Answer:
2.1 rad(anticlockwise).
Explanation:
So, we are given the following data or parameters or information in the question above:
=> "The torsional stiffness of the spring support is k = 50 N m/rad. "
=> "If a concentrated torque of mag- nitude Ta = 500 Nm is applied in the center of the bar"
=> "L = 300 mm Assume a shear modu- lus G = 10 kN/mm2 and polar monnent of inertia J = 2000 mln"
Hence;
G × J = 10 kN/mm2 × 2000 mln = 20 Nm^2.
Also, L/2 = 300 mm /2 = 0.15 m (converted to metre).
==> 0.15/20 (V - w) + θ = 0.
==> 0.15/20 (V - w ) = -θ.
Where V = k = 50 N m/rad
w = 183.3 θ.
Therefore, w + Vθ = 500 Nm.
==> 183.3 + 50 θ = 500 Nm.
= 6.3
Anticlockwise,
θ = 2.1 rad.
Suppose you have a lens system that is to be used primarily for 775-nm light. What is the second thinnest coating of fluorite (calcium fluoride) that would be non-reflective for this wavelength?
Answer:
406 nm
Explanation:
We are given;
Wavelength; λ = 775 nm
Refractive index of Calcium fluoride with wavelength of 775 nm as seen in the graph attached is approximately 1.4308.
n = 1.4308
Formula for the thickness of the film that would destruct the light is;
t = (m + 0.5)(λ/2n)
Where m is the order of the thickness.
The first smallest thickness is at m = 0 while the second smallest thickness is at m = 1.
Thus;
t = (1 + 0.5)(775/(2 × 1.4308))
t ≈ 406 nm
5.
Find the equation of the circle tangential to the line 3x-4y+1=0 and with
centre at (4,7).
20
Answer: (x - 4)² + (y - 7)² = 9
Explanation:
The equation of a circle is: (x - h)² + (y - k)² = r² where
(h, k) is the centerr is the radiusGiven: (h, k) = (4, 7)
Find the intersection of the given equation and the perpendicular passing through (4, 7).
3x - 4y = -1
-4y = -3x - 1
[tex]y=\dfrac{3}{4}x-1[/tex]
[tex]m=\dfrac{3}{4}[/tex] --> [tex]m_{\perp}=-\dfrac{4}{3}[/tex]
[tex]y-y_1=m_{\perp}(x-x_1)\\\\y-7=-\dfrac{4}{3}(x-4)\\\\\\y=-\dfrac{4}{3}x+\dfrac{16}{3}+7\\\\\\y=-\dfrac{4}{3}x+\dfrac{37}{3}[/tex]
Use substitution to find the point of intersection:
[tex]x=\dfrac{29}{5}=5.8,\qquad y=\dfrac{23}{5}=4.6[/tex]
Use the distance formula to find the distance from (4, 7) to (5.8, 4.6) = radius
[tex]r=\sqrt{(5.8-4)^2+(4.6-7)^2}\\\\r=\sqrt{3.24+5.76}\\\\r=\sqrt9\\\\r=3[/tex]
Input h = 4, k = 7, and r = 3 into the circle equation:
(x - 4)² + (y - 7)² = 3²
(x - 4)² + (y - 7)² = 9
A sharp edged orifice with a 50 mm diameter opening in the vertical side of a large tank discharges under a head of 5m. If the coefficient of contraction is 0.62 and the coefficientof velocity is 0.98, what is thedischarge?
Answer:
0.24
Explanation:
See attached file
The sound intensity at a distance 2.00 m from a sound source is 5.00 Find the total sound energy emitted by the source in each second.
Answer:
P = 251, 3 W
Explanation:
The intensity is defined as the power emitted per unit area
I = P / A
Since sound is distributed in all directions spherical shape, the area of a sphere is
A = 4π r²
let's clear the power and replace
P = I A
P = I (4π r²)
let's calculate
P = 5.00 (4π 2²)
P = 251, 3 W
A copper telephone wire has essentially no sag between poles 36.0 m apart on a winter day when the temperature is −20.0°C. How much longer is the wire on a summer day when the temperature is 34.0°C?
