(a) The plane’s altitude when it released the cargo is 1,960 m.
(b) The speed of the plane when it dropped the cargo is 240 m/s.
The given parameters:
time of motion of the cargo, t = 20 shorizontal distance of the cargo, X = 4800 mThe plane’s altitude when it released the cargo is calculated as follows;
\(h = v_0_y t + \frac{1}{2} gt^2\\\\h = 0(20) \ + \ \frac{1}{2} (9.8)(20)^2\\\\h = 1,960 \ m\)
The constant horizontal speed of plane when it dropped the cargo is calculated as follows;
\(v_x =\frac{X}{t} \\\\v_x = \frac{4800}{20} \\\\v_x =240 \ m/s\)
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A coin is dropped into a deep well and the time taken to hit the bottom is measured to be 2.48s. Calculate the following: a) The depth of the well b) The final velocity of the coin c) The mass of the coin, if the water slows it to a stop in 0.72s exerting an average force of 0.41N on the coin On the basis of which of Newton’s laws is this calculated? What does this law say?
Answer: I’m not sure but my guess would be A.
Explanation:
To solve this we must be knowing each and every concept related to velocity and its calculation. Therefore, the final velocity of the coin is 24.3 m/s.
What is velocity?Velocity is a vector-based evaluation of an object's rate of motion and direction of motion. As a result, in order to calculate velocity using this definition, we must be familiar with both magnitude and direction.
For example, if an item travels west with 5 meters a second (m/s), its velocity to the west will be 5 m/s. The most frequent and simplest approach to determine velocity is using the formula shown below.
Mathematically,
elapsed time = 2.48 s
depth of well = 30.17 m
final velocity = ?
V = g × t
g=acceleration due to gravity=9.81 m/s²
t=time
substituting all the given values in the above equation, we get
V = 9.81 ×2.48
=24.3 m/s
Therefore, the final velocity of the coin is 24.3 m/s.
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Which of the following is form of energy:
a) Power
b) Light
C) pressure
d) None
Answer:
Explanation:
b) light
An object is placed 50cm in front of a concave mirror of radius 60cm. How far from the mirror is the image?
Answer:To explian the exact calculation of this pruduct we must not try!
fish swimming in a horizontal plane has velocity v with arrowi = (4.00 î + 1.00 ĵ) m/s at a point in the ocean where the position relative to a certain rock is r with arrowi = (14.0 î − 2.80 ĵ) m. After the fish swims with constant acceleration for 19.0 s, its velocity is v with arrow = (23.0 î − 1.00 ĵ) m/s. (a) What are the components of the acceleration of the fish? ax = m/s2 ay = m/s2 (b) What is the direction of its acceleration with respect to unit vector î? ° counterclockwise from the +x-axis (c) If the fish maintains constant acceleration, where is it at t = 26.0 s? x = m y = m In what direction is it moving? ° counterclockwise from the +x-axis
Answer:
sorryyyyijyyyyyyyyyyyyyyyyyyyy&
Explanation:
soryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
"n 25 kg object is moving at a velocity or 10 ml. the obec has energy. Calculate it.
The energy of 25 kg object is moving at a velocity or 10 ml is 1250J.
What does a 25 kilogram object travelling at 10 m/s kinetic energy look like?KE = 1/2mv²
The mass is m = 25kg
The velocity is v = 10ms⁻¹
KE = 1/2 × 25 × 10²
⇒ KE = 1250J
Hence, Kinetic energy is 1250J
What is Kinetic energy?The energy an object has as a result of motion is known as kinetic energy. A force must be applied to an object in order to accelerate it. We must put in effort in order to apply a force. After the work is finished, energy is transferred to the item, which then moves at a new, constant speed.
What is velocity?The direction of a body or object's movement is defined by its velocity. In its basic form, speed is a scalar quantity. In essence, velocity is a vector quantity. It is the speed at which distance changes. It is the displacement change rate.
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A ball is dropped from the top of a 82-m-high building. What speed does the ball have in falling 3.6 s?
The speed of the ball have in falling 3.6 s is 35.5 m/s.
What is the speed of the ball?The speed of the ball is calculated using the equation of a body falling under the influence of gravity or velocity of free fall.
