Answer:
The angle is [tex]\phi = 0.45 0 ^o[/tex]
Explanation:
From the question we are told that
The objective focal length [tex]f = 1.33 \ m[/tex]
The eyepiece focal length is [tex]f_o = 2.82 \ cm = 0.0282 \ m[/tex]
The diameter of the sunlight is [tex]d = 25000km = 2.5 *10^{7} \ m[/tex]
The distance of the sun from from the earth is [tex]D = 1.5 *10^8 km = 1.5 *10^{11} \ m[/tex]
Generally the magnification of the object is mathematically evaluated as
[tex]m = -\frac{f_o }{f_e }[/tex]
The negative sign is because the lens of the telescope is diverging light
substituting values
[tex]m = -\frac{1.33 }{0.0282 }[/tex]
[tex]m = - 47.16 3[/tex]
Now we can obtain the angle made by the object (sunlight ) with respect to the telescope as follows
[tex]tan \theta = \frac{d}{D}[/tex]
substituting values
[tex]tan \theta = \frac{2.5 *10^{7}}{1.5*10^{11}}[/tex]
[tex]tan \theta = 0.0001667[/tex]
[tex]\theta= tan^{-1}[0.0001667][/tex]
[tex]\theta= 0.00955^o[/tex]
The magnification can also be mathematically represented as
[tex]m = \frac{\phi }{\theta }[/tex]
Where [tex]\phi[/tex] is the angle the image made with telescope
Since the negative sign indicate direction of light movement we will remove it from the calculation below
=> [tex]47.163 = \frac{\phi}{0.00955}[/tex]
=> [tex]\phi = 0.45 0 ^o[/tex]
A carton is given a push across a horizontal, frictionless surface. The carton has a mass m, the push gives it an initial speed of vi, and the coefficient of kinetic friction between the carton and the surface is μk.
(a) Use energy considerations to find an expression for the distance the carton moves before it stops. (Use any variable or symbol stated above along with the following as necessary)
(b) What if the initial speed of the carton is increased by a factor of 3, determine an expression for the new distance d the box slides in terms of the old distance.
Answer and Explanation:
Data provided in the question
Carbon mass = m
Initial speed = v_i
Coefficient = μk
Based on the above information, the expressions are as follows
a. By using the energy considerations the expression for the carton moving distance is
As we know that
[tex]Fd = \frac{1}{2} m (v_i^2- v_f^2)[/tex]
where,
[tex]v_f = 0[/tex]
[tex]F = u_kmg[/tex]
[tex](\mu_kg) d = \frac{1}{2} m v_i^2[/tex]
[tex]d = \frac{\frac{1}{2}v_i^2}{\mu_kg}[/tex]
[tex]d = \frac{v_i^2}{2 \mu_kg}[/tex]
b. The initial speed of the carton if the factor of 3 risen, so the expression is
[tex]v_i^1 = 3v_i[/tex]
[tex]d^i = \frac{(3v_i^2)}{2\mu_kg}[/tex]
[tex]= \frac{9v_i^2}{2\mu_kg}[/tex]
[tex]d^i = 9(d)[/tex]
In an experiment to measure the acceleration due to gravity g, two independent equally reliable measurements gave 9.67 m/s2 and 9.88 m/s2. Determine (i) the percent difference of the measurements (ii) the percent error of their mean. [Take the theoretical value of g to be 9.81 m/s2]
Answer and Explanation:
a. The computation of the percent difference between the measurements is shown below:-
The first value of g is 9.67 and the second value is 9.88
So, difference = 9.88 - 9.67
= 0.21
Percentage difference in measurement is
[tex]= \frac{0.21}{9.88}\times100[/tex]
= +/-2.13
Percent difference with 9.88
Difference = 9.88 - 9.81
= 0.07
[tex]= \frac{0.07}{9.81}\times100[/tex]
= +/-0.71%
b. The Computation of percent error of their mean is shown below:-
Mean of two values is
= [tex]\frac{9.67 + 9.88}{2}[/tex]
= 9.775
Difference = 9.81 - 9.775
= 0.035
Percentage difference is
[tex]= \frac{0.035}{9.81}\times 100[/tex]
= +/- 0.36%
describe the relation among density, temperature, and volume when the pressure is constant, and explain the blackbody radiation curve
Answer:
in all cases with increasing temperature the density should decrease.