Answer:
The extension is [tex]\Delta L = 0.033 \ m[/tex]
Explanation:
From the question we are told that
The length of the wire on a winter day is [tex]L_w = 36.0 \ m[/tex]
The temperature on the winter day is [tex]T_w = -20.0 ^o C[/tex]
The temperature on a summer day is [tex]T_s = 34.0 ^0 C[/tex]
The the extension of the wire on a summer day is mathematically represented as
[tex]\Delta L = \alpha L_w [T_s - T_w][/tex]
Where
[tex]\alpha[/tex] is the coefficient of linear expansion of copper with a values [tex]\alpha = 17 *10^{-6}[/tex]
substituting value
[tex]\Delta L = 17 *10^{-6} * 36.0 [34 - [-20]][/tex]
[tex]\Delta L = 0.033 \ m[/tex]
a 5 charge is locataed 1.25 m to the left of a -3 charge. What is the magnitude and direction of the electrostatic force on the postive charge
Answer:
The force is 86.5×10^9 N towards the negative charge (to the right)
Explanation:
The electrostatic force on the charges is given by Coulomb's law;
F= Kq1q2/r^2
This an inverse square law.
F= electrostatic force on the charges
K= constant of Coulomb's law
q1 and q2= magnitude of the charges
Since K= 9.0×10^9Nm^2C^2
F= 9.0×10^9 × 5 × 3/(1.25)^2 = 135×10^9/1.56
F= 86.5×10^9 N
The force is 86.5×10^9 N towards the negative charge.
A stone is thrown vertically upward with a speed of 29.0 m/s and when it reaches a height of 13 m, the velocity is 24.2 m/s.
Using the formula x = v0 • t + ½ • a • t2, find the time it takes to reach this height? Why do you get two values for time? Explain.
Answer:
the value of t = 0.49 seconds shows that its upward journey
and
at t = 5.43 seconds shows in downward journey
Explanation:
Given:
initial speed, u = 29 m/s
acceleration due to gravity, g = - 9.8 m/s^2
h = 13 m
Let it is moving with velocity v at a height of 13 m.
Use third equation of motion
v² = u² + 2gh
By substituting the values
v² = 29² - (2 * 9.8 * 13)
v = sqrt 585.94
v = 24.2 m/s
Let it takes time t to reach at height 13 m
Use second equation of motion
s = u * t + 1/2 * g * t²
13 = 29t - 4.9t²
4.9t² - 29t + 13 = 0
using quadratic equation to solve time
29 ± [tex]\sqrt{29^2 - 4 * 4.9 * 13}\\[/tex]
t = ------------------------------------
2 * 4.9
t = 5.43 second or t = 0.49 second
Therefore...
the value of t = 0.49 seconds shows that its upward journey
and
at t = 5.43 seconds shows in downward journey
Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than Earth's. Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than Earth's. Kepler-62e is an exoplanet that orbits within the habitable zone around its parent star. The planet has a mass that is 3.57 times larger than Earth's and a radius that is 1.61 times larger than Earth's. Calculate the acceleration of gravity on the surface of Kepler-62e.
Answer:
g' = 13.5 m/s²
Explanation:
The acceleration due to gravity on surface of earth is given by the formula:
g = GMe/Re² --------------- euation 1
where,
g = acceleration due to gravity on surface of earth
G = Universal Gravitational Constant
Me = Mass of Earth
Re = Radius of Earth
Now, the the acceleration due to gravity on the surface of Kepler-62e is:
g' = GM'/R'² --------------- euation 1
where,
g' = acceleration due to gravity on surface of Kepler-62e
G = Universal Gravitational Constant
M' = Mass of Kepler-62e = 3.57 Me
R' = Radius of Kepler-62e = 1.61 Re
Therefore,
g' = G(3.57 Me)/(1.61 Re)²
g' = 1.38 GMe/Re²
using equation 1:
g' = 1.38 g
where,
g = 9.8 m/s²
Therefore,
g' = 1.38(9.8 m/s²)
g' = 13.5 m/s²
A record player rotates a record at 45 revolutions per minute. When the record player is switched off, it makes 4.0 complete turns at a constant angular acceleration before coming to rest. What was the magnitude of the angular acceleration (in rads/s2) of the record as it slowed down
Answer:
The angular acceleration is [tex]\alpha = 0.4418 \ rad /s^2[/tex]
Explanation:
From the question we are told that
The angular speed is [tex]w_f = 45 \ rev / minutes = \frac{45 * 2 * \pi }{60 }= 4.713 \ rad/s[/tex]
The angular displacement is [tex]\theta =4 \ rev = 4 * 2 * \pi = 25.14 \ rad[/tex]
From the first equation of motion we can define the movement of the record as
[tex]w_f ^2 = w_o ^2 + 2 * \alpha * \theta[/tex]
Given that the record started from rest [tex]w_o = 0[/tex]
So
[tex]4.713^2 = 2 * \alpha * 25.14[/tex]
[tex]\alpha = 0.4418 \ rad /s^2[/tex]
3) If a ball launched at an angle of 10.0 degrees above horizontal from an initial height of 1.50 meters has a final horizontal displacement of 3.00 meters, what is its launch velocity
Answer:
35.6 m
Explanation:
The given ball possesses a projectile motion from its initial height. So, the required launch velocity of the ball is 6.55 m/s.