The equation of the motion of the body is given as follows:
v = u - gt
where;
u is the initial velocity
g = acceleration due to gravity
t = time
v = final velocity
Assuming u = 0 m/s, g = 9.8 m/s², t = 3.6 s
v = 0 - 9.8 * 3.6
v = 35.5 m/s
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Leslie incorrectly balances an equation as 2C4H10 + 12O2 → 8CO2 + 10H2O.
Which coefficient should she change?
Answer:
13 behind o2
Explanation:
answer is in photo above
Answer:
12
Explanation:
List the even numbers between 3 and 13 in set
notation
Answer:
{2,4,6,8,10,12}
Explanation:
Even Numbers
Any number that can be exactly divided by 2 is called an even number.
The even numbers between 3 and 13, written in set notation, are:
{2,4,6,8,10,12}
Answer:
4, 6, 8 , 10, 12
Explanation:
List the even numbers between 3 and 13 in set
notation
[4, 6, 8 , 10, 12]
thanks
Particles q₁ +8.0 μC, q2 +3.5 μC, and
93-2.5 μC are in a line. Particles q₁ and q2 are
separated by 0.10 m and particles q2 and q3 are
separated by 0.15 m. What is the net force on
particle q₂?
Remember: Negative forces (-F) will point Left
Positive forces (+F) will point Right
+8.0μ.C
+91
0.10 m
+3.5 C
+92
0.15 m
-2.5μ C
93
The net force on particle q₂, located between particles q₁ and q₃, is approximately 189000 N. The force exerted by particle q₁ on q₂ is positive and equals 252000 N, while the force exerted by particle q₃ on q₂ is negative and equals -63000 N.
To find the net force on particle q₂, we need to calculate the individual forces exerted on q₂ by particles q₁ and q₃ and then determine their sum.
The force between two charged particles can be calculated using Coulomb's law:
F = k * |q₁ * q₂| / r²
Where F is the force between the particles, k is the electrostatic constant (k ≈ 9.0 x \(10^9\) Nm²/C²), q₁ and q₂ are the charges of the particles, and r is the distance between them.
First, let's calculate the force exerted on q₂ by q₁:
F₁₂ = k * |q₁ * q₂| / r₁₂²
F₁₂ = (9.0 x \(10^9\) Nm²/C²) * |(8.0 μC) * (3.5 μC)| / (0.10 m)²
F₁₂ ≈ 252000 N
The force is positive because q₁ and q₂ have opposite charges.
Next, let's calculate the force exerted on q₂ by q₃:
F₂₃ = k * |q₂ * q₃| / r₂₃²
F₂₃ = (9.0 x \(10^9\)Nm²/C²) * |(3.5 μC) * (-2.5 μC)| / (0.15 m)²
F₂₃ ≈ -63000 N
The force is negative because q₂ and q₃ have the same charge.
Finally, we can find the net force on q₂ by summing the individual forces:
Net force = F₁₂ + F₂₃
Net force = 252000 N + (-63000 N)
Net force ≈ 189000 N
The net force on particle q₂ is approximately 189000 N.
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A rocket carrying a new 960-kg satellite into orbit misfires and places the satellite in an orbit with an altitude of 120 km, well below its operational altitude in low-Earth orbit.
(a) What would be the height of the satellite's orbit if its total energy were 550 MJ greater?
(b) What would be the difference in the system's kinetic energy? (Include the sign of the value in your answer.)
(c) What would be the difference in the system's potential energy? (Include the sign of the value in your answer.)
These answers are all in MJ. (Please answer the question instead of taking all of the points)
Answer:(a) To find the height of the satellite's orbit if its total energy were 550 MJ greater, we can use the following equation:
K2 + U2 = K1 + U1 + 550 MJ
Since the satellite is in a circular orbit, its kinetic energy is given by:
K = (1/2)mv^2
where m is the mass of the satellite, and v is its velocity.
We can use the following equation to relate the height of the satellite's orbit to its velocity:
v = sqrt(GM/R)
where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth plus the height of the satellite's orbit.
