Answer:
ρ= 1.378 10⁴ Ω / m
Explanation:
Let's use ohm's law
V = i R
R = V / i
let's calculate
R = 9.0 / 230 10⁻⁶
R = 3.9 10⁴ Ω
now we can use the definite of resistance
R = ρ [tex]\frac{L}{A}[/tex]
the area of a circle is
A = π r² = π (d/2)²
ρ = R A / L
ρ = π R [tex]\frac{d^2}{4L}[/tex]
let's calculate
ρ = π 3.9 10⁴ [tex]\frac{(1.5 \ 10^{-3}^2 }{4 \ 5 \ 10^{-2}}[/tex]
ρ= 1.378 10⁴ Ω / m
The tray dispenser in your cafeteria has broken and is not repairable. The custodian knows that you are good at design-ing things and asks you to help him build a new dispenser out of spare parts he has on his workbench. The tray dispenser supports a stack of trays on a shelf that is supported by four springs, one at each corner of the shelf. Each tray is rectangu-lar, with dimensions 45.3 cm by 35.6 cm. Each tray is 0.450 cm thick and has a mass of 580 g. The custodian asks you to design a new four-spring dispenser such that when a tray is removed, the dispenser pushes up the remaining stack so that the top tray is at the same position as the just-removed tray was. He has a wide variety of springs that he can use to build the dispenser. Which springs should he use
Answer:
you have to find 4 spring with this elastic constant k = 316 N / m
Explanation:
In this case for the design of the dispenser the four springs are placed in the four corner at the bottom, therefore we can use the translational equilibrium relationship
4 F_e -W = 0
where the elastic force is
F_e = k x
we substitute
4 kx = mg
k = [tex]\frac{mg}{4x}[/tex]
Each tray has a thickness of x = 0.450 cm = 0.450 10⁻² m, this should be the elongation of the spring so that when the tray is in position it will remain fixed.
let's calculate
k = [tex]\frac{0.580 \ 9.8}{4 \ 0.450 \ 10^{-2} }[/tex]
k = 3.1578 10² N / m
k = 316 N / m
therefore you have to find 4 spring with this elastic constant
What formula could be used to find distance if you know the speed an the time
Answer: d = st
Explanation:
We know that the distance is equal to the rate (speed) times the time
d = st
if a body of mass m is placed on earth ,what is the amount of potential energy possessed by it (g:-9.8m/s
Answer:
mgh
Explanation:
Assume the height of the body is 1.8m.
The gravity?of the body is G=mg
the height of the gravity center is about 0.9m
E=mgh
=m*9.8m/s*0.9m
= 8.82mJ
4. Which of these is exerted by an engine?
(1 Point)
Thrust
Water resistance
Friction
Air resistance
Air resistance is exerted by an engine
what are the types of energy sources based on
time of replacement ? write down their names
Answer:
solar energy
wind power
geothermal energy
hydraulic power
biomass energy
energy storage
(That's all I know).
We assume the foam plate has a positive charge when rubbed with paper towels.
Lift the pan away from the charged plate using the styrofoam cup. Briefly touch the rim of the pan to neutralize it. Place the neutralized pan on the plate and observe the tape rise. When the pan is on the plate, the rim of the plate has a _____________. This means that the pan base is ________________ charged because the net charge on the pan is __________. You know that this must be the case because as you lift the pan with the cup away from the plate, the tape on the rim goes down.
Answer:
POSITIVE CHARGE, NEGATIVE CHARGE, ZERO
Explanation:
To solve this completion exercise, we must remember that charges of the same sign repel each other and in a metallic object (frying pan) the charge is mobile.
Let's analyze the situation when we touch the pan, the charges are neutralized, therefore when we bring the pan to the plate that has a positive charge, it attracts the mobile negative charges in the pan, until it is neutralized, therefore on the opposite side of the pan. pan (edge with a glued tape) is left with a positive charge; therefore the edge and the tape, which is very light, have positive charges and repel each other.