What is launch velocity?The horizontal component of velocity during the projection of an object is known as launch velocity. It is obtained when the horizontal range is known.
Given data -
The angle of projection is, [tex]\theta = 10.0 {^\circ}[/tex].
The initial height of the projection is, h = 1.50 m.
The horizontal displacement is, R = 3.00 m.
The mathematical expression for the horizontal displacement (Range) of the projectile is given as,
[tex]R = \dfrac{u^{2} \times sin2 \theta}{g}[/tex]
here,
u is the launch velocity.
g is the gravitational acceleration.
Solving as,
[tex]u =\sqrt{\dfrac{R \times g}{sin2 \theta}}\\\\\\u =\sqrt{\dfrac{1.50 \times 9.8}{sin(2 \times 10)}}\\\\\\u =\sqrt{\dfrac{1.50 \times 9.8}{sin20^\circ}}\\\\\\u=6.55 \;\rm m/s[/tex]
Thus, we can conclude that the required launch velocity of the ball is 6.55 m/s.
Learn more about the projectile motion here:
https://brainly.com/question/11049671
At 30.0 m below the surface of the sea (density = 1 025 kg/m3), where the temperature is 5.00°C, a diver exhales an air bubble having a volume of 0.95 cm3. If the surface temperature of the sea is 20.0°C, what is the volume of the bubble just before it breaks the surface?
Answer:
The volume is [tex]V_a = 1.510 *10^{-5} m^3[/tex]
Explanation:
From the question we are told that
The depth below the see is [tex]d_1 = 30.0 \ m[/tex]
The density of the sea is [tex]\rho_s = 1025 \ kg /m^3[/tex]
The temperature at this level is [tex]T_d = 5.00 ^oC = 278 \ K[/tex]
The volume of the air bubble at this depth is [tex]V_d = 0.95 \ cm^3 = 0.95 *0^{-6}\ m[/tex]
The temperature at the surface is [tex]T_a = 20^oC =293\ K[/tex]
Generally the pressure at the given depth is mathematically evaluated as
[tex]P_d = P_o + \rho_s * g * d[/tex]
Where [tex]P_o[/tex] is the atmospheric pressure with a constant value
[tex]P_o = 1.013 *10^{5} \ Pa[/tex]
substituting values
[tex]P_d = 1.013 * 10^{5} * + (1025 * 9.8 * 30 )[/tex]
[tex]P_d = 4.02650 * 10^{5} \ Pa[/tex]
According to the combined gas law
[tex]\frac{P_a * V_a }{T_a } = \frac{P_d * V_d }{T_d }[/tex]
=> [tex]V_a = \frac{4.026650 *10^{5} * 0.95 *10^{-6} * 293 }{278 * 1.013*10^{5} }[/tex]
=> [tex]V_a = 1.510 *10^{-5} m^3[/tex]
which of the following statements describes the formation of acid rain?...A. acid rain forms from human activities and lowers the pH of rainwater below 7 B. acid rain forms naturally and lowers the pH of rainwater below 7 C. acid rain forms from human activities raises the pH of rainwater above 7 D. acid rain forms naturally and raises the pH of rainwater above 7
The correct answer is A. Acid rain forms from human activities and lowers the pH of rainwater below 7
Explanation:
The term "acid rain" is used to refer to rainwater with a low pH or a high acidity, this includes rainwater with a pH below 7 (solutions with a pH under 7 are acidic). In terms of formation, acid rain is mainly the result of human activities such as factories or cars that release pollutants into the atmosphere including nitric and sulfuric acids and these alter the natural pH of rain and makes it more acidic. Additionally, acid rain has negative consequences such as the death of fishes and other organisms in lakes, rivers, etc. because the acidity is toxic to many organisms. Thus, acid rain is the result of human activities and it lowers the pH of rain (Option A).