Therefore, we can express the kinetic energy of the satellite in terms of its height:
K = (1/2)m(GM/R)
Using these equations, we can rewrite the conservation of energy equation as:
(1/2)m(GM/(R1+h1)) - GMm/(R1+h1) = (1/2)m(GM/(R2+h2)) - GMm/(R2+h2) + 550 MJ
where R1 is the radius of the Earth, and R2 is the radius of the Earth plus h2.
Simplifying and solving for h2, we get:
h2 = [(GMm/(R1+h1)) - (GMm/(R2+h2)) - 550 MJ/(GM/(R2+h2))]^(-1) - R2
Plugging in the given values, we get:
h2 = 931 km
Therefore, the height of the satellite's orbit would be 931 km if its total energy were 550 MJ greater.
(b) To find the difference in the system's kinetic energy, we can use the following equation:
Delta K = K2 - K1
Substituting the expressions for K1 and K2, we get:
Delta K = (1/2)m(GM/(R2+h2)) - (1/2)m(GM/(R1+h1))
Plugging in the given values, we get:
Delta K = -7.5 x 10^9 J
The negative sign indicates that the system's kinetic energy has decreased.
(c) To find the difference in the system's potential energy, we can use the following equation:
Delta U = U2 - U1
Substituting the expressions for U1 and U2, we get:
Delta U = -GMm/(R2+h2) + GMm/(R1+h1)
Plugging in the given values, we get:
Delta U = 5.9 x 10^9 J
The positive sign indicates that the system's potential energy has increased.
Explanation:
A Measuring Cylinder liquid contains a volume of 120m³ the liquid was then poured into an empty beaker of mass 51g. The total mass was then found to be 145g .Calculate the mass of the liquid
The mass of liquid in the container is 94 grams and the density of the liquid is 0.78 grams/cm³ or 780 Kg/m³.
Given in the question
The volume of the liquid = Volume of the container
= 120 cm³
Total Mass = 145 grams
Mass of the empty Beaker = 51 grams
To find
Mass of the liquid
The density of the liquid
Now,
Total Mass = Mass of LIquid + Mass of the empty Beaker
Mass of LIquid = Total Mass - Mass of the empty Beaker
Put in the value, we get
Mass of liquid = 145 - 51 grams
Mass of liquid = 94 grams
Now, Density is the ratio of the mass of the substance and the volume, the substance occupies in the space. It is not a constant value and is variable with the variation in the temperature of the substance. Its S.I. unit is Kg/m³. B ut its other commonly used unit is gram/cm³.
The density of liquid = Mass of the liquid/ Volume of the liquid
Put in the value, we get
The density of the liquid = 94/120 grams/cm³
The density of the liquid = 0.78 grams/cm³ = 780 Kg/m³
Therefore, the mass of liquid in the container is 94 grams and the density of the liquid is 0.78 grams/cm³ or 780 Kg/m³.
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Your question was incomplete. Please find the full content below.
A Measuring Cylinder liquid contains a volume of 120cm³ the liquid was then poured into an empty beaker of mass 51g. The total mass was then found to be 145g . Calculate the mass of the liquid and the density of the liquid.
why fan videos be streamed from the cloud to a computer with no lost quality
Videos can be streamed from the cloud to a computer with no loss in quality because Digital signals are used to transmit data to and from the cloud.
How do digital signals work?
An established or one that represents data as a step made up of discrete values is known as a digital signal. There is no noise produced by digital signals. Electronic signals sent as pulses are used to transmit digital signals to computers. These signals can be found in things like digital phones and computers.
Because digital signals are used to transport data to and from the cloud, it should be noted that videos are said to stream from the cloud to a computer without quality degradation.
Videos can be streamed from the cloud to a computer with no loss in quality because Digital signals are used to transmit data to and from the cloud.
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Problem B.2: Escaping a Star (6 Points) It takes many years for a photon produced in a star's centre to reach its surface and escape into space. This is due to its constant interaction with other particles. To estimate the time it takes for a photon to escape a star's interior, we assume that the photon is deflected in equal time intervals into a random direction in a two-dimensional space (i.e., a random walk): At each step i, the photon moves a constant distance in an angle, thus changing its position: cos(4) sin(y) Ai, - c (a) Determine the distance R(n) from the centre (0,0) after n steps.
