Answer:
The speed of the ball when it reaches equilibrium position is 3.31 m/s
Explanation:
Given;
mass of the object, m = 0.25 kg
initial displacement of the object, h₁ = 0.56 m
spring constant, k = 105 N/m
displacement at equilibrium position, h₂ = 0
initial velocity of the object, v₁ = 0
velocity of the object at equilibrium position = v₂
The change in gravitational potential energy at the equilibrium position is given as;
ΔP.E = mg(h₂ - h₁)
The change in kinetic energy of the object at the equilibrium position is given as;
ΔK.E = ¹/₂m(v₂² - v₁²)
Apply the principle of conservation of mechanical energy;
ΔK.E + ΔP.E = 0
¹/₂m(v₂² - v₁²) + mg(h₂ - h₁) = 0
¹/₂m(v₂² - 0) + mg(0 - h₁) = 0
¹/₂mv₂² - mgh₁ = 0
¹/₂mv₂² = mgh
¹/₂v₂² = gh
v₂² = 2gh
v₂ = √2gh
v₂ = √(2 x 9.8 x 0.56)
v₂ = 3.31 m/s
Therefore, the speed of the ball when it reaches equilibrium position is 3.31 m/s
The rotating loop in an AC generator is a square 18 cm on each side. It is rotated at 60.0 Hz in a uniform magnetic field of 0.3T. Calculate the approximate value of the maximum amplitude of the power delivered to the loop for a loop resistance of 12 ohm ?
Answer:
The maximum amplitude power is 1.12 W
Explanation:
Given;
length of each side of the square, L = 18 cm = 0.18 m
angular frequency, f = 60 Hz
magnetic field, B = 0.3 T
resistance of the loop, R = 12 ohm
The area of the loop, A = L² = 0.18 m x 0.18 m = 0.0324 m²
The angular speed, ω = 2πf = 2π x 60 = rad/s = 377.04 rad/s
The maximum value of emf induced;
[tex]E_{max} = NBA \omega\\\\where; \\N \ is \ number \ of \ turns\\\\E_{max} = (1) \times 0.3 \times 0.0324 \times 377.04\\\\E_{max} = 3.665 \ V[/tex]
The maximum amplitude power is calculated as;
[tex]Power = \frac{(E_{max})^2 }{R} \\\\Power = \frac{(3.665)^2}{12} \\\\Power = 1.12 \ W[/tex]
A spinning satellite begins to unfold two solar panels as shown. As the
panels extend from the satellite, what is the result?
Its angular momentum of a satellite will drop even as satellite panel stretch because of the reduction in angular velocity brought on by the drag effect.
Why then do stars spin more quickly during their demise?A portion of the star's mass is blown off during the supernovae that come before the creation of black holes, taking some of the star's total angular momentum with it.The leftover material sinks into the star's core while continuing to spin rapidly.
What is the name of the spinning effect?Magnus effect: When there is relative movement between both the spinning item and the fluid, a sideways force is generated on a rotating cylindrical or spherical object immersed in the fluid (liquid or gas).In honor of the German chemist and physicist H.G.
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Give an example of a physical entity that is quantized. State specifically what the entity is and what the limits are on its values.
Answer:
A charge is a physical entity that has been quantized. The limits on its values are the value of a charged particle quantized in the state where 'n'...
Explanation:
One example of a physical entity that is quantized is:
The amount of money in your pocket.
The amount can't have any fraction of 1 cent.
Its value must be an integer-multiple of cents, or 0.01 dollar.
When it increases or decreases, it jumps from one integer number of cents to the next integer number. It doesn't "slide" from one to the next. It can never have a value between two integer numbers of cents.
Suppose the Earth were squeezed down to the size of a small mountain. The mass of the Earth would not change, just its volume and radius. If you were now standing on the surface, would the gravitational force on you be greater than, less than or the same as before the Earth was squeezed?
