The correct option is D) Force of 10N displaced a body through a distance of 1m.
This is because work is defined as the product of force and displacement in the direction of force. Mathematically, work (W) = force (F) x displacement (d) x cos(theta), where theta is the angle between the force vector and the displacement vector.WHY ABC INCORRECT ? In option A, the work done would be W = force x displacement x cos(theta) = 0, since there is no force acting on the object.In option B, the work done would be W = (1/2) x mass x velocity^2 = 500 J, which is not equal to 10 J.In option C, the work done would be W = force x displacement x cos(theta) = 100 J, which is also not equal to 10 J.In option D, the work done would be W = force x displacement x cos(theta) = 10 x 1 x cos(0) = 10 J, which is the given amount of energy. Therefore, option D is the correct answer.
6) How do you conduct a scientific study
write a flowchart
A scientific research consists of numerous critical phases. Here's a high-level summary of the procedure: Create a research question, then conduct a review of the literature. Create a hypothesis. Create your research, Gather information, Examine data, Interpret findings and communicate them.
Create a research question: Begin by picking a topic of interest and creating a clear and precise question that you wish to answer via your research.
Conduct a literature review : before beginning your study to establish what is already known about your issue and what research questions have not yet been answered.
Create a hypothesis: Based on your research topic and analysis of the literature, create a hypothesis that you can evaluate using your study
Plan your research as follows: Determine your data collecting and analysis approach, including the research design, population/sample, data gathering methods, and statistical analysis.
Gather information: Carry out your research and gather data in accordance with your approach.
Analyse data: Once you've gathered your information, use relevant statistical tools to test your hypothesis.
Results should be interpreted as follows: Interpret your findings and develop conclusions about your research issue based on your analysis.
Disseminate findings: Share your discoveries with others by publishing them in a scientific journal, giving a presentation at a conference, or another method.
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An impulse of 200 N.s is applied horizontally by a soccer player of mass 74 kg at the start of a sprint (initial velocity= 0). What is the player’s change in momentum and velocity reached
The velocity reached by the soccer player is 2.7 m/s.
Impulse applied by the soccer player = 200 Ns
Mass of the soccer player = 74 kg
According to impulse-momentum theorem, the average net external force multiplied by the time it takes for that force to take effect equals the impulse, which is equal to the change in momentum.
Impulse = Fnet × t
Fnet x t = ma × t = m × v
mv = ΔP
where ΔP is the change in momentum.
So,
The change in momentum of the player, ΔP = 200 Kgm/s
So, velocity reached, v = 200/74
v = 2.7 m/s
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Find the moment of inertia about the y-axis for three masses in an equilateral triangle if m = 2.00 kg and the sides are 0.500 m. (The connecting rods are massless).
How long does it take a current of 5 mA to deliver 15c of charge
Answer:
50 minutes
Explanation:
Since we need to find time, Time or T = Q / I. Thus, the time taken for current of 5mA to deliver 15c of charge is 3000 seconds which is equivalent to 50 minutes.
You and your family are attending an annual 4th of July fireworks display. During the show, you observe that the sound from the exploding fireworks arrives 2.5 seconds after the light from the explosions. Knowing that the air temperature that night was 26°C, determine the distance (in meters) between you and the fireworks.
Round to the nearest whole number.
Technical Note: The setup for this problem assumes that the sound from the exploding firework takes time to reach you (on the order of a second) but that you see the explosion without a time delay. This is an oversimplification! However, light travels really, really fast (about 300,000,000 m/s). The light travel time at a fireworks show is on the order of millionths of a second, so for the purposes of this problem it is OK to approximate that you are seeing the fireworks without a time delay.
Please show all work!
Answer: The speed of sound in air depends on temperature, pressure, and humidity. For dry air at 26°C, the speed of sound is approximately 346 meters per second.
Let's call the distance between you and the fireworks "d". We can use the fact that the time it takes for the sound to reach you is 2.5 seconds longer than the time it takes for the light to reach you:
d = speed of sound x time delay
d = 346 m/s x 2.5 s
d = 865 meters
Therefore, the distance between you and the fireworks is approximately 865 meters.
v=√gr tan 31.0 grados
This is an equation that can be used to calculate the velocity (V) required to launch an object from a ramp at an angle of 31.0 degrees with the horizontal, neglecting air resistance.