We must assume that the frying pan is insulated so that the net charge is zero, since the induction process.
Consequently the words to complete the sentence are
When the pan is on the plate, the edge of the plate has a _POSITIVE CHARGE_____.
This means that the base of the container is loaded NEGATIVE CHARGE_____ because the net charge of the container is ___ZERO_
A 680 nm laser illuminates a double slit apparatus with a slit separation distance of 7.83 μm. On the viewing screen, you measure the distance from the central bright fringe to the 2nd bright fringe to be 88.2 cm. How far away (in meters) is the viewing screen from the double slits?
Answer:
L = 5.08 10⁻¹ m = 50.8 cm
Explanation:
In a double slit experiment for constructive interference is given by
d sin θ = m λ
let's use trigonometry to find a relationship with the distance
tan θ = y / L
these experiments are very small angles
tan θ = [tex]\frac{sin \ \theta}{cos \ \theta}[/tex] = sin θ
when substituting
sin θ = y / L
substituting in the first equation
d y / L = m λ
L = [tex]\frac{d \ y}{m \ \lambda}[/tex]
let's calculate
L = [tex]\frac{ 0.783 \ 10^{-6} \ 88.2 \ 10^{-2} }{2 \ 680 \ 10^{-9}}[/tex]
L = 5.08 10⁻¹ m
The distance of viewing screen from the double slits will be L = 5.08 *10⁻¹ m = 50.8 cm
What is constructive interference?
This position, where the resulting wave is larger than either of the two original, is called constructive interference.
In a double slit experiment for constructive interference is given by
d sin θ = m λ
let's use trigonometry to find a relationship with the distance
[tex]tan\theta=\dfrac {y}{L}[/tex]
these experiments are very small angles
tan θ = = sin θ
when substituting
[tex]sin\theta = \dfrac{y}{l}[/tex]
substituting in the first equation
[tex]\dfrac{dy}{L}=m\lambda[/tex]
[tex]L=\dfrac{dy}{L\lambda}[/tex]
let's calculate
[tex]L=\frac{0.783\times 10^{-6}\times 88.2\times 10^{-2}}{2.680\times 10^{-9}}[/tex]
L = 5.08 10⁻¹ m
Hence the distance of viewing screen from the double slits will be L = 5.08 10⁻¹ m = 50.8 cm
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A painter sits on a scaffold that is connected to a rope passing over a pulley. The other end of the rope rests in the hands of the painter who wants to lift the scaffold. She plans to pull downward on the loose end of the rope, thinking that the scaffold will then rise vertically with her along for the ride. The scaffold has a mass of 52 kg, and her mass is 63 kg. The painter pulls downward on the rope with a force of 600.0 N, while she and the scaffold are hanging from the other end above the ground.
Required:
a. What is the net acceleration on the system consisting of the painter and the scaffold?
b. What is the magnitude of the normal force exerted on the painter by the scaffold?
Solution :
a). From Newtons second law,
F = ma
The total tension force is 2T.
∴ 2T - (m + M)g = (m+ M)a
Then
[tex]$a=\frac{2T-(m+M)g}{m+M}$[/tex]
[tex]$a=\frac{2\times 600-(52+63)9.8}{52+63}$[/tex]
[tex]$=0.63 \ m/s^2$[/tex]
b). From the person,
F = ma
T - Mg + N = Ma
or N = Ma + Mg - T
= (63 x 9.8) + (52 x 9.8) - 600
= 617.4 + 509.6 - 600
= 527 N
A skater with an initial speed of 5.90 m/s stops propelling himself and begins to coast across the ice, eventually coming to rest. Air resistance is negligible. (a) The coefficient of kinetic friction between the ice and the skate blades is 0.0500. Find the deceleration caused by kinetic friction. (b) How far will the skater travel before coming to rest
Answer:a) - 0.4905 m/s² b) distance = 35.48 m
Explanation:
Given that
The initial velocity of the skater = 5.90 m/s
kinetic friction coefficient = 0.0500
final velocity = 0 m/s(since it comes to rest)
deceleration cause by the kinetic friction = ?