Black body radiation is a construction that maintains a constant temperature and a hole is opened, this hole is called a black body,
Explanation:
Let's start for ya dream gas
PV = nRT
Since it indicates that the pressure is constant, we see that the volume is directly proportional to the temperature.
The density of is defined by
ρ = m / V
As we saw that volume increases with temperature, this is also true for solid materials, using linear expansion. Therefore in all cases with increasing temperature the density should decrease.
Black body radiation is a construction that maintains a constant temperature and a hole is opened, this hole is called a black body, since all the radiation that falls on it is absorbed or emitted.
This type of construction has a characteristic curve where the maximum of the curve is dependent on the tempera, but independent of the material with which it is built, to explain the behavior of this curve Planck proposed that the diaconate in the cavity was not continuous but discrete whose energy is given by the relationship
E = h f
A very long, straight horizontal wire carries a current such that 8.25×1018 electrons per second pass any given point going from west to east.
What is the magnitude of the magnetic field this wire produces at a point 5.00 cm directly above it?
Answer: The magnitude of the magnetic field this wire produces is 5.56 × 10^-6 T
Explanation: Please see the attachments below
This question involves the concepts of Biot-Savart Law and magnetic field. It can be solved by the application of Biot-Savart Law on a current-carrying wire.
The magnitude of the magnetic field is "5.28 x 10⁻⁶ T".
Using the Biot-Savart Law to find out the magnitude of the magnetic field produced by the wire at a point 5 cm above it, directly:
[tex]B = \frac{\mu_o I}{2\pi r}\\\\[/tex]
where,
B = magnetic field = ?
μ₀ = permeability of free space = 4π x 10⁻⁷ N/A²
I = current = [tex]\frac{ne}{t} = (8.25\ x\ 10^{18}\ elctrons/sec)(1.6\ x\ 10^{-19}\ C /electron)[/tex] = 1.32 A
r = radius = distance above wire = 5 cm = 0.05 m
Therefore,
[tex]B = \frac{(4\pi\ x\ 10^{-7}\ N/A^2)(1.32\ A)}{2\pi(0.05\ m)}[/tex]
B = 5.28 x 10⁻⁶ T
Learn more about magnetic field here:
https://brainly.com/question/23096032?referrer=searchResults
The attached picture shows the illustration of magnetic field due to a wire.
A box experiencing a gravitational force of 600 N. is being pulled to the right with a force of 250 NA 25 N. frictional force acts on the box as it moves to the right what is the net force in the Y direction
Answer:
32
Explanation:
Answer:
0
Explanation:.
When an old LP turntable was revolving at 3313 rpm, it was shut off and uniformly slowed down and stopped in 5.5 seconds. What was the magnitude of its angular acceleration (in rad/s2) as it slowed down?
Answer:
-0.63 rad/s²
Explanation:
Given that
Initial angular velocity of the turntable, w(i) = 33 1/3 rpm
Final angular velocity of the turntable, w(f) = 0 rpm
Time taken to slow down, t = 5.5 s
The calculation is attached in the photo below
Elements more massive than iron (e.g. silver, uranium and lead) are created from supernova events (an explosion of a star)
a) true
b) false
Answer:
(a) True
Explanation:
A supernova is a powerful light explosion that occurs in massive stars.
During a supernova, the star releases very large amounts of energy as well as neutrons, which allows elements heavier than iron, such as silver, uranium and lead, to be produced.
Therefore, the correct option is "a" True
Elements more massive than iron (e.g. silver, uranium and lead) are created from supernova events.