In the equation, g is the acceleration due to gravity (approximately 9.8 m/s^2) and r is the radius of curvature of the ramp. Since the radius is not given, we can assume it to be constant or ignore it altogether if it is not necessary.
The expression tan 31.0 degrees represents the slope of the ramp. By taking the tangent of the angle, we can determine the vertical component of the slope. This is important because it affects the force of gravity acting on the object. By taking the square root of the product of g and tan 31.0 degrees, we can determine the velocity needed to launch the object at the given angle.
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--The complete question is, What does this equation describes, V=√gr tan 31.0 grados?--
Three different mass projectiles are launched from the top of a building each at different angles of
elevation. Each particle has the same initial kinetic energy. Which particle has the greatest kinetic
energy just as it impacts with the ground?
The projectile with the smallest angle of elevation will have the greatest kinetic energy just before impact.
All three projectiles have the same initial kinetic energy, which means that they all start with the same amount of energy. However, the kinetic energy of a projectile is related to its velocity and mass.
When a projectile is launched at an angle of elevation, its initial velocity will have both horizontal and vertical components. The vertical component of velocity will affect the time it takes for the projectile to reach the ground, but it does not affect the kinetic energy of the projectile just before impact.
Therefore, the projectile with the greatest kinetic energy just as it impacts with the ground will be the one with the largest horizontal component of velocity, which means it will travel the furthest horizontally before hitting the ground.
The horizontal component of velocity is determined by the angle of elevation and the initial velocity of the projectile. Therefore, the projectile with the smallest angle of elevation will have the largest horizontal component of velocity and therefore the greatest kinetic energy just before impact.
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Two ohmic resistors (R, and R₂) are connected in series with a cell.
Find the resistance and power of R2, given that the current flowing
through R, and R₂ is 0.25A and that the voltage across the cell is 6 V, R₁ = 1 22.
R₂=?
R₁-19
V=6 V
I=0,25 A
Answer:
23 ohm
Explanation:
I = I1 = I2 = 0.25A
V = 6 V
V = V1 + V2
6 = I1R1 + I2R2
6 = ( 0.25 × 1 ) + ( 0.25 × R2 )
6 = 0.25 + 0.25 R2
6 - 0.25 = 0.25 R2
5.75 = 0.25 R2
5.75 ÷ 0.25 = R2
R2 = 23 ohm
A jar of tea is placed in sunlight until it
reaches an equilibrium temperature of 32.4
◦C .
In an attempt to cool the liquid, which has a
mass of 177 g , 95.3 g of ice at 0.0
◦C is added.
At the time at which the temperature of the
tea is 30.7
◦C , find the mass of the remaining
ice in the jar. The specific heat of water
is 4186 J/kg ·
◦ C . Assume the specific heat
capacity of the tea to be that of pure liquid
water.
Answer in units of g.
The tea absorbs 2613420 J of heat energy when it is placed in sunlight until it reaches an equilibrium temperature of 32.4°C.
To calculate the heat energy absorbed by the tea, we can use the formula:
Q = mcΔT
where Q is the heat energy absorbed by the tea, m is the mass of the tea, c is the specific heat capacity of water, and ΔT is the temperature change of the tea.
Using the given values, we get:
m = 500 g
c = 4186 J/kg·°C
ΔT = 32.4°C - 20°C = 12.4°C
Substituting these values into the formula, we get:
Q = (500 g)(4186 J/kg·°C)(12.4°C) = 2613420 J
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--The complete Question is, A jar of tea with a mass of 500 g is initially at a temperature of 20°C. If the jar is placed in sunlight until it reaches an equilibrium temperature of 32.4°C, how much heat energy is absorbed by the tea? Assume the specific heat capacity of the tea to be that of pure liquid water, which is 4186 J/kg·°C.--
Calculate the moment of force F=8i-4j+3k about point 0(2i +0j+k).if the force is applied at the point p(6i+2j+3k)
Answer:
Moment of the force = (-10i-28j+32k)Nm
Explanation:
Moment of a force is expressed mathematically as force(F) multipled by its distance(d) and its unit is in newton metre (Nm).
F×d
(8i-4j+3k)×[(6i+2j+3k)-(2i+0j+k)]
-10i-28j+32k
How is thermal energy transferred during conduction? Check all that apply.