we know that
F = μN
and N= mg
Therefore;
F = μ m g....................(1)
also that
F = m a........................(2)
with our common Force, F, equating (1) and (2), we have that
m a = - μ m g
a = - μ g
a = - 0.05 × 9.81
a = - 0.4905 m/s²
The deceleration cause by the kinetic friction is a = - 0.4905 m/s²
b)
The distance the skater travels before stopping
is given as
Vf² = v₀² - 2 a x
final velocity = 0 m/s(since it comes to rest)
Therefore We have that
0 = v₀² - 2 a x
x = - v₀² / 2 a
x = 5.90² / (2 x 0.4905 )
34.81/0.981
x = 35.48 m
Or
using
v²-u² = 2aS final velocity = 0 m/s(since it comes to rest)
0²-5.90² = -2×0.4905×S
34.81=0.981S
S= 34.81/0.981
S=35.48m
what is the relation of pressure of a liquid with its depth and density?
Answer:
★ Pressure and depth have a directly proportional relationship. This is due to the greater column of water that pushes down on an object submerged. Conversely, as objects are lifted, and the depth decreases, the pressure is reduced.
Explanation:
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A diesel engine lifts the 225 kg hammer of a pile driver 20 m in 5 seconds. How much work is done on
the hammer? What is the power?
Answer:
a. Workdone = 44100 Joules
b. Power = 8820 Watts.
Explanation:
Given the following data:
Mass = 225kg
Distance = 20m
Time = 5 seconds
To find the workdone;
Workdone = force * distance
But force = mg
We know that acceleration due to gravity is equal to 9.8m/s²
Force = 225*9.8 = 2205N
Substituting the values into the equation, we have;
Workdone = 2205 * 20
Workdone = 44100 Joules
b. To find the power;
Power = workdone/time
Power = 44100/5
Power = 8820 Watts.
help please i will mark brainlist!!!
Answer:
.50 M
Explanation:
5*.50=2.5 + 2*.25=.5 = 3n
6*.50= 3N
Final answer is .50M
Question 2 (1 point)
70 cm are equivalent to how many m? State your answer using Scientific Notation.
70 x 10^-2 m
b
7.5 x 10^-2 m
이
ОООО
с
.75 X 10^-2 m
d
0.75 x10^-2 m
uction
Answer:
A) 70 x 10^-2
Explanation:
it would be 70 times negative 100 which equals 0.70
You are standing on the bottom of a lake with your torso above water. Which statement is correct?
a. You feel a buoyant force only when you momentarily jump up from the bottom of the lake.
b. There is a buoyant force that is proportional to the weight of your body below the water level.
c. There is a buoyant force that is proportional to the volume of your body that is below the level of the water.
d. There is no buoyant force on you since you are supported by the lake bottom.
Answer:
c. There is a buoyant force that is proportional to the volume of your body that is below the level of the water.
Explanation:
Buoyancy can be defined as a force which is created by the water displaced by an object.
Simply stated, buoyancy is directly proportional to the amount of water that is being displaced by an object.
Hence, the greater the amount of water an object displaces; the greater is the force of buoyancy pushing the object up.
The buoyancy of an object is given by the formula;
[tex] Fb = pgV [/tex]
[tex] But, \; V = Ah [/tex]
[tex] Hence, \; Fb = pgAh [/tex]
Where;
Fb = buoyant force of a liquid acting on an object.
g = acceleration due to gravity.
p = density of the liquid.
v = volume of the liquid displaced.
h = height of liquid (water) displaced by an object.
A = surface area of the floating object.
The unit of measurement for buoyancy is Newton (N).
