is given by the formula;
G.P.E = mgh
Where;
G.P.E represents potential energy measured in Joules.
m represents the mass of an object.
g represents acceleration due to gravity measured in meters per seconds square.
h represents the height measured in meters.
Substituting into the formula, we have;
Work done = 102 * 2.29 * 9.8
Work done = 2289.084 Joules
A rugby player passes the ball 7.00 m across the field, where it is caught at the same height as it left his hand.
(a) At what angle was the ball thrown if its initial speed was 12.0 m/ s, assuming that the smaller of the two possible angles was used?
(b) What other angle gives the same range, and why would it not be used?
(c) How long did this pass take?
Answer:
a) θ = 14.23º, b) θ₂ = 75.77, c) t = 0.6019 s
Explanation:
This is a missile throwing exercise.
a) the reach of the ball is the distance traveled for the same departure height
R = [tex]\frac{v_o^2 \ sin 2 \theta }{g}[/tex]
sin 2θ = [tex]\frac{Rg}{v_o^2}[/tex]
sin 2θ = 7.00 9.8 / 12.0²
2θ = sin⁻¹ (0.476389) = 28.45º
θ = 14.23º
the complementary angle that gives the same range is the angle after 45 that the same value is missing to reach 90º
θ ’= 90 -14.23
θ’= 75.77º
b) the two angles that give the same range are
θ₁ = 14.23
θ₂ = 75.77
the greater angle has a much greater height so the time of the movement is greater and has a greater chance of being intercepted by the other team.
C) the time of the pass can be calculated with the expression
x = v₀ₓ t
t = x / v₀ₓ
t = 7 / 11.63
t = 0.6019 s
herical piece of candy is suspended in flowing water. The candy has a density of 1950 kg/m3 and has a 1.0 cm diameter. The water velocity is 1.0 m/s, the water density is assumed to be 1000.0 kg/m3, and the water viscosity is 1.010-3 kg/m/s. The diffusion coefficient of the candy solute in water is 2.010-9 m2/s, and the solubility of the candy solute in water is 2.0 kg/m3. Calculate the mass tran
Answer: Below is the complete question
A spherical piece of candy is suspended in flowing water. The candy has a density of 1950 kg/m3 and has a 1.0 cm diameter. The water velocity is 1.0 m/s, the water density is assumed to be 1000.0 kg/m3, and the water viscosity is 1.0x10-3 kg/m/s. The diffusion coefficient of the candy solute in water is 2.0x10-9 m2/s, and the solubility of the candy solute in water is 2.0 kg/m3. Calculate the mass transfer coefficient (m/s)
answer:
mass transfer coefficient = 9.56 * 10^-5 m/s
Explanation:
Candy density = 1950 kg/m^3
Candy diameter = 1 cm
Velocity of water = 1 m/s
water density = 1000 kg/m^3
Viscosity of water = 1 * 10^-3 kg/m/s
diffusion coefficient of candy in water = 2 * 10^-9 m^2/s
solubility of candy = 2 kg/m^3
Determine the mass transfer coefficient ( m/s )
( Sh) mass transfer coefficient ( flow across sphere ) = 2 + 0.6Re^1/2 * SC^1/3
where : Re = vdp / μ , Sh = KLd / Deff
attached below is the remaining solution .
mass transfer coefficient = 9.56 * 10^-5 m/s
A car is traveling at 118 km/h when the driver sees an accident 85 m ahead and slams on the brakes. What minimum constant deceleration is required to stop the car in time to avoid a pileup
Answer:
The constant minimum deceleration required to stop the car in time to avoid pileup is 6.32 m/s²
Explanation:
From the question, the car is traveling at 118 km/h, that is the initial velocity, u = 118km/h
The distance between the car and the accident at the moment when the driver sees the accident is 85 m, that is s = 85 ,
Since the driver slams on the brakes and the car will come to a stop, then the final velocity, v = 0 km/h = 0 m/s
First, convert 118 km/h to m/s
118 km/h = (118 × 1000) /3600 = 32.7778 m/s
∴ u = 32.7778 m/s
Now, to determine the deceleration, a, required to stop,
From one of the equations of motion for linear motion,
v² = u² + 2as
Then
0² = (32.7778)² + 2×a×85
0 = 1074.3841 + 170a
∴ 170a = - 1074.3841
a = - 1074.3841 / 170
a = - 6.3199
a ≅ - 6.32 m/s²
Hence, the constant minimum deceleration required to stop the car in time to avoid pileup is 6.32 m/s²
The temperature of a body falls from 30°C to 20°C in 5 minutes. The air
temperature is 13°C. Find the temperature after a further 5 minutes.
Answer:
15.88
is the correct answer
If a conducting loop of radius 10 cm is onboard an instrument on Jupiter at 45 degree latitude, and is rotating with a frequency 2 rev/s; What is the maximum emf induced in this loop? If its resistance is 0.00336 ohms, how much current is induced in this loop? And what is the maximum power dissipated in the loop due to its rotation in Jupiter's magnetic field?
Answer:
a) fem = - 2.1514 10⁻⁴ V, b) I = - 64.0 10⁻³ A, c) P = 1.38 10⁻⁶ W
Explanation:
This exercise is about Faraday's law
fem = [tex]- \frac{ d \Phi_B}{dt}[/tex]
where the magnetic flux is
Ф = B x A
the bold are vectors
A = π r²
we assume that the angle between the magnetic field and the normal to the area is zero
fem = - B π 2r dr/dt = - 2π B r v
linear and angular velocity are related
v = w r
w = 2π f
v = 2π f r
we substitute
fem = - 2π B r (2π f r)
fem = -4π² B f r²
For the magnetic field of Jupiter we use the equatorial field B = 428 10⁻⁶T
we reduce the magnitudes to the SI system
f = 2 rev / s (2π rad / 1 rev) = 4π Hz
we calculate
fem = - 4π² 428 10⁻⁶ 4π 0.10²
fem = - 16π³ 428 10⁻⁶ 0.010
fem = - 2.1514 10⁻⁴ V
for the current let's use Ohm's law
V = I R
I = V / R
I = -2.1514 10⁻⁴ / 0.00336
I = - 64.0 10⁻³ A
Electric power is
P = V I
P = 2.1514 10⁻⁴ 64.0 10⁻³
P = 1.38 10⁻⁶ W