Thermal energy is transferred between particles that are not touching each other.
Thermal energy is transferred between particles that are in direct contact with each other.
Thermal energy is transferred between objects of different temperatures.
Thermal energy is transferred between objects of the same temperature.
Thermal energy is transferred from slow-moving particles to fast-moving particles.
Thermal energy is transferred from fast-moving particles to slow-moving particles.
The correct options for how thermal energy is transferred during conduction are " Thermal energy is transferred between particles that are in direct contact with each other.", "Thermal energy is transferred between objects of different temperatures.", and "Thermal energy is transferred from fast-moving particles to slow-moving particles." The correct options are B, C, and F.
During conduction, thermal energy is transferred through a material or between objects in direct contact with each other. The transfer of thermal energy occurs because of temperature differences between the two objects or regions. When two objects at different temperatures are in direct contact with each other, the hot object transfers thermal energy to the cold object through collisions between the particles of the two objects. The fast-moving particles in the hot object collide with the slow-moving particles in the cold object, transferring thermal energy from the hot object to the cold object. This process continues until the two objects reach thermal equilibrium, meaning they have the same temperature and there is no more net transfer of thermal energy between them.
Option A is not true because thermal energy is actually transferred between particles that are in direct contact with each other, not particles that are not touching each other.
Option D is not true because thermal energy does not transfer between objects that are already at the same temperature. Heat transfer only occurs when there is a temperature difference.
Option E is not true because thermal energy actually flows from hot objects to cold objects. Therefore, thermal energy is transferred from fast-moving particles to slow-moving particles, not the other way around.
Therefore, The correct answers are B, C, and F.
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An electromagnetic wave traveling through water (n1 = 1.3) is incident upon a boundary with glass (n2 = 1.5). What is the angle (in degrees) of the refracted ray (θ2) is the incident angle θ1 = 25°?
The refracted angle of the electromagnetic wave in glass (θ₂) is approximately 59.64° when the incident angle (θ₁) is 25°.
The refracted angle, denoted as θ₂, can be calculated using Snell's Law, which relates the incident angle, refracted angle, and the refractive indices of the two media involved.
Snell's Law states:
n₁ × sin(θ₁) = n₂ × sin(θ₂)
where:
n₁ = refractive index of the first medium (water) = 1.3
θ₁ = incident angle of the wave in the first medium = 25°
n₂ = refractive index of the second medium (glass) = 1.5
θ₂ = refracted angle of the wave in the second medium
Plugging in the given values:
n₁ = 1.3
θ₁ = 25°
n₂ = 1.5
Can rearrange Snell's Law to solve for θ₂:
θ₂ = arcsin((n₁/n₂) × sin(θ₁))
Now we can substitute in the values and calculate θ₂:
θ₂ = arcsin((1.3/1.5) × sin(25°))
θ₂ = arcsin(0.8667)
θ₂ ≈ 59.64°
So the refracted angle of the electromagnetic wave in glass (θ₂) is approximately 59.64° when the incident angle (θ₁) is 25°.
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the total mass of an object is 25.8kg. what is the gravitational potential energy of the mass at an attitude of 27.66 m?
Answer:
7.00 KJ
Explanation:
GPE = mgh
m equals mass (kg)
g is a constant which equals 9.81 m/s
h equals height (m)
GPE = (25.8 kg)(9.81 m/s)(27.66 m)
GPE = 7,000.69 J or 7.00 KJ
What approximate temperature is required to begin fusion in a star?
A. 93 billion kelvins
B. Fusion occurs randomly and is not based on temperature.
C. 14 million kelvins
D. 9 billion kelvins
Answer:
The approximate temperature required to begin fusion in a star is C. 14 million kelvins. This temperature is high enough to overcome the electrostatic repulsion between positively charged atomic nuclei, allowing them to fuse and form heavier elements.
(a) What is the characteristic time constant (in s) of a 25.5 mH inductor that has a resistance of 3.80 ?
(b) If it is connected to a 12.0 V battery, what is the current (in A) after 12.5 ms?
L/R = L / R is the formula for an RL circuit's time constant. 7.50 mH 3.00 = 2.50 ms with LR = 7.50 mH 3.00.