Answer:
This problem involves the concept of a random walk, which is a mathematical model of a path consisting of a succession of random steps.
The question asks for the distance, R(n), from the center of a star after n steps of a photon, assuming a 2D random walk.
The random walk in two dimensions has a step length of A_i and the direction of the steps is uniformly distributed in [0, 2π). The change in position after each step can be written in Cartesian coordinates (Δx, Δy), where Δx = A_i cos(θ_i) and Δy = A_i sin(θ_i).
The displacement from the center after n steps is given by the vector sum of all the individual steps. This vector sum can be written in terms of its Cartesian coordinates, (X, Y), where X = Σ Δx and Y = Σ Δy. This sum over n random vectors is itself a random variable. The net displacement R(n) from the center of the star after n steps is given by the magnitude of the net displacement vector:
R(n) = √(X² + Y²)
Because each step is independent and has a random direction, the expected value of the cosine and sine for any step is zero. This means that the expected values of X and Y are both zero.
However, the mean square displacement is not zero. Because the steps are independent, the mean square displacement in each direction is additive. For a 2D random walk:
<X²> = Σ <(Δx)²> = n <(A cos θ)²> = n A²/2
<Y²> = Σ <(Δy)²> = n <(A sin θ)²> = n A²/2
Because <X²> = <Y²>, we can write:
<R²> = <X²> + <Y²> = n A²
So, the root mean square distance (the square root of the mean square displacement) after n steps is:
R(n) = √(<R²>) = √(n) * A
Therefore, the distance R(n) that the photon is expected to be from the center of the star after n steps grows as the square root of the number of steps, with each step having a length A. Please note that this result holds for a 2D random walk. A real photon in a star would be performing a 3D random walk, which would have slightly different characteristics.
At what angle should a circular road be banked so that a car running at 50 Km/hr be safe to go round the circular turn of 200 m radius?
Angle of 5.61° should be banked so that car running at 50 Km/hr be safe to go round the circular turn of 200 m radius.
What is Banking of Road?The process of raising outer edge of the road over its inner edge through certain angle θ is called as banking of road. Banking of road is nothing but the process of making the angle between the surface of road to horizontal surface of the road. The angle made by this two surfaces is called as angle of banking. Banking of road is done for safe turn at high speed.
Angle of banking is given by the formula,
tanθ = v²÷Rg
Where θ = angle of banking
R = Radius of circular turn
g = acceleration due to gravity
Given,
velocity of the car v = 50km/hr = 13.88 m/s
Radius of the circular orbit = 200 m
From formula,
tanθ = 13.88² ÷ (200×9.8)
tanθ = 0.09829
θ = tan⁻¹(0.09829)
θ = 5.61°
Hence angle must be backed at 5.61° to have safe turn.
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a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
When the teacher asked the student to make words out of the jumbled word gzeysktqix, the student was being tested on his ability to unscramble words. Unscrambling words is the process of taking a word or series of letters that are out of order and rearranging them to form a word that makes sense.
When trying to unscramble a word, it is important to look for any patterns that can help identify smaller words within the jumbled letters. This can help make the process easier and quicker. For example, in the jumbled word gzeysktqix, one might notice that the letters "sktqix" appear together.
This could indicate that these letters could potentially form a word. By looking at the remaining letters, one could notice that the letters "g", "z", "e", and "y" could also form smaller words. After some rearranging, the letters can be unscrambled to form the words "sky", "zig", "sex", and "yet". These are just a few examples, as there are likely many other words that can be formed from this jumbled word.
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When Peter tosses an egg against a sagging sheet, the egg doesn't break due to
A) reduced impulse.
B) reduced momentum.
C) both of these
D) neither of these
It has to do with impulse or force. Just how the sheet has no volume. There is no sufficient impulse to crack the shell.
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
The sagging sheet gives the impact with the egg additional time, which prevents the egg from breaking when it is hurled against it. This lessens the force the egg would have applied to the wall had it been flung at it.
It has to do with impulse or force. Just how the sheet has no volume. There is no sufficient impulse to crack the shell.
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A Hiker walks 4.5km at 35 degrees north east then turns due south and goes 4.5 km. What is the total displacement
The total displacement travelled by the hiker who travelled 4.5kms at 35 degrees and 4.5kms towards south is 6.36kms.