Explanation:
Much greater. Gravitational force depends on the mass and separation distance. Shrinking the earth means the mass remains the same while the radius gets smaller. Since gravitational force is inversely proportional to the square of the separation distance, as shown by Newton's universal gravitational law
[tex]\:\:\:F_G = G \dfrac{mM_E}{R^2}[/tex]
shrinking the radius even by a factor of 10 will cause your weight, which also happens to be the gravitational force of the earth on you, to be 100 times more.
If the mass of the Earth remains the same and only its volume and radius are decreased, then the average density of the Earth would increase significantly.
What is gravitational force?Gravity, also known as gravitational force, pulls objects with mass towards each other. We frequently consider the force of gravity from Earth.
If the Earth's mass remains constant while its volume and radius are reduced, the average density of the Earth increases significantly.
This is due to the fact that the mass has been compressed into a much smaller volume.
As a result, standing on the surface, the gravitational force on you would be greater than before the Earth was compressed to the size of a small mountain.
When the Earth is compressed, the distance between you and the center of the Earth decreases while the mass remains constant.
Thus, your gravitational force increases.
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suppose a 1 square meter panel of colar cells has an efficiency of 20% and recieves the equivlent of 6 hours of direct sunlight per day. What average power, in watts, does the panel produce
Answer:
The average power per day is 1008 kW.
Explanation:
Solar constant = 1.4 kW/m2
efficiency = 20 %
area, a = 1 square meter
time = 6 hours
Energy falling on the panel in 6 hours = 1.4 x 6 x 3600 kJ
The output is
= 20 % of 1.4 x 6 x 3600
= 0.2 x 1.4 x 6 x 3600
= 6048 kJ
Average power per day is
= 6048/6 = 1008 kW
A farmhand pushes a 23 kg bale of hay 3.9 m across the floor of a barn. If she exerts a horizontal force of 91 N on the hay, how much work has she done?
Answer:
W = 354.9 J
Explanation:
Given that,
The mass of a bale of hay, m = 23 kg
The displacement, d = 3.9 m
The horizontal force exerted on the hay, F = 91 N
We need to find the work done. We know that,
We know that,
Work done, W = Fd
So,
W = 91 N × 3.9 m
W = 354.9 J
So, the required work done is 354.9 J.
Vectors 퐴, 퐵and 퐶are added together. 퐴has a magnitude of 20.0 units and makes an angle of 60.0° counterclockwise from the negativex-axis. 퐵has a magnitude of 40.0 units and makes an angle of 30.0° counterclockwise from the positive x-axis.퐶has a magnitude of 35.0 units and makes an angle of 60.0° clockwise from the negative y-axis. Determine the magnitude of the resultant vector 퐴+퐵+퐶and its direction as an angle measured counterclockwise from the positive x-axis.
Answer:
Magnitude = 15.86 units
direction = 69 degree below negative X axis
Explanation:
A = 20 units at 60.0° counterclockwise from the negative x - axis
B = 40 units at 30.0° counterclockwise from the positive x - axis
C = 35 units at 60.0° clockwise from the negative y - axis
Write the vectors in the vector form
[tex]\overrightarrow{A} =20 (- cos 60 \widehat{i} - sin 60 \widehat{j})=- 10\widehat{i} - 17.3 \widehat{j}\\\\\overrightarrow{B} =40 (cos 30 \widehat{i} + sin 30 \widehat{j})= 34.6\widehat{i} +20 \widehat{j}\\\\\overrightarrow{C} =35 (- sin 60 \widehat{i} - cos 60 \widehat{j})=- 30.3\widehat{i} - 17.5 \widehat{j}\\\\Now\\\\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = (- 10 + 34.6 - 30.3) \widehat{i} + (-17.3 + 20-17.5)\widehat{j}\\\\[/tex]
[tex]\\\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = - 5.7\widehat{i} -14.8\widehat{j}[/tex]
The magnitude is given by
[tex]= \sqrt{5.7^2 + 14.8^2} = 15.86 units[/tex]
The direction is given by
[tex]tan\theta = \frac{- 14.8}{- 5.7}\\\\\theta= 69^o[/tex]
below negative X axis.