What does the RF circuit time constant mean?Circuit capacitance and circuit resistance combine to form the RC time constant ().(C). In contrast, a capacitor linked in series with a resistor takes time to charge up to around 36.8% of its full value. It is a significant metric since it represents the growth or decay rate of the circuit.
Tau is relatively simple since = RC. The time constant of an RC circuit is important because it ties the values of R and C to the capacitor voltage directly. A capacitor may be charged to a 63% charge by applying a single continuous charge, according to experiments.
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What is torque? In general terms
Torque is a measure of the force that can cause an object to rotate about an axis. (answer taken from Khan Academy).
The electrical signals sent to the brain indicate the
loudness, pitch, and quality
pitch
of a sound wave.
loudness
quality
The electrical signals sent to the brain indicate the loudness, pitch, and quality of a sound wave.
Option A is correct
What are electrical signals?An electrical signal is described as a voltage or current which conveys information, usually it means a voltage. It is the term can be used for any voltage or current in a circuit.
The apparent strength of a sound wave is referred to as loudness, and it is commonly expressed in decibels. (dB). The perceived sound is louder the larger the amplitude of the sound wave.
The apparent highness or lowness of a sound is known as pitch, and it is based on the sound wave's frequency. When compared to lower frequency sound waves, higher frequency sound waves are perceived as having a higher pitch.
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In the sketch below, the cylinder A has a mass of 13 kg and cross-sectional area of 2 m2 . The piston B has a cross-sectional area of 15000 mm2 and negligible weight. If the apparatus is filled with oil, ρ = 780 kg/m3 , with the aid of a complete free body diagram calculate the force F required for equilibrium.
the force F required for equilibrium is 128.397 N.
How do we calculate?
There are two main forces: the weight of the cylinder A and the hydraulic pressure acting on the piston B. The weight of A is given by:
W = m*g = 13 kg * 9.81 m/s^2 = 127.53 N
P = rho x gx h
where
h = (15000 mm^2) / (2 m^2) = 0.0075 m
pressure is:
P = 780 kg/m^3 * 9.81 m/s^2 * 0.0075 m = 57.79 N/m^2
Force = P*A
A = 15000 mm^2 = 0.015 m^2
Force = 57.79 N/m^2 * 0.015 m^2 = 0.867 N
Solving for the force required for equilibrium:
Force = W + P*A
Force = 127.53 N + 57.79 N/m^2 * 0.015 m^2
= 127.53 N + 0.867 N
= 128.397 N
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Suppose you are hiking down the Grand Canyon. At the top, the temperature early in the morning is a cool 3 °C. By late afternoon, the temperature at the bottom of the canyon has warmed to a sweltering 34 °C. What is the difference, between the higher and lower temperatures in Fahrenheit degrees.
The difference, between the higher and lower temperatures in Fahrenheit degrees is 87.8 °F.
What is the difference, between the temperatures?The difference, between the higher and lower temperatures in Fahrenheit degrees is calculated as follows;
The difference in the temperatures = 34 °C - 3°C = 31 °C
Convert the temperature to Fahrenheit degrees as follows;
31 °C = 1.8C + 32
31 °C = 1.8 x 31 + 32
31 °C = 87.8 °F
Thus, the difference, between the higher and lower temperatures in Fahrenheit degrees is calculated using the conversion factor.
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Why are water and hydrogen peroxide different substances even though they are both made up of
hydrogen and oxygen atoms?
Answer:
Water and hydrogen peroxide are different substances because they have different chemical formulas and molecular structures. Water has the chemical formula H2O, meaning that it has two hydrogen atoms and one oxygen atom. Hydrogen peroxide has the chemical formula H2O2, meaning that it has two hydrogen atoms and two oxygen atoms. The difference in their molecular structures leads to different chemical and physical properties, such as boiling points, melting points, and reactivity.
Explanation:
A stone of mass 2 kg rolls off the flat roof of a building reaches the ground with a speed of 10 m/s.
a.Calculate the kinetic energy of the stone when it reaches the ground
b the gravitational potential energy of the stone when it was on the roof
cthe height of the roof. Neglect air resistance.
Answer:
KE = 100J and PE = 100J
Explanation:
[tex]KE = 0.5*m*v^2\\PE = m*g*h\\KE = 0.5*2*100 = 100 J[/tex]
Potential energy at the start has to equal the kinetic energy at the end due to conservation of energy
11.