What is displacement?Displacement can be defined as the change in position of an object with respect to time. It is a vector quantity, has direction and magnitude both. It is represented as an arrow which points from the starting position to the final position that the object has travelled. For example, an object that moves from A position to B position, then the object's position changes.
The distance travelled by the hiker is 4.5kms towards northeast at 35 degrees and 4.5kms towards south.
The total distance travelled by the hiker = \(\sqrt(4.5)^{2}+ (4.5)^{2}\)
Total distance travelled by the hiker = √(20.25+20.25)
Total Distance= √40.5km
Total distance travelled by the hiker = 6.36kms
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A train travels 8.81 m/s in a -51.0° direction.
The train accelerates for 2.23 s, changing its
velocity to 9.66 m/s in a 37.0° direction.
What is [delta]x?
The displacement of the train after 2.23 seconds is 25.4 m.
Resultant velocity of the trainThe resultant velocity of the train is calculated as follows;
R² = vi² + vf² - 2vivf cos(θ)
where;
θ is the angle between the velocity = (90 - 51) + 37 = 76⁰R² = 8.81² + 9.66² - 2(8.81 x 9.66) cos(76)
R² = 129.75
R = √129.75
R = 11.39 m/s
Displacement of the trainThe displacement of the train is the change in position of the train after a given period of time.
The displacement is calculated as follows;
Δx = vt
Δx = 11.39 m/s x 2.23 s
Δx = 25.4 m
Thus, the displacement of the train after 2.23 seconds is 25.4 m.
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Can you Help with 18 19 20 im not sure about anything in this class
The temperature of the boiler is 150.9°C, the thermal energy absorbed each hour is 1.62 x 10^9 joules, and the amount of thermal energy lost per hour is 1.61 x 10^9 joules.
The Carnot cycle is a theoretical thermodynamic cycle that consists of four reversible processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression. It is a highly efficient cycle that provides the maximum possible efficiency for a heat engine operating between two given temperatures.
18. The efficiency of a Carnot engine is given by the equation:
efficiency = 1 - (T_C / T_H)
where T_C is the temperature of the cold reservoir and T_H is the temperature of the hot reservoir. We can rearrange this equation to solve for T_H:
T_H = T_C / (1 - efficiency)
Substituting the given efficiency and waste heat temperature values, we get:
T_H = 36.3°C / (1 - 0.761) = 150.9°C
Therefore, the temperature of the boiler is 150.9°C.
19. The efficiency of a Carnot engine is given by the equation:
efficiency = 1 - (T_C / T_H)
where T_C is the temperature of the cold reservoir and T_H is the temperature of the hot reservoir. We can rearrange this equation to solve for the thermal energy absorbed each hour:
thermal energy absorbed per hour = power output / efficiency
Substituting the given values, we get:
thermal energy absorbed per hour = 115 kW / (1 - (13°C / 569°C)) = 1.62 x 10^9 J/h
Therefore, the thermal energy absorbed each hour is 1.62 x 10^9 joules.
20. In a Carnot engine, all the input energy must be converted either into work output or waste heat. Therefore, the amount of thermal energy lost per hour is equal to the difference between the thermal energy absorbed and the power output:
thermal energy lost per hour = thermal energy absorbed per hour - power output
Substituting the given values, we get:
thermal energy lost per hour = 1.62 x 10^9 J/h - 115 kW x 3600 s/h = 1.61 x 10^9 J/h
So, the amount of thermal energy lost per hour is 1.61 x 10^9 joules.
Hence, The boiler has a temperature of 150.9°C, absorbs 1.62 × 109 joules of thermal energy every hour, and loses 1.61 x 109 joules of thermal energy every hour.
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An atom X has atomic number 15 it accepts 3 electrons in other to become stable. Determine the charge on the atom before accepting electrons
Answer:
15X30 + 3 e = 12Y30
Above an atom with 15 electrons (15 neutrons) accepts 3 electrons and thus reduces its charge by 3, but the number of neutrons remains the same
If the atom had a charge of 18 before accepting the electrons, it's charge would be reduced by three to 15
18X30 + 3e = 15Y30
From the question I am not sure the atomic number of 15 is before or after accepting the electrons
In any case the charge is reduced by three and the atomic mass is unchanged
Calculate the molar heat capacity at pressure and volume constant ( ) when knowing = = 1.4 and the gas density: 0 = 1.3 /3 .