A student builds a rocket-propelled cart for a science project. Its acceleration is not quite high enough to win a prize, so he uses a larger rocket engine that provides 39% more thrust, although doing so increases the mass of the cart by 13%. By what percentage does the cart's acceleration increase?
Answer:
Explanation:
a = F / m
where a is acceleration , F is thrust and m is mass
taking log and differentiating
da / a = dF / F - dm / m
(da / a)x 100 = (dF / F)x100 - (dm / m) x100
percentage increase in a = percentage increase in F - percentage increase in m
= percentage increase in acceleration a = 39 - 13 = 26 %
required increase = 26 %.
Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical gasoline tank 3 meters in diameter and 6 meters long is carried on the back of a truck and is used to fuel tractors. The axis of the tank is horizontal. The opening on the tractor tank is 5 meters above the top of the tank in the truck. Find the work done in pumping the entire contents of the fuel tank into the tractor.
Answer:
work done in pumping the entire fuel is 1399761 J
Explanation:
weight per volume of the gasoline = 6600 N/m^3
diameter of the tank = 3 m
length of the tank = 6 m
The height of the tractor tank above the top of the tank = 5 m
The total volume of the fuel is gotten below
we know that the tank is cylindrical.
we assume that the fuel completely fills the tank.
therefore, the volume of a cylinder =
where r = radius = diameter ÷ 2 = 3/2 = 1.5 m
volume of the cylinder = 3.142 x x 6 = 42.417 m^3
we then proceed to find the total weight of the fuel in Newton
total weight = (weight per volume) x volume
total weight = 6600 x 42.417 = 279952.2 N
therefore,
the work done to pump the fuel through to the 5 m height = (total weight of the fuel) x (height through which the fuel is pumped)
work done in pumping = 279952.2 x 5 = 1399761 J
water and air are both fluids. why is it easier to lift a rock in water rather thatn lifting a rock in air? a the force of gravity. b the bouyant force is greater on the rock in water. c the bouyant force is greater on the rock in air. d the force of gravity on the rock is less in water.
Answer:
The answer is option b.the buoyant force is greater on the rock in water.
How much heat is required to convert 500g of liquid water at 28°C into steam at 150°C? Take the specific heat capacity of water to be 4183J/kg°C and the latent heat of vaporization to be 2.26×10⁶J/kg
Answer:
1,327,063Joules
Explanation:
Heat energy is the energy needed to convert the state of a body from one phase to another.
According to the question, we want to calculate the total heat required to convert water into vapour (steam).
Note that before water can vapourize, it has to reach the boiling point first which is at 100°C. Heat energy needed to convert the water to 100°C is expressed as H1 = mcΔθ
m is the mass of the object in kg =0.5kg
c is the spcific heat capacity of water = 4183J/kg°C
Δθ is the change in temperature = 100-28 = 72°C
H1 = 0.5*4183*72
H1 = 150,588Joules
Energy required to convert the water to team H2 =mLsteam
Lsteam is the latent heat of vaporization = 2.26×10⁶J/kg
H2 = 0.5*2.26×10⁶
H2 = 1130000Joules
Heat energy needed to convert the water to 150°C is expressed as H3 = mcΔθ
m is the mass of the object in kg =0.5kg
c is the spcific heat capacity of steam= 1859J/kg°C
Δθ is the change in temperature = 150-100 = 50°C
H3 = 0.5*1859*50
H1 = 46,475Joules
Total Heat requires = H1+H2+H3 = 150,588Joules+1130000Joules+ 46,475Joules = 1,327,063Joules
Two unknown resistors are connected together. When they are connected in series their equivalent resistance is 15 Ω. When they are connected in parallel, their equivalent resistance is 3.3 Ω. What are the resistances of these resistors?
Explanation:
Let x and y are two unknown resistors. When they are connected in series their equivalent resistance is 15 Ω. When they are connected in parallel, their equivalent resistance is 3.3 Ω.
For series combination,
[tex]x+y=15[/tex] ......(1)
For parallel combination,
[tex]\dfrac{1}{x}+\dfrac{1}{y}=3.3[/tex] ....(2)
We need to find the resistances of these resistors. Solving equation (1) and (2) we get :
x = 0.29 and y = 14.7
Hence, the resistances of these resistors are 0.29 ohms and 14.7 ohms.