A uniform 2.0-kg rod that is 0.92 m long is suspended at rest from the ceiling by two springs, one at each end. Both springs hang straight down from the ceiling. The springs have identical lengths when they are unstretched. Their spring constants are 29 N/m and 66 N/m. Find the angle that the rod makes with the horizontal.
Answer:
11.7°
Explanation:
See attached file
An aluminum bar 600mm long, with diameter 40mm, has a hole drilled in the center of the bar. The hole is 40mm in diameter and 100mm long. If modulus of elasticity is for the aluminum is 85GN/m^2, calculate the total contraction on the bar due to compressive load of 180kN?
Answer:
1.228 x [tex]10^{-6}[/tex] mm
Explanation:
diameter of aluminium bar D = 40 mm
diameter of hole d = 30 mm
compressive Load F = 180 kN = 180 x [tex]10^{3}[/tex] N
modulus of elasticity E = 85 GN/m^2 = 85 x [tex]10^{9}[/tex] Pa
length of bar L = 600 mm
length of hole = 100 mm
true length of bar = 600 - 100 = 500 mm
area of the bar A = [tex]\frac{\pi D^{2} }{4}[/tex] = [tex]\frac{3.142* 40^{2} }{4}[/tex] = 1256.8 mm^2
area of hole a = [tex]\frac{\pi(D^{2} - d^{2}) }{4}[/tex] = [tex]\frac{3.142*(40^{2} - 30^{2})}{4}[/tex] = 549.85 mm^2
Total contraction of the bar = [tex]\frac{F*L}{AE} + \frac{Fl}{aE}[/tex]
total contraction = [tex]\frac{F}{E} * (\frac{L}{A} +\frac{l}{a})[/tex]
==> [tex]\frac{180*10^{3}}{85*10^{9}} *( \frac{500}{1256.8} + \frac{100}{549.85})[/tex] = 1.228 x [tex]10^{-6}[/tex] mm
Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.
(a) What is the longest wavelength for which there will be destructive interference at point Q?
(b) What is the longest wavelength for which there will be constructive interference at point Q?
Answer:
a. for destructive interference
λmax= 240m
b. for constructive interference
λmax = 120m
Explanation:
The cost of energy delivered to residences by electrical transmission varies from $0.070/kWh to $0.258/kWh throughout the United States; $0.110/kWh is the average value.
Required:
At this average price, calculate the cost of:
a. leaving a 40-W porch light on for two weeks while you are on vacation?
b. making a piece of dark toast in 3.00 min with a 970-W toaster
c. drying a load of clothes in 40.0 min in a 5.20 x 10^3-W dryer.
Answer:
Cost = $ 1.48
Cost = $ 0.005
Cost = $ 0.38
Explanation:
given data
electrical transmission varies = $0.070/kWh to $0.258/kWh
average value = $0.110/kWh
solution
when leaving a 40-W porch light on for two weeks while you are on vacation so cost will be
first we get here energy consumed that is express as
E = Pt .................1
here E is Energy Consumed and Power Delivered is P and t is time
so power is here 0.04 KW and t = 2 week = 336 hour
so
put value in 1 we get
E = 0.04 × 336
E = 13.44 KWh
so cost will be as
Cost = E × Unit Price .............2
put here value and we get
Cost = 13.44 × 0.11
Cost = $ 1.48
and
when you making a piece of dark toast in 3.00 min with a 970-W toaster
so energy consumed will be by equation 1 we get
E = Pt
power is = 0.97 KW and time = 3 min = 0.05 hour
put value in equation 1 for energy consume
E = 0.97 × 0.05 h
E = 0.0485 KWh
and we get cost by w\put value in equation 2 that will be
cost = E × Unit Price
cost = 0.0485 × 0.11
Cost = $ 0.005
and
when drying a load of clothes in 40.0 min in a 5.20 x 10^3-W dryer
from equation 1 we get energy consume
E = Pt
Power Delivered = 5.203 KW and time = 40 min = 0.67 hour
E = 5.203 × 0.67
E = 3.47 KWh
and
cost will by put value in equation 2
Cost = E × Unit Price
Cost = 3.47 × 0.11
Cost = $ 0.38
A certain dam generates 120 MJ of mechanical (hydroelectric) energy each minute. If the conversion from mechanical to electrical energy is then 15% efficient, what is the dam's electrical power output in W?