PLEASE HELP ME WITH THIS ONE QUESTION
What is the rest energy of a proton? (c = 2.9979 x 10^9 m/s, mp = 1.6726 x 10^-27)
A) 8.18 x 10^-14 J
B) 2.73 x 10^-22 J
C) 1.5053 x 10^-10 J
D) 1.5032 x 10^-10 J
Answer:
D) 1.5032 x 10^-10 J
Explanation:
The rest energy of a proton, E₀, follows the equation:
E₀ = mp*rate²
Where mass of proton, mp = 1.6726 x 10^-27kg
rate = 2.9979 x 10^8 m/s (2.9979 x 10^9 m/s is not the speed light)
E₀ = 1.6726 x 10^-27kg * (2.9979 x 10^8 m/s)²
E₀ =1.5032 x 10^-10 J
Right answer is:
D) 1.5032 x 10^-10 JAn unstretched ideal spring hangs vertically from a fixed support. A 0.4 kg object is then attached to the lower end of the spring. The object is pulled down to a distance of 0.35 m below the unstretched position and released from rest at time t= 0. A graph of the subsequent vertical position y of the lower end of the spring as a function of t is given above, where y= 0 when the spring was initially unstretched. At which time is the upward velocity of the object the greatest?
Answer:
The correct answer will be "0.25 sec".
Explanation:
The graph of the given question is attached below.
According to the graph of the question,
Time,
T = 1 sec
For the upward velocity,
⇒ [tex]t = \frac{T}{4}[/tex]
By putting the value, we get
⇒ [tex]=\frac{1}{4}[/tex]
⇒ [tex]=0.25 \ sec[/tex]
In a science fiction novel two enemies, Bonzo and Ender, are fighting in outer spce. From stationary positions, they push against each other. Bonzo flies off with a velocity of 1.1 m/s, while Ender recoils with a velocity of -4.3 m/s. Determine the ratio Bonzo/mEnder of the masses of these two enemies.
Answer:
the ratio Bonzo/mEnder of the masses of these two enemies is 3.91
Explanation:
Given the data in the question;
Velocity of Bonzo [tex]V_{Bonzo[/tex] = 1.1 m/s
Velocity of Ender [tex]V_{Ender[/tex] = -4.3 m/s
the ratio Bonzo/mEnder of the masses of these two enemies = ?
Now, using the law of conservation of momentum.
momentum of both Bonzo and Ender are conserved
so
Initial momentum = final momentum
we have
0 = [tex]m_{Bonzo[/tex] × [tex]V_{Bonzo[/tex] + [tex]m_{Ender[/tex] × [tex]V_{Ender[/tex]
[tex]m_{Bonzo[/tex] × [tex]V_{Bonzo[/tex] = -[ [tex]m_{Ender[/tex] × [tex]V_{Ender[/tex] ]
[tex]m_{Bonzo[/tex] / [tex]m_{Ender[/tex] = -[ [tex]V_{Ender[/tex] / [tex]V_{Bonzo[/tex] ]
we substitute
[tex]m_{Bonzo[/tex] / [tex]m_{Ender[/tex] = -[ -4.3 m/s / 1.1 m/s ]
[tex]m_{Bonzo[/tex] / [tex]m_{Ender[/tex] = -[ -3.9090 ]
[tex]m_{Bonzo[/tex] / [tex]m_{Ender[/tex] = 3.91
Therefore, the ratio Bonzo/mEnder of the masses of these two enemies is 3.91
How would an observer on train A, which is moving at nearly the speed of light, view a clock on train B, which is moving at the same speed and in the same direction?