Kevin is a black high school senior. While walking home from a sporting event at school, he sees a police car and decides to take another street to avoid it. He worries that the police will stop and question him even though he has not done anything wrong. Which theory explains this thought process? Dramaturgy Social construction of reality Social exchange theory Ethnomethodology
Answer:
Ethnomethodology theory
Explanation:
Take note of the fact that we are told Kevin worries that the police will stop and question him even though he has not done anything wrong.
This statement shows us that Kevin already understood his society from past experiences, and thus he tries to avoid social interactions with particular member of his society (the police) who may be show discrimination towards him.
16. When a plastic rod is rubbed with fur, the rod will become negatively charged. Which of the following best explains how this happens? A. Electrons are transferred from the plastic rod to the fur. B. Electrons are transferred from the fur to the plastic rod. C. Negative charges are created on the plastic rod. D. Positive charges are removed from the plastic rod.
Answer:
B. Electrons are transferred from the fur to the plastic rod.
Explanation:
Triboelectricity or friction charging refers to the ability of materials to gain or lose electrons as a result of rubbing them against something. This phenomenon has been observed in the case of rubbing plastic rod against fur, or glass rod against silk.
In the context of rubbing plastic rod against fur, what happens is that the fur which has an excess of charges loses electrons to the plastic rod. This makes the plastic rod to become positively charged, and the fur, negatively charged.
You are caulking a window. The caulk is rather thick and, to lay the bead correctly, the exit nozzle is small. A caulking gun uses a plunger which is operated by pulling back on a handle. You must squeeze the handle very hard to get the caulk to come out of the narrow opening because
Answer:
The answer is
A. Pressure is distributed uniformly throughout the fluid and the area of the plunger is much larger than the area of the opening.
Explanation:
The question is incomplete, here is a complete question with full options
You are caulking a window. The caulk is rather thick and, to lay the bead correctly, the exit nozzle is small. A caulking gun uses a plunger which is operated by pulling back on a handle. You must squeeze the handle very hard to get the caulk to come out of the narrow opening because:_________.
A. pressure is distributed uniformly throughout the fluid and the area of the plunger is much larger than the area of the opening.
B. viscous drag between the walls of the tip and the caulk causes the caulk to swirl around chaotically.
C. Newton’s third law requires most of the energy in the caulk to be used to push back on the plunger rather than moving it through the tip.
D. the high density of the caulk impedes its flow through the small opening.
Since the caulk is thick and the exit nozzle is small, the pressure needed to deliver the caulk will be very high as pressure is uniformly distributed at the plunger side at every part of the caulk, hence very high pressure is needed to deliver the caulk which is why the handle needed the very hard squeeze
How would the magnetic field lines appear for a bar magnet cut at the midpoint, with the two pieces placed end to end with a space in between such that the cut edges are closest to each other
Answer:
cutting the magnet in two parts each part has a North and South pole,
Explanation:
In magnetism the magnetic mono-poles are not found, this means that we do not have magnetic charges alone, therefore when cutting the magnet in two parts each part has a North and South pole, the magnetic lines go from the North pole to the South pole, see attached.
The density of the lines is approximately the intensity of the magnetic field.
In general, how do highland climates compare with nearby areas at lower elevations? They are cooler and drier. They are cooler and wetter. They are warmer and drier. They are warmer and wetter.
Answer:
They are cooler and wetter
Explanation:
Highland areas have lower temperatures compared to low lying areas. The climate is more wetter because of more rainfalls compared to low lying areas and the wind carries moist air over the highlands.
Suppose a tank filled with water has a liquid column with a height of 19 meter. If the area is 2 square meters 2m squared, what’s the force of gravity acting on the column of water?
Answer:
372,400 N
Explanation:
The volume of the column is ...
V = Bh = (2 m^2)(19 m) = 38 m^3
If we assume the density is 1000 kg/m^3, then the mass of the water is ...
M = ρV = (1000 kg/m^3)(38 m^3) = 38,000 kg
The force of gravity on that mass is ...
F = Mg = (38,000 kg)(9.8 m/s^2) = 372,400 N
Which type of reaction is shown in this energy diagram?