Answer:
electric energy ( power ) = 300000 W
Explanation:
given data
mechanical (hydroelectric) energy = 120 MJ/min = 2000000 J/s
efficiency = 15 % = 0.15
solution
we know that Efficiency of electric engine is expression as
Efficiency = Mechanical energy ÷ electric energy ......................1
and here dam electrical power output is
put here value in equation 1
electric energy ( power ) = Efficiency × Mechanical energy ( power )
electric energy ( power ) = 0.15 × 2000000 J/s
electric energy ( power ) = 300000 W
The friends spend some time thinking about a beam of light traveling from one medium to another medium with higher index of refraction, which strikes the boundary obliquely. Which of Tristan's statements is correct
Answer:
"When light moves from a material in which its speed is high to a material in which its speed is lower, the angle of refraction θ2is less than the angle of incidence θ1and the ray is bent toward the normal."
Explanation:
Refraction is a phenomenon that occurs when light rays change direction after passing through a surface or medium. This is also known as 'bending'. Snell's law provides the relationship between the angle of incidence and refraction in the equation below:
n₁sinФ₁ = n₂sinФ₂
where n1 and n2 represent the two media and theta refers to the angles formed. When light hits a medium with a high refractive index, the speed of light becomes slower.
So, Tristan is right when he says that, "When light moves from a material in which its speed is high to a material in which its speed is lower, the angle of refraction θ2is less than the angle of incidence θ1and the ray is bent toward the normal."
5) what is the weight of a
if its weight
is 5N in moon?
body in the earth,
Answer:
Weight of object on moon is 5N ,as we know. Weight of object on moon is 1/3 the of object on earth,so
let weight of object on earth = X
5N= X/3
X = 3×5 = 15N
Hence the weight of the object on earth will
be 15N
To understand the standard formula for a sinusoidal traveling wave.
One formula for a wave with a y displacement (e.g., of a string) traveling in the x direction is
y(x,t)=Asin(kxâÏt).
All the questions in this problem refer to this formula and to the wave it describes.
1) What is the phase Ï(x,t) of the wave?
Express the phase in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï
Ï(x,t)=
2) What is the wavelength λ of the wave?
Express the wavelength in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï.
λ=
3) What is the period T of this wave?
Express the period in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï.
T=
4) What is the speed of propagation v of this wave?
Express the speed of propagation in terms of one or more given variables ( A, k, x, t, and Ï) and any needed constants like Ï.
v=
Answer:
1) Φ=zero
2) λ = 2π / k
3) T = 2π / w
4) v = w / k
Explanation:
The equation of a traveling wave is
y = A sin (ka - wt + Ф)
Let's answer using this equation the different questions
1) we see that the equation given in the problem the phase is zero
2) wavelength
k = 2π /λ
λ = 2π / k
3) The perido
angular velocity is related to frequency
w = 2π f
frequency and period are related
f = 1 / T
w = 2 π / T
T = 2π / w
4) the wave speed is
v = λ f
λ = 2π / k
f = w / 2π
v = 2π /k w /2π
v = w / k
What is the average acceleration? Please show work!
Answer:
Explanation:
Average acceleration
= (final velocity - initial velocity) /time
= (50-0)km/h /30 s
= 50 * 1000 / 3600 m/s /s
= 13.89 m/s^2
In a fixed-target experiment positrons are fired at a target of electrons at rest. What positron energy is required to produce a Z (mZ = 91.188 GeV)?