A. The clock on train B would appear narrower and run more slowly.
B. The clock on train B would appear to be the same width and to run at the same rate. C. The clock on train B would appear narrower and run faster.
D. The clock on train B would appear wider and run more slowly.
Answer:
B.
Explanation:
If both train A and train B are moving in the same direction and the exact same speed then from an observer's viewpoint within either train everything would seem as though it is not moving. Therefore, the clock on train B would appear to be the same width and to run at the same rate. In order for this to be the case the speed of both trains would need to be exactly the same, any difference in speed will cause the clock on the opposite train to appear distorted and run either faster or slower depending on the speed of the train you are on.
Answer:
The trains are moving at the same speed, so the answer is A.
In June 1985, a laser beam was sent out from the Air Force Optical Station on Maui and reflected back from the shuttle Discovery as it passed by 354 km overhead. The diameter of the central maximum of the beam at the shuttle position was 500 nm. What is the effective diameter of the circular laser aperture at the Maui ground station
This question is incomplete, the complete question is;
In June 1985, a laser beam was sent out from the Air Force Optical Station on Maui and reflected back from the shuttle Discovery as it passed by 354 km overhead. The diameter of the central maximum of the beam at the shuttle position was said to be 9.1 m, and the beam wavelength was 500 nm.
What is the effective diameter of the circular laser aperture at the Maui ground station
Answer:
the effective diameter of the circular laser aperture at the Maui ground station is 4.747 cm
Explanation:
Given the data in the question;
Separation between observer and point L = 354 km = 354000 m
Linear separation D = 9.1 m
wavelength λ = 500 nm = 500 × 10⁻⁹ m
Now, for small angles;
θ = D / L
θ = 9.1 m / 354000 m
θ = 2.57 × 10⁻⁵ rad
For a circular aperture;
sinθ = ( 1.22 × λ ) / d
for small angles;
θ = ( 1.22 × λ ) / d
so
θ = 2 × θ
θ = 2 × [( 1.22 × λ ) / d]
we substitute
2.57 × 10⁻⁵ = 2 × [( 1.22 × 500 × 10⁻⁹ ) / d]
2.57 × 10⁻⁵ = 0.00000122 / d
d = 0.00000122 / 2.57 × 10⁻⁵
d = 0.04747 m
d = ( 0.04747 × 100 )m
d = 4.747 cm
Therefore, the effective diameter of the circular laser aperture at the Maui ground station is 4.747 cm
Calculate the heat energy conducted per hour through the side walls of a cylindrical steel
boiler of 1.00 m diameter and 3.0 m long if the internal and external temperatures of the
walls are 140 °C and 40 °C respectively and the thickness of the walls is 6.0 mm. (Thermal
conductivity of steel, k = 42 Wm-4°C-4)
Explanation:
heat caoacity and heat is difference
The heat energy conducted per hour through the side walls of the cylindrical steel boiler is 27708847 kJ.
What is thermal conductivity?The rate at which heat is transported by conduction through a material's unit cross-section area when a temperature gradient exits perpendicular to the area is known as thermal conductivity.
In the International System of Units (SI), thermal conductivity is measured by Wm⁻¹K⁻¹.
Diameter of the cylindrical steel boiler: d = 1.00m.
Length of the cylindrical steel boiler: l = 3.00m.
thickness of the walls is = 6.0 mm = 0.006 m
Temperature gradient is = (140-40) °C/0.006 m = 1666.67 °C/m
Thermal conductivity of steel, = 42 W/m-°C.
Hence, the heat energy conducted per hour through the side walls of the cylindrical steel boiler = 42×3600×1666.67 ×2π×0.5(0.5+3.0) Joule
= 27708847 kJ
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Two horizontal forces are acting on a box. The box moves only along the x axis. There is no friction between the box and the surface. Suppose that = +5.9 N and the mass of the box is 3.6 kg. Find the magnitude and direction of when the acceleration of the box is +7.1 m/s^2.