(a) The molar heat capacity at pressure is 29.1 J/K.mol.
(b) The molar heat capacity at volume is 20.785 J/K.mol.
Molar heat capacity of gas at volumeMolar heat capacity of a gas at constant volume is defined as the quantity of heat required to raise the temperature of one mole of the gas by 1 degree Kelvin when its volume is constant.
Cv = R/(γ - 1)
where;
R is universal gas constant = 8.314 J/K.mol.γ is heat ratio = 1.4Cv = (8.314) / (1.4 - 1)
Cv = 20.785 J/K.mol
Molar heat capacity of gas at pressureMolar heat capacity of a gas at constant volume is defined as the quantity of heat required to raise the temperature of one mole of the gas by 1 degree Kelvin when its pressure is constant.
γ = Cp/Cv
Cp = γCv
Cp = 1.4 x 20.785
Cp = 29.1 J/K.mol
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A team of ecologists are studying four different ecosystems with varying levels of biodiversity. The ecologists categorize the different levels of biodiversity for the four ecosystems as shown in the table below.
Genetic Diversity Species Diversity Habitat Diversity
Ecosystem A Low Low Medium
Ecosystem B Medium High Medium
Ecosystem C High Low Low
Ecosystem D Medium Low High
Based on the information above, which ecosystem most likely experienced a recent population bottleneck?
Ecosystem A, because its low genetic diversity could have resulted from an event that reduced the variation in the gene pool.
Ecosystem A, because its low genetic diversity could have resulted from an event that reduced the variation in the gene pool.
A
Ecosystem B, because its high species diversity could have resulted from increased competition among its members.
Ecosystem B, because its high species diversity could have resulted from increased competition among its members.
B
Ecosystem C, because its low habitat diversity indicates an increase in available niches.
Ecosystem C, because its low habitat diversity indicates an increase in available niches.
C
Ecosystem D, because its low species diversity indicates that it also has low species evenness.
Answer:
B. Ecosystem B, because its high species diversity could have resulted from increased competition among its members.
Explanation:
This is because, in the ecosystem with varying level of biodiversity, Ecosystem B has medium level of species diversity found in them with High medium level of habitat diversity which causes increasing competitions among them.
As an object moves, the distance it travels increases with time.
Agree
Disagree
Answer: Agree
Explanation:
The idea is that it will be at a farther place at a later period.
Marisa has the hard job of slowing the sled to a stop at the other end of the pond. The sled has a mass of 5 kg. According to the graph, what is the Net Force that she applies in order to stop the sled?
a
- 0.5 m/s
b
49.05 N
c
- 2.50 kg m/s
d
- 2.50 N
Answer:
d. - 2.50 N
Explanation:
- 2.50 N is the net force that Marisa applied on the sled. Marisa applied force in order to stop the sled and requires less amount of force due to its lower mass. The value of force is negative because the force is applied in opposite direction of the sled's movement. The value of force is positive when it is applied in the direction of the object's motion so the value of force is - 2.50 N which is applied in opposite direction of the body's motion.
Use Eq. (9.20) to calculate the moment of inertia of a uniform, solid disk with mass M and radius R for an axis per- pendicular to the plane of the disk and passing through its center
Circular disc's moment of inertia around axis passing through mass and parallel to disc Icm=MR22
Explain about the moment of inertia?The phrase "moment of inertia" in physics refers to the precise calculation of a body's inertia with respect to rotation, or the resistance a body exhibits when a torque is applied to alter its rate of rotation around an axis (turning force).
It is a broad (additive) property: the moment of inertia for a point mass is equal to the mass squared by the perpendicular distance from the axis of rotation. Because it resists rotational motion, the moment of inertia is referred to as such and not as a moment of force.
Moment of inertia is the propensity of an object to continue rotating at a constant speed or in a condition of rest. More torque is needed to shift this state the higher the moment of inertia.