Answer:
Explanation:
electron rest mass = 0.511MeV/C²
postion rest mass = 0.511MeV/C²
boson rest mass = 91.188GeV/C²
= 91188 MeV/C²
An electric heater is constructed by applying a potential different of 120V across a nichrome wire that has a total resistant of 8 ohm .the current by the wire is
Answer:
15amps
Explanation:
V=IR
I=V/R
I = 120/8
I = 15 amps
The buoyant force on an object placed in a liquid is (a) always equal to the volume of the liquid displaced. (b) always equal to the weight of the object. (c) always equal to the weight of the liquid displaced. (d) always less than the volume of the liquid displaced.
Answer:
(c) always equal to the weight of the liquid displaced.
Explanation:
Archimedes principle (also called physical law of buoyancy) states that when an object is completely or partially immersed in a fluid (liquid, e.t.c), it experiences an upthrust (or buoyant force) whose magnitude is equal to the weight of the fluid displaced by that object.
Therefore, from this principle the best option is C - always equal to the weight of the liquid displaced.
Calculate the moment of inertia of a skater given the following information.
(a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius.
(b) The skater with arms extended is approximately a cylinder that is 74.0 kg, has a 0.150 m radius, and has two 0.750 m long arms which are 3.00 kg each and extend straight out from the cylinder like rods rotated about their ends.
Answer:
(a) I = 0.363 kgm^2
(b) I = 1.95 kgm^2
Explanation:
(a) If you consider the shape of the skater as approximately a cylinder, you use the following formula to calculate the moment of inertia of the skater:
[tex]I_s=\frac{1}{2}MR^2[/tex] (1)
M: mass of the skater = 60.0 kg
R: radius of the cylinder = 0.110m
[tex]I_s=\frac{1}{2}(60.0kg)(0.110m)^2=0.363kg.m^2[/tex]
The moment of inertia of the skater is 0.363 kgm^2
(b) In the case of the skater with his arms extended, you calculate the moment of inertia of a combine object, given by cylinder and a rod (the arms) that cross the cylinder. You use the following formula for the total moment of inertia:
[tex]I=I_c+I_r\\\\I=\frac{1}{2}M_1R^2+\frac{1}{12}M_2L^2[/tex] (2)
M1: mass of the cylinder = 74.0 kg
M2: mass of the rod = 3.00kg +3.00kg = 6.00kg
L: length of the rod = 0.750m + 0.750m = 1.50m
R: radius of the cylinder = 0.150
[tex]I=\frac{1}{2}(74.0kg)(0.150m)^2+\frac{1}{12}(6.00kg)(1.50m)^2\\\\I=1.95kg.m^2[/tex]
The moment of inertia of the skater with his arms extended is 1.95 kg.m^2
a 1000 kg car accelerates from 0 to 15 m/s in 5.0 s with negligible friction and air resistance. what is the average power delivered by the engine
Answer:
30.16 hp
Explanation:
Given :
m= 1000 kg
v=15 m/s
t=5.0 s
The average power delivered by the engine can be determined by using the given formula
[tex]Average\ power\ =\ \frac{0.5*m*v^2\ }{t}[/tex]
where m=,mass, v=velocity and t=time
Now putting the value of m,v and t in the previous equation we get
[tex]Average \ power\ =\ \frac{0.5*1000*15*15}{5} \\Average \ power\ =\ 22,500\ w\\Average \ power\ =\frac{22,500}{746} \\Average \ power\ =30.16\ hp[/tex]
To convert w to hp we divide by 746
Therefore 30.16 hp is the answer.
A truck running at 115 km / h slows down at a rate of 4 m / s every 2 seconds. How far will it travel to a stop? choose the correct option 1) 335.04m 2) 205.04m 3) 255.04m
Answer:
3) 255.04 m
Explanation:
Given:
v₀ = 115 km/h = 31.944 m/s
v = 0 m/s
a = -(4 m/s) / 2s = -2 m/s²
Find: Δx
v² = v₀² + 2aΔx
(0 m/s)² = (31.944 m/s)² + 2 (-2 m/s²) Δx
Δx = 255.11 m
Closest answer is option 3.