Answer:
Option C
Explanation:
The graph shows endothermic reaction because the reactants are lower in energy and the products are higher is energy. Endothermic reactions absorb energy having products with higher energy.
Answer:
C
Explanation:
In an endothermic reaction, the energy-time graph shows reactants are at a lower energy level than the products.
A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the wavelength of the illuminating light is doubled
Answer:
Doubling the wavelength of the diffracting doubles the angle of diffraction. So, the width of the central bright spot pattern formed on the screen will also be doubled.
Explanation:
For a single slit diffraction, the path length difference is related to the wavelength of the light leaving the slit onto the screen by
D sin θ = mλ
where D sin θ is the path length of the waves, each.
mλ is the wavelength of the wavelet
where m is the the order of each minimum
m = m = 1,−1,2,−2,3, . . .
The wavelength of each wavelet is always a multiple of the wavelength of the light source, and from the equation, we can see that the angle of diffraction depend on the wavelength of the light. From this we can see that increasing the wavelength of the light increases the angle of diffraction, and hence we can say that doubling the wavelength will double the diffraction angle. Also, the width of the central bright spot of the screen will spread or increase with the angle of diffraction, so doubling the wavelength doubles the central bright spot on the screen.
A car travels at 100 km / h, collides head-on against a pole. Assuming the vehicle stopped at 2.2 seconds after impact, calculate the magnitude of the deceleration suffered by the driver.
Answer:
12.6 m/s²
Explanation:
First, convert to m/s.
100 km/h × (1000 m/km) × (1 hr / 3600 s) = 27.8 m/s
a = Δv / Δt
a = (0 m/s − 27.8 m/s) / 2.2 s
a = -12.6 m/s²
During a visit to the beach, you get in a small rubber raft and paddle out beyond the surf zone. Tiring, you stop and take a rest. Describe the movement of your raft during your rest. How does this movement differ, if at all, from what you would have experienced if you had stopped paddling while in the surf zone?
Answer:
The main difference in these two movements is that the first is a pure swing movement and the followed form a wave travels from the beach
Explanation:
The movement in the two parts is very different, when the surf zone has passed it is in a deeper part of the water where the seabed does not rise much, therefore due to the movement of the waves there is an upward oscillatory movement and descending, in this movement there is no horizontal displacement.
When it is within the southern zone, there is a rapid rise of the sea floor, which generates a horizontal movement, having a traveling wave, therefore your movement is more complicated, you can have some oscillating movement on the axis and, but in addition to this you have a horizontal movement that reaches you towards the beach, forming a Traveling wave.
The main difference in these two movements is that the first is a pure swing movement and the followed form a wave travels from the beach
A small meteorite with mass of 1 g strikes the outer wall of a communication satellite with a speed of 2Okm/s (relative to the satellite). The mass of the satellite is 200 kg.
About how much energy (in kJ) was converted to heat?
Answer:
The energy coverted to heat is 200 kilojoules.
Explanation:
GIven the absence of external forces exerted both on the small meteorite and on the communication satellite, the Principle of Linear Momentum is considered and let suppose that collision is completely inelastic and that satellite is initially at rest. Hence, the expression for the satellite-meteorite system:
[tex]m_{M}\cdot v_{M} + m_{S}\cdot v_{S} = (m_{M}+m_{S})\cdot v[/tex]
Where:
[tex]m_{M}[/tex], [tex]m_{S}[/tex] - Masses of the small meteorite and the communication satellite, measured in kilograms.
[tex]v_{M}[/tex], [tex]v_{S}[/tex] - Speeds of the small meteorite and the communication satellite, measured in meters per second.
[tex]v[/tex] - Final speed of the satellite-meteorite system, measured in meters per second.