In this scenario, you are standing on the bottom of a lake with your torso above water. Thus, there is a buoyant force that is proportional to the volume of your body that is below the level of the water.
1. Weather factors include
a. average air temperature.
b. annual precipitation.
c. humidity.
d. two of the above
2. The dew point is the temperature at which
a. dew forms on surfaces.
b. water vapor starts to condense.
c. relative humidity is 100 percent.
d. all of the above
3. Relative humidity may decrease if
a. water vapor condenses out of the air.
b. water evaporates into the air.
c. air temperature decreases.
d. two of the above
4. Which type of cloud forms at high altitudes?
a. cirrocumulus
b. altocumulus
c. stratocumulus
d. nimbostratus
5. Which type of cloud forms when strong air currents carry warm air upward?
a. cirrus
b. stratus
c. cumulus
d. cirrostratus
6. The type of fog that forms
6. The type of fog that forms when cool air moves over a warm lake is called
a. radiation fog.
b. advection fog.
c. steam fog.
d. upslope fog.
7. Rain that passes through a layer of freezing air near the ground become
a. glaze.
b. hail.
c. sleet.
d. snow.
Answer:
1. D
Climate is generally defined as the weather condition that prevails in a particular region over a long period of time. Climate is usually measured by examining the pattern of variation in several climatic factors such as rainfall, temperature, relative humidity, wind, pressure, etc. While the weather of a place can change within a space of few hours, it takes years for a change in climatic condition to occur.
2. d
3. c
4.a.
5. c
6. a.
7. c
Explanation:
The correct answers are (1) d. two of the above (average air temperature and humidity), (2)c. the relative humidity is 100 percent, (3)d. two of the above (water vapor condenses out of the air and air temperature decreases), (4)a. cirrocumulus, (5)c. cumulus, (6)c. steam fog, and (7)c. sleet.
What is temperature?Temperature is a physical quantity that measures the average kinetic energy of the particles in a substance or system. It is a measure of how hot or cold something is, and is typically measured in units such as degrees Celsius or Fahrenheit. Temperature can also be thought of as a measure of the direction in which heat energy flows, with heat energy naturally flowing from areas of higher temperature to areas of lower temperature.
Here in the Question,
1. Weather factors include d. two of the above (average air temperature and annual precipitation are two factors that affect weather, but humidity is also an important factor that can influence the feel of the air).
2. The dew point is the temperature at which b. water vapor starts to condense. When air cools, it can reach a point where it is unable to hold all of its moisture in the form of water vapor. At this point, the water vapor starts to condense into visible droplets, such as dew, and the temperature at which this happens is called the dew point. When the dew point is reached, the relative humidity is at 100 percent.
3. Relative humidity may decrease if d. two of the above (water vapor condenses out of the air and air temperature decreases) occur. If the air cools and reaches the dew point, water vapor will start to condense into droplets, which can reduce the amount of water vapor in the air and lower the relative humidity. Similarly, if the temperature drops without any change in water vapor content, the relative humidity will decrease because colder air can hold less moisture than warmer air.
4. The type of cloud that forms at high altitudes is a. cirrocumulus. These clouds are typically found at altitudes above 18,000 feet and are characterized by small, white, puffy clouds arranged in rows or ripples. They are often a sign of fair weather but can also indicate an approaching storm.
5. The type of cloud that forms when strong air currents carry warm air upward is c. cumulus. Cumulus clouds are large, puffy clouds that can develop vertically, forming a towering cloud with a flat top. They are often associated with thunderstorms and can produce heavy rain, hail, and lightning.
6. The type of fog that forms when cool air moves over a warm lake is c. steam fog. Steam fog, also called evaporation fog or sea smoke, occurs when cold, dry air moves over a warm, moist surface and causes water vapor to rise and condense into fog. This type of fog is often seen over bodies of water during the fall and winter.