When you are told that the wind has a "Small Coriolis force" associated with it, what is that "small force" exactly
Answer:
Coriolis force is a type of force of inertia that acts on objects that is in motion within a frame of reference that rotates with respect to an inertial frame. Due to the rotation of the earth, circulating air is deflected result of the Coriolis force, instead of the air circulating between the earth poles and the equator in a straight manner. Because of the effect of the Coriolis force, air movement deflects toward the right in the Northern Hemisphere and toward the left in the Southern Hemisphere, eventually taking a curved path of travel.
If you could see stars during the day, this is what the sky would look like at noon on a given day. The Sun is near the stars of the constellation Gemini. Near which constellation would you expect the Sun to be located at sunset?
Answer:
The sun will be located near the Gemini constellation at sunset
what is thermodynamic?
Answer:
Thermodynamics is a branch of physics which deals with the energy and work of a system. It was born in the 19th century as scientists were first discovering how to build and operate steam engines. Thermodynamics deals only with the large scale response of a system which we can observe and measure in experiment.
Answer:
thermodynamics is the branch of physics which deals with the study of heat and other forms energy and their mutual relationship(relation ship between them)
Explanation:
i hope this will help you :)
Indiana Jones is in a temple searching for artifacts. He finds a gold sphere with a radius of 2 cm sitting on a pressure sensitive plate. To avoid triggering the pressure plate, he must replace the gold with something of equal mass. The density of gold is 19.3.103 kg/m3, and the volume of a sphere is V = 4/3 Ar3. Indy has a bag of sand with a density of 1,602 kg/m3.
(A) What volume of sand must he replace the gold sphere with? If the sand was a sphere, what radius would it have?
Answer:
Volume of Sand = 0.4 m³
Radius of Sand Sphere = 0.46 m
Explanation:
First we need to find the volume of gold sphere:
Vg = (4/3)πr³
where,
Vg = Volume of gold sphere = ?
r = radius of gold sphere = 2 cm = 0.02 m
Therefore,
Vg = (4/3)π(0.2 m)³
Vg = 0.0335 m³
Now, we find mass of the gold:
ρg = mg/Vg
where,
ρg = density of gold = 19300 kg/m³
mg = mass of gold = ?
Vg = Volume of gold sphere = 0.0335 m³
Therefore,
mg = (19300 kg/m³)(0.0335 m³)
mg = 646.75 kg
Now, the volume of sand required for equivalent mass of gold, will be given by:
ρs = mg/Vs
where,
ρs = density of sand = 1602 kg/m³
mg = mass of gold = 646.75 kg
Vs = Volume of sand = ?
Therefore,
1602 kg/m³ = 646.75 kg/Vs
Vs = (646.75 kg)/(1602 kg/m³)
Vs = 0.4 m³
Now, for the radius of sand sphere to give a volume of 0.4 m³, can be determined from the formula:
Vs = (4/3)πr³
0.4 m³ = (4/3)πr³
r³ = 3(0.4 m³)/4π
r³ = 0.095 m³
r = ∛(0.095 m³)
r = 0.46 m
A heavier car is always safer in a crash than a lighter car.
Answer:
not true because the mass from the heavy car will cause it to damage more
Explanation:
Answer: answer on edmentum is false your welcome
Explanation:
It is false because it's more heavy so more damage l.
A spring hangs vertically. A 250 g mass is attached to the spring and allowed to come to rest. The spring stretches 8 cm as the mass comes to rest. What is the spring constant of the spring
Answer:
spring constant = 31.25N/m
Explanation:
spring constant = force/extension
mass = 250g = 0.25kg
extension = 8cm = 0.08m
force = mg = 0.25 x 10 = 2.5N
spring constant = 2.5/0.08 = 31.25N/m
A 60-μC charge is held fixed at the origin and a −20-μC charge is held fixed on the x axis at a point x = 1.0 m. If a 10-μC charge is released from rest at a point x = 40 cm, what is its kinetic energy the instant it passes the point x = 70 cm?