Answer:
sorry I don't know I am only in 7th grade
A soccer player kicks a ball. Why does the action force exerted by the player's foot cause a different motion than the reaction force?
The reaction force is greater than the action force.
The action force and the reaction force act on different objects.
The action force is greater than the reaction force.
The action force and the reaction force act in opposite directions.
Answer:
D because of POE
Explanation:
the reaction force is the ball exerting the same newtons of force back to your leg opposite of the ball, but the reaction force and the action force is never stronger than each-other. and action is only being done on the soccer ball, so process of elimination, the answer is D
Answer:
B
Explanation:
it can only have a different motion if it is acted upon a different ball
Six artificial satellites complete one circular orbit around a space station in the same amount of time. Each satellite has mass m and radius of orbit L. The satellites fire rockets that provide the force needed to maintain a circular orbit around the space station. The gravitational force is negligible.
Rank the net force acting on each satellite from their rockets. Rank from largest to smallest.
a. m=200 kg and L= 5000m
b. m=400 kg and L=2500m
c. m=100kg and L=2500m
d. m=100kg and L=10000m
e. m=800kg and L=5000m
f. m=300kg and L=7500m
Answer:
b = e > a = c = f > d
Explanation:
Since the satellites complete one circular orbit in the same amount of time, their speed is the same.
The force needed to maintain the orbit is the centripetal force given by F = mv²/L where m = mass of artificial satellite and L = radius of orbit.
So, for artificial satellite a
a. m=200 kg and L= 5000m
F = mv²/L
F = 200 kgv²/5000 m
F = 0.04v² N
So, for artificial satellite b
b. m=400 kg and L= 2500m
F = mv²/L
F = 400 kgv²/2500 m
F = 0.16v² N
So, for artificial satellite c
c. m=100 kg and L= 2500m
F = mv²/L
F = 100 kgv²/2500 m
F = 0.04v² N
So, for artificial satellite d
d. m=100 kg and L= 10000m
F = mv²/L
F = 100 kgv²/10000 m
F = 0.01v² N
So, for artificial satellite e
e. m=800 kg and L= 5000m
F = mv²/L
F = 800 kgv²/5000 m
F = 0.16v² N
So, for artificial satellite f
f. m=300 kg and L= 7500m
F = mv²/L
F = 300 kgv²/7500 m
F = 0.04v² N
So, the net force are in the order b = e > a = c = f > d
An object that gives off electromagnetic waves based on its temperature
demonstrates which phenomenon?
A. Emission spectra
B. Blackbody radiation
C. Quantum mechanics
D. Photoelectric effect
Answer:
B) Blackbody radiation
MARK THIS AS BRAINLIEST PLEAWESSS :)
Answer:
Black body radiation
Explanation:
A professional quarterback throws a 0.40 kg football. what is the force of weight?
Answer:
3.92N
Explanation:
Force= mass×accelerarion due gravity
But mass= 0.40kg
acceleration due to gravity = 9.8 m/s^2
Force = 0.40×9.8
Force=3.92N
the two factors that affect the amount of heat
Answer:
The two important factors that affect heat energy are specific heat and temperature. Specific heat is a heat-constant of a material per unit mass per degree of temperature change (in units of energy per mass and temperature), like Joules/Kg-°C .
Thank you.....
Have a good day.....
Definition of Xenophobia
Answer:
dislike of or prejudice against people from other countries.
Explanation:
Answer: dislike of or prejudice against people from other countries.
Explanation:
A motor has an output of 1000 watts. When the motor is working a full capacity, how much time will it require to lift a 50 Newton weight 100 meters?
The time required to lift the weight is 5 seconds.
What is time?Time is the measure of past or present events or occurrences. The S.I unit of time is seconds (s).
To calculate the time required to lift the weight, we use the formula below.