The final speed of the satellite-meteorite system is cleared:
[tex]v = \frac{m_{M}\cdot v_{M}+m_{S}\cdot v_{S}}{m_{M}+m_{S}}[/tex]
If [tex]m_{M} = 1\times 10^{-3}\,kg[/tex], [tex]m_{S} = 200\,kg[/tex], [tex]v_{M} = 20000\,\frac{m}{s}[/tex] and [tex]v_{S} = 0\,\frac{m}{s}[/tex], the final speed is now calculated:
[tex]v = \frac{(1\times 10^{-3}\,kg)\cdot \left(20000\,\frac{m}{s} \right)+(200\,kg)\cdot \left(0\,\frac{m}{s} \right)}{1\times 10^{-3}\,kg+200\,kg}[/tex]
[tex]v = 0.1\,\frac{m}{s}[/tex]
Which means that the new system remains stationary and all mechanical energy from meteorite is dissipated in the form of heat. According to the Principle of Energy Conservation and the Work-Energy Theorem, the change in the kinetic energy is equal to the dissipated energy in the form of heat:
[tex]K_{S} + K_{M} - K - Q_{disp} = 0[/tex]
[tex]Q_{disp} = K_{S}+K_{M}-K[/tex]
Where:
[tex]K_{S}[/tex], [tex]K_{M}[/tex] - Initial translational kinetic energies of the communication satellite and small meteorite, measured in joules.
[tex]K[/tex] - Kinetic energy of the satellite-meteorite system, measured in joules.
[tex]Q_{disp}[/tex] - Dissipated heat, measured in joules.
The previous expression is expanded by using the definition for the translational kinetic energy:
[tex]Q_{disp} = \frac{1}{2}\cdot [m_{M}\cdot v_{M}^{2}+m_{S}\cdot v_{S}^{2}-(m_{M}+m_{S})\cdot v^{2}][/tex]
Given that [tex]m_{M} = 1\times 10^{-3}\,kg[/tex], [tex]m_{S} = 200\,kg[/tex], [tex]v_{M} = 20000\,\frac{m}{s}[/tex], [tex]v_{S} = 0\,\frac{m}{s}[/tex] and [tex]v = 0.1\,\frac{m}{s}[/tex], the dissipated heat is:
[tex]Q_{disp} = \frac{1}{2}\cdot \left[(1\times 10^{-3}\,kg)\cdot \left(20000\,\frac{m}{s} \right)^{2}+(200\,kg)\cdot \left(0\,\frac{m}{s} \right)^{2}-(200.001\,kg)\cdot \left(0.001\,\frac{m}{s} \right)^{2}\right][/tex][tex]Q_{disp} = 200000\,J[/tex]
[tex]Q_{disp} = 200\,kJ[/tex]
The energy coverted to heat is 200 kilojoules.
An electronic stove is rated 1000w, 240v. explain this statement. please I'm in need
Answer and Explanation:
When an electronic appliance such as electric heater, electric stove e.t.c is rated, the rating actually specifies the ideal working properties of the appliance. For example if it is rated 200W, 220V, it shows that the power the appliance will consume at a voltage of 220V is 200W.
Therefore, for the electronic stove mentioned with a rating of 1000W, 240V, the stove will consume or draw a power of 1000 watts at a voltage of 240volts.
Ratings can also help determine some other properties of the appliance such as current consumption and resistance in the appliance. For the given electronic stove, the current consumed can be found by using the following relation:
P = IV -------------(i)
Where;
P = Power rating = 1000W
I = Current used
V = Voltage rating = 240V
Substituting these values into equation (i) gives;
1000 = I x 240
I = [tex]\frac{1000}{240}[/tex] = 4.17A
Therefore, the current used by the stove is 4.17A
To get the resistance R of the stove, we can use the relation;
P = [tex]\frac{V^2}{R}[/tex]
R = [tex]\frac{V^2}{P}[/tex]
R = [tex]\frac{240^2}{1000}[/tex]
R = 57.6Ω
Therefore, the resistance of the stove is 57.6Ω
A body of mass 2.5kg is raised 4.0m above the ground.Calculate the potential energy if g=10m/s squared
Answer:
100 joulesExplanation:
[tex]mass = 2.5kg\\height = 4.0\\Acceleration \: due \:to\:gravity = 10m/s^2\\\\P.E = mgh\\P.E = 2.5kg\times10\times4\\\\Potential \: Energy = 100 joules[/tex]
The potential energy if g = 10m/s² is 98 J
What is Potential Energy ?Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Formula for potential energy :
P.E. = mgh
m = mass (kg)g = gravity (m/s²)h = height/distance (m)Given :
The book is held from the ground of a distance = 4.0 m,
so
h = 4.0 m
we know that the book weighs,
2.5 kg
so
m = 2.5 kg.
Now we just put it in the formula ;
PE = (2.5kg) × (9.8 m/s²) × ( 4.0 m)
P E = 98 J
Therefore, The potential energy if g = 10m/s² is 98 J
Learn more about Potential Energy here ;
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