Answer:
Ek = 8,79 [J]
Explanation:
We are going to solve this problem, using the energy conservation principle
State 1 or initial state (charges at rest t=0)
E₁ = Ek + U₁
As charge are at rest Ek = 0
And U₁ has two components
U₁₂ = K * Q₁*Q₂ / 0,4 and U₃₂ = K*Q₃*Q₂ / 0,6
U₁₂ = 9*10⁹* 60*10⁻⁶*10*10⁻⁶/0,4 ⇒ U₁₂ = 9*60*10*10⁻³/0,4
U₃₂ = - 9*10⁹* 20*10⁻⁶*10*10⁻⁶/0,6 ⇒ U₃₂ = - 9*20*10*10⁻³/0,6
U₁₂ = 540*10⁻2/0,4 [J] ⇒13,5 [J]
U₃₂ = - 180*10⁻² /0,6 [J] ⇒ - 3 [J]
Then E₁ = E₁₂ + E₃₂
E₁ = 10,5 [J]
At the moment of Q₂ passing x = 40 cm or 0,4 m
E₂ = Ek + U₂
We can calculate the components of U₂ in this new configuration
U₂ = U₁₂ + U₃₂
U₁₂ = 9*10⁹* 60*10⁻⁶*10*10⁻⁶/0,7 ⇒ U₁₂ = 9*60*10*10⁻³/0,7
U₁₂ = 540*10⁻²/0,7 U₁₂ = 7,71 [J]
U₃₂ = - 9*10⁹* 20*10⁻⁶*10*10⁻⁶/0,3 ⇒ U₃₂ = - 9*20*10*10⁻³/0,3
U₃₂ = - 9*20*10⁻²/0,3
U₃₂ = - 6
U₂ = 7,71 -6
U₂ = 1,71 [J]
Then as
E₂ = Ek + U₂ and E₂ = E₁
Then
Ek + U₂ = E₁
Ek = 10,5 - U₂
Ek = 10,5 - 1,71
Ek = 8,79 [J]
A ballast is dropped from a stationary hot-air balloon that is at an altitude of 576 ft. Find (a) an expression for the altitude of the ballast after t seconds, (b) the time when it strikes the ground, and (c) its velocity when it strikes the ground. (Disregard air resistance and take ft/sec2.)
Answer:
a) [tex]S = \frac{1}{2}gt^2\\[/tex]b) 6secsc) 192ftExplanation:
If a ball dropped from a stationary hot-air balloon that is at an altitude of 576 ft, an expression for the altitude of the ballast after t seconds can be expressed using the equation of motion;
[tex]S = ut + \frac{1}{2}at^{2}[/tex]
S is the altitude of the ballest
u is the initial velocity
a is the acceleration of the body
t is the time taken to strike the ground
Since the body is dropped from a stationary air balloon, the initial velocity u will be zero i.e u = 0m/s
Also, since the ballast is dropped from a stationary hot-air balloon, the body is under the influence of gravity, the acceleration will become acceleration due to gravity i.e a = +g
Substituting this values into the equation of the motion;
[tex]S = 0 + \frac{1}{2}gt^2\\ S = \frac{1}{2}gt^2\\[/tex]
a) An expression for the altitude of the ballast after t seconds is therefore
[tex]S = \frac{1}{2}gt^2\\[/tex]
b) Given S = 576ft and g = 32ft/s², substituting this into the formula in (a);
[tex]576 = \frac{1}{2}(32)t^2\\\\\\576*2 = 32t^2\\1152 = 32t^2\\t^2 = \frac{1152}{32} \\t^2 = 36\\t = \sqrt{36}\\ t = 6.0secs[/tex]
This means that the ballast strikes the ground after 6secs
c) To get the velocity when it strikes the ground, we will use the equation of motion v = u + gt.
v = 0 + 32(6)
v = 192ft