7. Rain that passes through a layer of freezing air near the ground becomes c. sleet. Sleet is formed when raindrops fall through a layer of freezing air near the ground and freeze into small ice pellets before hitting the surface. It is different from hail, which forms in strong thunderstorms when updrafts carry raindrops upward into colder air where they freeze and then fall back to the ground, and snow, which forms in clouds when water vapor freezes directly into ice crystals. Glaze is a type of ice that forms when rain falls onto a surface that is below freezing, forming a layer of ice on top of the surface.
Therefore, The correct answers are:1. Weather factors include average air temperature, annual precipitation, and humidity. 2. The dew point is the temperature at which water vapor starts to condense. 3. Relative humidity may decrease if water vapor condenses out of the air or if the air temperature decreases. 4. The type of cloud that forms at high altitudes is cirrocumulus. 5. The type of cloud that forms when strong air currents carry warm air upward is cumulus. 6. The type of fog that forms when cool air moves over a warm lake is steam fog. 7. Rain that passes through a layer of freezing air near the ground becomes sleet, which is different from hail and snow.
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Consider a uniformly charged sphere of total charge Q and radius R centered at the origin. We want to find the electric field inside the sphere (r
Answer:
Hello your question is incomplete attached below is the complete question
answer :
Total charge enclosed within the sphere : [tex]\frac{q_{r1} }{4\pi e_{0}R^3 } . r[/tex]
Total charge enclosed outside the sphere : [tex]\frac{q}{4\pi e_{0}r^2 } .r[/tex]
Explanation:
Given data:
Total charge of a uniformly charged sphere = Q
radius = R
first step : find the electric field inside and outside the uniformly charged sphere
2nd step : determine the total charge enclosed within and outside the sphere
make a sketch of the uniformly charged sphere
Attached below is a detailed solution
A 120 W lightbulb and a 90 W lightbulb each operate at a voltage of 120 V. Part A Which bulb carries more current? Which bulb carries more current? 120 W lightbulb 90 W lightbulb The currents are equal. It is impossible to determine.
Answer:
120 W lightbulb
Explanation:
Let the two lightbulb be A and B respectively.
Given the following data;
Power A = 120W
Power B = 90W
Voltage = 120V
To find the current flowing through each lightbulb;
a. For lightbulb A
Power = current * voltage
120 = current * 120
Current = 120/120
Current = 1 Ampere.
b. For lightbulb B
Current = power/voltage
Current = 90/120
Current = 0.75 Amperes
Therefore, the lightbulb that carries more current is A with 1 Ampere.
The bulb that carries more current is :
- A with 1 Ampere.
Let the two lightbulb be A and B respectively.
Given :Power A = 120WPower B = 90WVoltage = 120VTo find the current flowing through each lightbulb;
a. For lightbulb APower = current * voltage120 = current * 120Current = 120/120Current = 1 Ampere.b. For lightbulb BCurrent = power/voltageCurrent = 90/120Current = 0.75 AmperesThus, the lightbulb that carries more current is A with 1 Ampere.
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What is the maximum centripetal acceleration experienced by a person standing still on the surface of the Earth? Where must they be located?
Answer:
The person must be located in the Equator Line. The maximum centripetal acceleration experienced by a person is 0.0337 meters per square second.
Explanation:
Physically speaking, the centripetal acceleration ([tex]a_{r}[/tex]), measured in meters per square second, experienced by a person is defined by the following expression:
[tex]a_{r} = \omega^{2}\cdot r[/tex] (1)
Where:
[tex]\omega[/tex] - Angular speed of the Earth, measured in radians per second.
[tex]r[/tex] - Distance perpendicular to the rotation axis, measured in meters.
Since rotation axis passes through poles and distance described above is directly proportional to centripetal acceleration. The person must be located in the Equator Line, which is equivalent to the radius of the planet.