Which of the following animals do not communicate with infrasound?
bats
elephants
cats
giraffes
A container holds a gas consisting of 5.75 moles of oxygen molecules. One in a million of these molecules has lost a single electron. NA=6.022×1023mol−1 , e=1.60×10−19C.
What is the net charge of the gas?
Express your answer to three significant figures and include the appropriate units.
Answer:The oxygen molecules have lost a total of 0.94 coulombs in charge of their electrons.
Explanation:No
A 15.0 kg log starts from rest then falls over a 30 m waterfall to the lake below
Answer:
17.3 m/s
Explanation:
We can use the conservation of energy principle to find the velocity of the log when it hits the water. At the top of the waterfall, the log has gravitational potential energy, and at the bottom, it has kinetic energy. We can assume that there is no energy lost to friction or air resistance.
The gravitational potential energy of the log at the top of the waterfall is given by:
U = mgh
where m is the mass of the log, g is the acceleration due to gravity, and h is the height of the waterfall. Substituting the given values, we get:
U = (15.0 kg)(9.81 m/s^2)(30 m) = 4414.5 J
At the bottom of the waterfall, all of the gravitational potential energy has been converted to kinetic energy:
U = (1/2)mv^2
where v is the velocity of the log when it hits the water. Solving for v, we get:
v = sqrt(2U/m)
Substituting the value of U and m, we get:
v = sqrt(2(4414.5 J)/(15.0 kg)) = 17.3 m/s
Therefore, the velocity of the log when it hits the water is approximately 17.3 m/s.
Hope this helps!
Say an impulse is applied opposite the go-kart's direction of travel. What happens to
the go-kart if its momentum + impulse = 0?
The go kart stops comes to a stop.
The go kart slows down but keeps moving.
The go kart speeds up.
There is no change in the speed of the go kart.
If the impulse is strong enough and lasts for a sufficient amount of time, the go-kart will eventually come to a stop.
Option A is correct.
What is meant by impulse?impulse is described as the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector quantity.
If the force is insufficient to stop the go-kart entirely, it will slow down but continue to move. The force and duration of the impulse, along with the mass and speed of the go-kart, will all affect how much deceleration occurs.
Given that momentum plus impulse equals zero, the go-kart's change in momentum as a result of the impulse will be equal in amount but will move in the opposite direction of its original momentum.
As a result, the go-kart's final momentum will be zero, suggesting that it has either stopped or is travelling very slowly.
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A surface at 27 °C emits radiation at a rate of 100 W. At what rate does an identical surface at 54 °C emit radiation
The rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W.
What is Stefan-Boltzmann Law?The Stefan-Boltzmann Law states that the rate of radiation emitted by a blackbody is proportional to the fourth power of its absolute temperature.
The rate of radiation emitted by an identical surface at 54°C can be found using the Stefan-Boltzmann Law.
Therefore, we can calculate the rate of radiation emitted by the surface at 54°C using the following equation:
Power emitted = σ x (Temperature)⁴
Where σ is the Stefan-Boltzmann constant, which is equal to 5.67 x 10⁻⁸ Wm⁻²K⁻⁴.
Plugging in the given values, we have:
Power emitted = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴ x (54 + 273)⁴
Power emitted = 2,170,812.96 W
Therefore, the rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W. This is due to the fact that the fourth power of the absolute temperature of the surface is much higher at 54°C than at 27°C.
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The rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W.
What is Stefan-Boltzmann Law?The Stefan-Boltzmann Law states that the rate of radiation emitted by a blackbody is proportional to the fourth power of its absolute temperature.
The rate of radiation emitted by an identical surface at 54°C can be found using the Stefan-Boltzmann Law.
Therefore, we can calculate the rate of radiation emitted by the surface at 54°C using the following equation:
Power emitted = σ x (Temperature)⁴
Where σ is the Stefan-Boltzmann constant, which is equal to 5.67 x 10⁻⁸ Wm⁻²K⁻⁴.
Plugging in the given values, we have:
Power emitted = 5.67 x 10⁻⁸ Wm⁻²K⁻⁴ x (54 + 273)⁴
Power emitted = 2,170,812.96 W
Therefore, the rate of radiation emitted by an identical surface at 54°C is 2,170,812.96 W. This is significantly higher than the rate of radiation emitted by the surface at 27°C, which was 100 W. This is due to the fact that the fourth power of the absolute temperature of the surface is much higher at 54°C than at 27°C.