Formula:
P = Fd/t.................. Equation 1Where:
P = PowerF = Weightd = distance.t = timemake t the subject of the equation.
t = Fd/P................ Equation 2From the question,
Given:
F = 50 Nd = 100 mP = 1000 WSubstitute these values into equation 2
t = (50×100)/1000t = 5 seconds.Hence, The time required to lift the weight is 5 seconds.
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A motorist travels due North at 90 km/h for 2 hours. She changes direction and travels West at 60 km/for 1 hour.
a) Calculate the average speed of the motorist [4]
b) Calculate the average velocity of the motorist.
Answer:
a. 50km/hr.
b. 10km/hr
Explanation:
Average speed, which is calculated by dividing the total distance travelled by the time interval as follows:
Average speed = total distance travelled ÷ time
Average velocity is calculated by dividing the total displacement by the time interval as follows:
Average velocity = change in displacement (∆x) ÷ time (t)
According to this question, a motorist travels due North at 90 km/h for 2 hours. She then changes direction and travels West at 60 km/for 1 hour.
Total distance of this journey is 90 + 60 = 150
Total time taken = 1 + 2 = 3hours
Average speed = 150/3
= 50km/hr.
b.) Average velocity = x2 - x1/t
Average velocity = 90 - 60/3
= 30/3
= 10km/hr
20 points, im begging for help‼️
How much capacitance is needed to
store 0.00100 J of energy when the
charge on the capacitor is
4.86 x 10-5 C?
[?] x 10?!F
Answer:
Capacitance= 1.18×10^-6
Answer: 1.18*10^-6
Explanation:
What is the source of almost all energy on Earth?
Earth’s hot core
the Sun
stored carbon
moving water
Answer:
the sun
Explanation:
The sun is the source of almost all energy on Earth beacuse both plants and animal on Earth derive their energy from the sun.
Source of energy on EarthThe Earth is one of the planets that make up the solar system. The Sun is the center of the universe and the Earth revolves round the sun.
The source of almost all energy on Earth is from the sun. The energy from the sun is callled solar energy.
This energy from the sun can be used by the planet to manufatcure its own food. The plants are consumed by animals to provide energy their metabolic activities.
Thus, we can conclude that the sun is the source of almost all energy on Earth beacuse both plants and animal on Earth derive their energy from the sun.
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A light-emitting diode (LED) connected to a 3.0 V power supply emits 440 nm blue light. The current in the LED is 11 mA , and the LED is 51 % efficient at converting electric power input into light power output. How many photons per second does the LED emit?
Answer:
3.73 * 10^16 photons/sec
Explanation:
power supply = 3.0 V
Emits 440 nm blue light
current in LED = 11 mA
efficiency of LED = 51%
Calculate the number of photons per second the LED will emit
first step : calculate the energy of the Photon
E = hc / λ
=( 6.62 * 10^-34 * 3 * 10^8 ) / 440 * 10^-9
= 0.0451 * 10^-17 J
Next :
Number of Photon =( power supply * efficiency * current ) / energy of photon
= ( 3 * 0.51 * 11 * 10^-3 ) / 0.0451 * 10^-17
= 3.73 * 10^16 photons/sec
4. You currently have TWO 9 volt batteries connected to a 82 resistor. How
much current is flowing through the circuit? *
1.125 A
5 A
72 A
2.25 A
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Explanation:
Total voltage = 9 × 2 = 18v
Resistance = 82 Ω
Ohm's law::
V = IR
18v = 82 Ω × I
18v /82 /Ω = I
18/82 Ampere is the current
During hockey practice, two pucks are sliding across the ice in the same direction. At one instant, a 0.18-kg puck is moving at 16 m/s while the other puck has a mass of 0.14 kg and a speed of 3.8 m/s. What is the velocity of the center of mass of the two pucks?