In addition, the angular speed of the Earth can be calculated in terms of its period ([tex]T[/tex]), measured in seconds:
[tex]\omega = \frac{2\pi}{T}[/tex] (2)
If we know that [tex]r = 6.371\times 10^{6}\,m[/tex] and [tex]T = 86400\,s[/tex], then the maximum centripetal acceleration experienced by a person is:
[tex]a_{r} = \left(\frac{2\pi}{86400\,s} \right)^{2}\cdot (6.371\times 10^{6}\,m)[/tex]
[tex]a_{r} = 0.0337\,\frac{m}{s^{2}}[/tex]
The maximum centripetal acceleration experienced by a person is 0.0337 meters per square second.
The person standing still on the surface of the earth must be located in the equator line
Recall: the the centripetal acceleration at the Equator is about 0.03 m/s2.
This then means that the maximum centripetal acceleration of a person standing in the equator line is 0.03 m/s2
What is meant by maximum centripetal acceleration?The maximum centripetal acceleration as the name implies is the maximum speed of a body or object in a circular path
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If the diameter of a moose eye is 40 mm, what is the total refractive power of the anterior portion of the eye?
Answer:
-the ratio of the speed of light
in air to the speed of light in the substance.
-speed of light in air 300,000 km/sec, which decreases when it passes through a transparent substance.
-e.g.. speed of light in substance = 200,000 km/sec, R.I. = 300,000/200,000 = 1.5
Explanation:
A 50kg mass is sitting on a frictionless surface. An unknown constant force pushes the mass for 2 seconds until the mass reaches a velocity of 3m/s. What was the force acting on the mass?
Answer:
75N
Explanation:
a = v/t = 3/2
F = ma = 50(3/2) = 75
1. If a wave has a wavelength of 5.5m and a frequency of 45hz, what is its speed?
Answer:
By using the most simple velocity equation, velocity = distance / time, meaning the speed would be 247.5 meters per second.
List down the types of centripetal force?
Answer: Just a few examples are the tension in the rope on a tether ball, the force of Earth's gravity on the Moon, friction between roller skates and a rink floor, a banked roadway's force on a car, and forces on the tube of a spinning centrifuge. Any net force causing uniform circular motion is called a centripetal force.
Answer:
roller skates and a rink floor, a banked roadway's force on a car, and forces on the tube of a spinning centrifuge
Explanation:
1. A block with mass 20 kg is
sliding up a plane (Ukinetic=0.3,
inclined at 10°) at a speed of
2 m/s to the right (positive
X-direction). How far does it
go up along the plane before
it comes to rest momentarily?
Answer: 0.435 m
Explanation:
Given
mass m=20 kg
initial speed u=2 m/s
coefficient of kinetic friction [tex]\mu_k=0.3[/tex]
deceleration which opposes the motion is given by
[tex]\Rightarrow a=g\sin \theta+\mu_kg\cos \theta\\\Rightarrow a=g(\sin \theta +\mu_k\cos \theta)[/tex]
[tex]\Rightarrow a=9.8(\sin 10^{\circ}+0.3\times \cos 10^{\circ})\\\Rightarrow a=4.59\ m/s^2[/tex]
using [tex]v^2-u^2=2as[/tex]
[tex]\Rightarrow s=\dfrac{2^2}{2\times 4.59}=0.435\ m[/tex]
A simple pendulum is used to measure gravity using the following theoretical equation,TT=2ππ�LL/gg ,where L is the length of the pendulum, g is gravity, andT is the period of pendulum.Twenty measurements of T give a mean of 1.823 seconds and a standard deviation of 0.0671 s. The device used to measure time has a resolution of 0.02 s. The pendulum length is measured once to be 0.823 m (with a scale having a resolution of 0.001 m). Determine the value of g and its uncertainty (assume 90% confidence where necessary). You may use any method of uncertainty propagation that we covered in class.