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When an object is dropped to the ground from a height of h meters, the time it takes for the object to reach the ground is given by the equation t = √h/4.9, where t is measured in seconds. Solve the equation for h. Use the result to determine the height from which an object was dropped if it hits the ground after falling for 5 seconds
The object was dropped from a height of 122.5 meters.
The equation t = √h/4.9 relates the time it takes for an object to fall to the ground (t) to the height from which it was dropped (h). The equation states that the time it takes for the object to reach the ground can be calculated as the square root of the height divided by 4.9, with t measured in seconds.
To solve for h in the equation t = √h/4.9, we can square both sides:
t^2 = h/4.9
Multiplying both sides by 4.9:
4.9 * t^2 = h
So, the height from which an object was dropped can be calculated as:
h = 4.9 * t^2
If an object falls for 5 seconds, then:
h = 4.9 * 5^2
= 4.9 * 25
= 122.5 meters
Key points:
The equation t = √h/4.9 relates the time it takes for an object to fall to the ground to the height from which it was dropped.To solve for h, we square both sides of the equation and multiply both sides by 4.9.The height from which an object was dropped can be calculated as 4.9 times the square of the time it took for the object to fall.If we know the time it took for an object to fall, we can use the equation to calculate the height from which it was dropped.Learn more about falling object here:
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A tennis player tosses a tennis ball straight up and then catches it after 2.21 s at the same height as the point of release.
(a) What is the acceleration of the ball while it is in flight?
magnitude
_____ m/s2
direction
---Select---
(b) What is the velocity of the ball when it reaches its maximum height?
magnitude
_____ m/s
direction
---Select---
(c) Find the initial velocity of the ball.
____ m/s upward
(d) Find the maximum height it reaches.
____ m
(a) To determine the acceleration of the ball while it is in flight, we can use the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
In this case, the ball is thrown straight up, so its final velocity at the highest point is 0 m/s. The initial velocity is unknown, the acceleration is due to gravity and is approximately -9.8 m/s^2 (negative since it acts in the opposite direction of motion), and the time of flight is 2.21 s.
Using the equation, we can solve for the acceleration:
0 = u - 9.8 * 2.21
u = 9.8 * 2.21
u ≈ 21.658 m/s
Therefore, the acceleration of the ball, while it is in flight, is approximately 21.658 m/s^2 in the upward direction.
(b) When the ball reaches its maximum height, its velocity is 0 m/s. This occurs when the ball is momentarily at rest before falling back down. Therefore, the magnitude of the velocity when the ball reaches its maximum height is 0 m/s.
(c) To find the initial velocity of the ball, we can use the equation:
v = u + at
At the highest point, the final velocity is 0 m/s, the acceleration is -9.8 m/s^2 (due to gravity), and the time is 2.21 s.
0 = u - 9.8 * 2.21
u = 9.8 * 2.21
u ≈ 21.658 m/s upward
Therefore, the initial velocity of the ball is approximately 21.658 m/s upward.
(d) The maximum height reached by the ball can be determined using the equation for vertical displacement:
s = ut + (1/2)at^2
At the highest point, the final displacement is 0 m, the initial velocity is 21.658 m/s upward, and the time of flight is 2.21 s.
0 = 21.658 * 2.21 + (1/2) * (-9.8) * (2.21)^2
0 = 47.864 + (-5.5294)
5.5294 = 47.864
Therefore, there seems to be an error in the calculations as the equation does not hold true. Please check the given values and equations to ensure accuracy.
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Hint: sin2θ + cos2θ = 1 .
Consider the 692 N weight held by two
cables shown below. The left-hand cable had
tension 570 N and makes an angle of θ2 with
the ceiling. The right-hand cable had tension
530 N and makes an angle of θ1 with the
ceiling. a) What is the angle θ1 which the righthand cable makes with respect to the ceiling?
Answer in units of ◦.
b) What is the angle θ2 which the left-hand
cable makes with respect to the ceiling?
Answer in units of ◦.
a) The angle θ1 which the righthand cable makes with respect to the ceiling is sin^(-1)(692 N / 530 N).
b) The angle θ2 which the left-hand cable makes with respect to the ceiling is sin^(-1)(692 N / 570 N).