Answer:
10.66 m/s
Explanation:
Applying,
The law of conservation of momentum,
Total momentum before collision = Total momentum after collision
mu+m'u' = V(m+m').............. Equation 1
Where m = mass of the first puck, u = initial velocity of the first puck, m' = mass of the second puck, u' = initial velocity of the second puck, V = Velocity of the center of the two pucks
make V the subject of the equation
V = (mu+m'u')/(m+m').............. Equation 2
Given: m = 0.18 kg, u = 16 m/s, m' = 0.14 kg, u' = 3.8 m/s
Substitute these values into equation 2
V = [(0.18×16)+(0.14×3.8)]/(0.18+0.14)
V = (2.88+0.532)/(0.32)
V = 3.412/0.32
V = 10.66 m/s
Suppose that 2 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 43 cm. (a) How much work is needed to stretch the spring from 33 cm to 35 cm
Answer:
0.035 J
Explanation:
Applying,
W = ke²/2.............. Equation 1
Where W = workdone by the stretching the spring, k = spring constant, e = extension.
make k the subject of the equation
k = 2W/e²............... Equation 2
From the question
Given: W = 2 J, e = (43-28) = 15 cm = 0.15 m
Substitute these values into equation 2
k = (2×2)/(0.15²)
k = 177.78 N/m
Hence, work need to stretch the spring from 33 cm to 35 cm
therefore,
e = 35-33 = 2 cm = 0.02 m
Substitute into equation 1
W = 177.78(0.02²)/2
W = 0.035 J
what happened on march 21 every year in the northern hemisphere
Answer:
B. The Spring equinox
Explanation:
The vernal equinox marks the moment the sun crosses the celestial equator. The vernal equinox happens on March 19, 20, or 21 every year in the Northern Hemisphere. In the Southern Hemisphere, this same event marks the beginning of fall. (Source: What Exactly Is The Spring Equinox? - Dictionary.com)
Hopefully this helps.
1. Calculate the density of a 5.00 g marble which, when placed in a
graduated cylinder containing 60 milliliters of water, raised the volume of
the water to 68 milliliters.
2. An elevator with a mass of 1000kg is lifted 20 meters. How much work
was done on the elevator?
3. Calculate the potential energy of a 12 kg cat at the top of a 42 meter-
high hill.
4. Calculate the kinetic energy in joules of a 1500 kg car that is moving at a
speed of 10 m/s.
Answer:
1. 0.625 g/mL
2. 2×10⁵ J
3. 5040 J
4. 75000 J
Explanation:
1. Determination of the density.
We'll begin by calculating the volume of the marble. This can be obtained as follow:
Volume of water = 60 mL
Volume of water + Marble = 68 mL
Volume of marble =?
Volume of marble = (Volume of water + Marble) – (Volume of water)
Volume of marble = 68 – 60
Volume of marble = 8 mL
Finally, we shall determine the density of the marble. This can be obtained as follow:
Mass of marble = 5 g
Volume of marble = 8 mL
Density of marble =?
Density = mass / volume
Density of marble = 5 / 8
Density of marble = 0.625 g/mL
2. Determination of the work done.
Mass (m) = 1000 Kg
Height (h) = 20 m
Acceleration due to gravity (g) = 10 m/s²
Workdone (Wd) =?
The work done can be obtained as follow:
Wd = mgh
Wd = 1000 × 10 × 20
Wd= 2×10⁵ J
3. Determination of the potential energy.
Mass (m) = 12 Kg
Height (h) = 42 m
Acceleration due to gravity (g) = 10 m/s²
Potential energy (PE) =?
The potential energy can be obtained as follow:
PE = mgh
PE = 12 × 10 × 42
PE = 5040 J
4. Determination of the kinetic energy.
Mass (m) = 1500 Kg
Velocity (v) = 10 m/s
Kinetic energy (KE) =?
The kinetic energy can be obtained as follow:
KE = ½mv²
KE = ½ × 1500 × 10²
KE = 750 × 100
KE = 75000 J