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One particular lightbulb has a 0.22-meter length of the tungsten wire used as its filament. This tungsten wire filament has a resistance of 19 ohms at a temperature of 20°C. The tungsten wire filament has a resistance of 240 ohms when this bulb is operated at a potential difference of 120 volts.
Calculate the cross-sectional area of this tungsten wire filament. [Show all work, including the equation and substitution with units.]
Calculate the power of this lightbulb when it is being operated at a potential difference of 120 volts. [Show all work, including the equation and substitution with units.]
The cross-sectional area of this tungsten wire filament is 6.544 x 10⁻⁹m² and the power of this lightbulb when it is being operated at a potential difference of 120 volts is 60 watts.
What is resistance?The amount that a substance or a device obstructs the passage of an electric current is known as its resistance. It is described as the proportion of the voltage across a conductor to the current flowing through it.
How do you determine it?The resistance formula may be used to get the tungsten wire filament's cross-sectional area:
R = (ρ * L) / A
where R is the resistance, is the tungsten's resistivity, L is the wire's length, and A is its cross-sectional area.
The resistance of the wire is 19 ohms at 20 °C. To find A, we can rearrange the equations as follows:
A = (ρ * L) / R
Inputting the values results in:
A = (5.6 x 10^-8 Ωm * 0.22 m) / 19 Ω
A = 6.544 x 10^-9 m^2
The tungsten wire filament's cross-sectional area is 6.544 x 10^-9 m^2, as a result.
The power formula may be used to determine the lightbulb's power:
P = V^2 / R
where P denotes power, V denotes potential difference, and R denotes resistance of the tungsten wire filament at 120 volts.
The wire's resistance at 120 volts is 240 ohms. Inputting the values results in:
P = (120 V)^2 / 240 Ω
P = 60 W
Therefore, while the lightbulb is operating at a 120 volt potential difference, its output is 60 watts.
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14. Two identical corks float in separate beakers. One beaker contains
water. The other contains a very salty water. Which of the following
statements is true?
The corks both float at the same level in the liquid.
The cork in the very salty water floats at a lower level than the other cork.
The corks will eventually sink.
Both corks are subject to the same buoyant force.
Answer:
Both Corks are subject to the same buoyant force
Explanation:
The buoyant force depends on the volume of the displaced liquid and the density of the liquid, but not the density of the floating object. So the buoyant forces will be the same on each cork whether the water it's floating in is normal or salty.
What speed must you toss a baseball straight upwards so that it takes 5 seconds to return to you?
The velocity of tossing the baseball is 24.5 m/s.
Time taken by the ball, t = 5 s
Displacement of the ball, s = 0
An object can be kept moving without the application of force. The only time a force is needed is to keep an acceleration going. Additionally, there is a downward force as well as a downward acceleration in the case of an upwardly moving projectile.
Applying the second equation of motion,
s = ut + 1/at²
s = ut + 1/2 (-g)t²
0 = ut - 1/2 gt²
ut = 1/2 gt²
Therefore, the velocity of toss,
u = 1/2 gt
u = 1/2 x 9.8 x 5
u = 24.5 m/s
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Question 3: 2D Kinematics (Vectors) For the the vectors A and B in Figure below, use the method of components to find the magnitude and the direction or: (5 marks each) (a) Vector sum of [A+B], (b) Vector sum of [A-B]. (c) Vector difference of [B-A]. (d) Vector difference of [2A-B].
The question is incomplete. Here is how to get magnitude and direction
How to get magnitude and direction
To find the magnitude and direction of a vector, follow these steps:
Write the vector in component form:
For a two-dimensional vector, write it as <x, y>, where x and y are the components of the vector along the x-axis and y-axis, respectively. For a three-dimensional vector, write it as <x, y, z>, where x, y, and z are the components of the vector along the x-axis, y-axis, and z-axis, respectively.
Calculate the magnitude of the vector:
The magnitude of a vector is the length of the vector, which can be found using the Pythagorean theorem. For a two-dimensional vector <x, y>, the magnitude is sqrt(x^2 + y^2). For a three-dimensional vector <x, y, z>, the magnitude is sqrt(x^2 + y^2 + z^2).
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