We may utilise the tension of the right-hand cable as well as its vertical and horizontal components to determine the angle 1. θ2 = sin^(-1)(692 N / 570 N).
We may apply the ideas of trigonometry and vector addition to address this issue.
a) The tension of the right-hand wire as well as its vertical and horizontal components can be used to determine the angle 1.
T1sin(1) calculates the vertical component of the right-hand cable's tension, which is equal to the object's weight (692 N).
T1sin(θ1) = 692 N
We may rearrange the equation to find 1:
θ1 = sin^(-1)(692 N / T1)
We can find 1 by substituting the given tension value, T1 = 530 N:
θ1 = sin^(-1)(692 N / 530 N)
b) Similarly, we can use the formula to determine the angle 2 the left-hand cable's tension and its vertical and horizontal components.
The vertical component of the left-hand cable's tension is given by T2sin(θ2), and it should also be equal to the weight of the object (692 N).
T2sin(θ2) = 692 N
To find θ2, we can rearrange the equation:
θ2 = sin^(-1)(692 N / T2)
Substituting the given tension value T2 = 570 N, we can solve for θ2:
θ2 = sin^(-1)(692 N / 570 N)
Calculating these angles using the given tension values will provide the answers in degrees.
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A proton is initially moving at 3.0 x 105 m/s. It moves 3.5 m in the direction of a uniform electric field of magnitude 120 N/C. What is the kinetic energy of the proton at the end of the motion
Answer:
The kinetic energy is \(K_f = 1.424 *10^{-15} \ J\)
Explanation:
From the question we are told that
The initial speed of the proton is \(v_p = 3.0 * 10^{5} \ m/s\)
The distance covered is \(d = 3.5 \ m\)
The magnitude of the electric field is \(E = 120\ N/C\)
Generally the mass of a proton is \(m = 1.67 *10^{27} \ kg\)
and the charge on a proton is \(q= 1.60*10^{-19} \ C\)
Now according to work energy theorem,
\(Work \ Done(W) = Kinetic \ Energy \ Change\)
=> \(W = K_f -K_i\)
=> \(K_f = W +K_i\)
Where \(K_f\) is final kinetic energy and \(K_i\) is initial kinetic energy which is mathematically represented as
\(K_i = \frac{1}{2} * m * v_p^2\)
Now the net workdone(W) is mathematically represented as
\(W = F * d = q* E* d\)
So
\(K_f = q* E * d + \frac{1}{2} * m * v_p^2\)
substituting values
\(K_f = 1.60*10^{-19}* 120 * 3.5 + \frac{1}{2} * 1.67*10^{-27} *(3.0*10^{5})^2\)
\(K_f = 1.424 *10^{-15} \ J\)
A baseball (m = 140 g) traveling at 30. m/s moves a fielder's glove backward 35 cm when the ball is caught.
What was the average force exerted by the ball on the glove?
Answer:
180
Explanation:
1) E=F*L, where E - energy of the baseball, F - the required force, L - backward moving (0.35m);
2) E=mV²/2, where E - energy of the baseball, m - the mass of the baseball (0.14kg), V - the velocity of the baseball (30m/s).
3) if E=F*L and E=mV²/2, then F*L=mV²/2, from which
\(F=\frac{mV^2}{2L};\)
4) according to the last formula
\(F=\frac{0.14*900}{2*0.35}=\frac{126}{0.7}=180(N).\)
The force exerted by the ball on the glove is 180 Newtons.
In mechanics, a force is any action that has the potential to change, maintain, or deform a body's motion. The three principles of motion outlined by Isaac Newton in his Principia Mathematica are frequently used to illustrate the concept of force (1687).
Newton's first law states that a body at rest or moving uniformly in a straight line will stay in that state until a force is applied to it. According to the second law, a body will accelerate (change in velocity) in the direction of any external force acting on it.
Given:
A baseball (m = 140 g) traveling at 30 m/s moves a fielder's glove backward 35 cm when the ball is caught,
Calculate the value of force as shown below,
Force = m × V² / 2L
Force = 0.140 × 30² / 2 × 0.35
Force = 0.140 × 900 / 0.70
Force = 126 / 0.7
Force = 180 N
Thus, the force exerted by the ball is 180 Newtons.
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