Answer:
g ±Δg = (9.8 ± 0.2) m / s²
Explanation:
For the calculation of the acceleration of gravity they indicate the equation of the simple pendulum to use
T = [tex]2\pi \sqrt{ \frac{L}{g} }[/tex]
T² = [tex]4\pi ^2 \frac{L}{g}[/tex]4pi2 L / g
g = [tex]4\pi ^2 \frac{L}{T^2}[/tex]
They indicate the average time of 20 measurements 1,823 s, each with an oscillation
let's calculate the magnitude
g = [tex]4\pi ^2 \frac{0.823}{1.823^2}[/tex]4 pi2 0.823 / 1.823 2
g = 9.7766 m / s²
now let's look for the uncertainty of gravity, as it was obtained from an equation we can use the following error propagation
for the period
T = t / n
ΔT = [tex]\frac{dT}{dt}[/tex] Δt + [tex]\frac{dT}{dn}[/tex] ΔDn
In general, the number of oscillations is small, so we can assume that there are no errors, in this case the number of oscillations of n = 1, consequently
ΔT = Δt / n
ΔT = Δt
now let's look for the uncertainty of g
Δg = [tex]\frac{dg}{dL}[/tex] ΔL + [tex]\frac{dg}{dT}[/tex] ΔT
Δg = [tex]4\pi ^2 \frac{1}{T2}[/tex] ΔL + 4π²L (-2 T⁻³) ΔT
a more manageable way is with the relative error
[tex]\frac{\Delta g}{g} = \frac{\Delta L }{L} + \frac{1}{2} \frac{\Delta T}{T}[/tex]
we substitute
Δg = g ( \frac{\Delta L }{L} + \frac{1}{2} \frac{\Delta T}{T}DL / L + ½ Dt / T)
the error in time give us the stanndard deviation
let's calculate
Δg = 9.7766 ([tex]\frac{0.001}{0.823} + \frac{1}{2} \ \frac{0.671}{1.823}[/tex])
Δg = 9.7766 (0.001215 + 0.0184)
Δg = 0.19 m / s²
the absolute uncertainty must be true to a significant figure
Δg = 0.2 m / s2
therefore the correct result is
g ±Δg = (9.8 ± 0.2) m / s²
What is a black hole's escape velocity?
The simplest definition of a black hole is an object that is so dense that not even light can escape its surface. If we squished the Earth's mass into a sphere with a radius of 9 mm, the escape velocity would be the speed of light. Just a wee-bit smaller, and the escape velocity is greater than the speed of light.
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A freight train has a mass of [02] kg. The wheels of the locomotive push back on the tracks with a constant net force of 7.50 × 105 N, so the tracks push forward on the locomotive with a force of the same magnitude. Ignore aerodynamics and friction on the other wheels of the train. How long, in seconds, would it take to increase the speed of the train from rest to 80.0 km/h?
Answer:
t = 300.3 seconds
Explanation:
Given that,
The mass of a freight train, [tex]m=1.01\times 10^7\ kg[/tex]
Force applied on the tracks, [tex]F=7.5\times 10^5\ N[/tex]
Initial speed, u = 0
Final speed, v = 80 km/h = 22.3 m/s
We need to find the time taken by it to increase the speed of the train from rest.
The force acting on it is given by :
F = ma
or
[tex]F=\dfrac{m(v-u)}{t}\\\\t=\dfrac{m(v-u)}{F}\\\\t=\dfrac{1.01\times 10^7\times (22.3-0)}{7.5\times 10^5}\\\\t=300.3\ s[/tex]
So, the required time is 300.3 seconds.
A spring with a constant of 76 N/m is extended by 0.9 m. How much energy is stored in the extended spring?
Answer:
[tex]E=30.78\ J[/tex]
Explanation:
The force constant of the spring, k = 76 N/m
The extension in the spring, x = 0.9 m
We need to find the energy is stored in the extended spring. The energy stored in the spring is given by :
[tex]E=\dfrac{1}{2}kx^2\\\\E=\dfrac{1}{2}\times 76\times (0.9)^2\\\\E=30.78\ J[/tex]
So, 30.78 J of energy is stored in the spring.
A cat is sleeping on the floor in the middle of a 2.8-m-wide room when a barking dog enters with a speed of 1.40 m/s. As the dog enters, the cat (as only cats can do) immediately accelerates at 0.85 m/s2 toward an open window on the opposite side of the room. The dog (all bark and no bite) is a bit startled by the cat and begins to slow down at 0.10 m/s^2 as soon as it enters the room.
Required:
How far is the cat in front of the dog as it leaps through the window?
Answer:
the cat is 0.4238 m in front of the dog as it leaps through the window
Explanation:
Given that;
acceleration a = 0.85 m/s²
speed v = 1.40 m/s
the cat is at rest, so initial velocity u = 0
we know that, since the cat is sleeping on the floor in the middle of a 2.8-m-wide room, it needs to cover (2.8 m / 2 ) distance to get to the window;
using the second equation equation of motion;
s = ut + 1/2 at²
we substitute
2.8/2 = 0×t + 1/2 × 0.85 × t²
1.4 = 0.425t²
t = √( 1.4 / 0.425 )
t = 1.81497 sec
now, at acceleration 0.10 m/s²
the dog has to cover the distance;
s = ut + 1/2 at²
s = ( 1.4 × 1.81497) - 1/2 × 0.10 × 1.81497²
s = 2.540958 - 0.1647
s = 2.3762 m
The cant in front of the dog as it leaps through the window;
distance = 2.8 m - 2.3762 m
distance = 0.4238 m
Therefore, the cat is 0.4238 m in front of the dog as it leaps through the window
Identical balls are dropped from the same initial height and bounce back to half the initial height. In Case 1, the ball bounces off a cement floor, and in Case 2, the ball bounces off a piece of stretchy rubber. Two cases of a ball dropping and bouncing off of a surface. In case one, the ball approaches a cement floor, comes in contact, momentarily comes to rest, and then bounces off with a velocity smaller than the approach velocity. In case 2, the ball approaches a piece of stretchy rubber. When the ball comes in contact with the rubber, it deforms the rubber and comes momentarily to rest. The ball bounces off again with a velocity smaller than the approach velocity, and the rubber regains its original shape. In both cases, the balls are dropped from the same initial height and reach the same final height. In which case is the magnitude of the ball's change in momentum the greatest
Answer:
the impulse must be the same in these two cases F t = m ([tex]\sqrt{2g h_f } - \sqrt{2g h_o}[/tex])
Explanation:
For this exercise we use the relationship between momentum and momentum
I = Δp
F t = m v_f - m v₀
To know the speed we use the conservation of energy
starting point. Highest point
Em₀ = U = m g h
fincla point. Just before the crash
Em_f = K = ½ m v²
energy is conserved
Em₀ = Em_f
m g h = ½ m v²
v = [tex]\sqrt{2gh}[/tex]
we substitute in the impulse relation
F t = m ([tex]\sqrt{2g h_f } - \sqrt{2g h_o}[/tex])
therefore we can see that as in case the initial and final heights are equal, the impulse must be the same in these two cases
A spring is stretched 5 mm by a force of 125 N. How much will the spring stretch
when 250 N force is applied?
Answer:
10 mm
Explanation:
We'll begin by calculating the spring constant of the spring. This can be obtained as follow:
Extention (e) = 5 mm
Force (F) = 125 N
Spring constant (K) =?
F = Ke
125 = K × 5
Divide both side by 5
K = 125 / 5
K = 25 N/mm
Finally, we shall determine how much the spring will stretch when a 250 N force is applied. This can be obtained as follow:
Force (F) = 250 N
Spring constant (K) = 25 N/mm
Extention (e) =?
F = Ke
250 = 25 × e
Divide both side by 25
e = 250 / 25
e = 10 mm
Thus, the spring will stretch 10 mm when a 250 N force is applied.