Let's make a free-body diagram.
As the problem says, the propulsion force is the horizontal component of the ground reaction force, which is the only horizontal component in the system.
\(P=F\cdot\cos 78\)Where F = 1.7mg, let's find F.
\(\begin{gathered} P=1.7mg\cdot\cos 78=1.7\cdot m\cdot9.8\cdot\cos 78 \\ P=3.46m \end{gathered}\)So, the propulsion force is 3.46 times the mass of the dog. Now, let's use Newton's Second Law.
\(\begin{gathered} \Sigma F_x=ma_x \\ P=ma_x \\ 3.46m=ma_x \\ a_x=3.46\cdot\frac{m}{s^2} \end{gathered}\)Therefore, the horizontal acceleration is 3.46 m/s^2.Now let's use Newton's Second Law for vertical forces.
\(\begin{gathered} \Sigma F_y=ma_y \\ N-W=ma_y_{} \\ F\cdot\sin 78-W=ma_y \\ 1.7mg\cdot\sin 78-mg=ma_y \\ mg(1.7\cdot\sin 78-1)=ma_y \\ g(1.7\cdot\sin 78-1)=a_y \\ a_y=9.8(1.7\cdot\sin 78-1) \\ a_y\approx6.5\cdot\frac{m}{s^2} \end{gathered}\)Therefore, the magnitude of the vertical acceleration is 6.5 m/s^2.
ayuden ha resolver este ejercicio porfa
Answer:
un café y a seguir pensando porque no se la respuesta xd
You are driving home from school St at 97 km/h for 190 km and then it begins to rain and you slow to 61 km/h instantly you arrive home after five hours how far is your hometown from school
The distance of your hometown from school is 318.64 km.
Given data
Distance S = 190 km
Speed v = 97 km / h
Now, the time taken to travel S distance is calculated as,
t = S / v
t = 180 / 95
t = 1.958 hrs
Now, the total time is given as
Total time T = 4.0 h
So, remaining time t ' = T - t = 4 hrs - 1.958 hrs = 2.042 hrs
Now, the velocity after travel 190 km is v ' = 63 km/ h
Distance travel in this velocity S ' = v ' t '
= 128.6 km
Now, the distance of your hometown from school , S " = S + S '
= 190 km + 128.6 km = 318.64 km
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A substance heats and cools quickly. What do you know about this substance ?
A substance that heats and cools quickly has a low specific heat capacity
Which of the following is NOT a way that a U-235 atom could fission?
Answer: A.
just did it
Explanation:
Part F
Imagine you were a sportscaster at the Olympics. You'd created a mathematical model similar to the one you just did. Imagine that you had a
computer program that could do an instantaneous analysis of video motion using that model. How could you use it in your sportscast?
A program that could do an instantaneous analysis of video motion will be useful it in a sportscast to analyze events as they occur.
Why will a program be needed?A motion video is defined as the display of video images at a rate (such as thirty frames per second) that causes objects to appear to move smoothly and continuously.
Sports inherently involve fast and accurate motion, which can be difficult for competitors to master but also for coaches and trainers to analyze and audiences to follow. Because of the nature of most sports, monitoring with sensors or other devices attached to players or equipment is generally not possible. This opens up a plethora of opportunities for the use of computer vision techniques to assist competitors, coaches, and the audience
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An 8.0 Kg mass is placed at = 3 where should a 10 Kg mass be placed along the − so that the center of mass will be located ay = 4.5?
Answer:
Therefore, the 10 kg mass should be placed at x = 5.7 m along the x-axis to achieve a center of mass located at y = 4.5 m.
Explanation:
To find the position along the x-axis where a 10 kg mass should be placed such that the center of mass is located at y = 4.5, we can use the formula for the center of mass:
x_cm = (m1 * x1 + m2 * x2) / (m1 + m2)
Here, m1 and x1 represent the mass and position of the 8 kg mass, respectively. m2 is the mass of the 10 kg mass, and we need to find x2, its position.
Given:
m1 = 8 kg
x1 = 3 m
x_cm = unknown (to be found)
m2 = 10 kg
y_cm = 4.5 m
Since the center of mass is at y = 4.5, we only need to consider the y-coordinate when calculating the center of mass position along the x-axis.
To solve for x2, we can rearrange the formula as follows:
x2 = (x_cm * (m1 + m2) - m1 * x1) / m2
Substituting the given values:
x2 = (x_cm * (8 kg + 10 kg) - 8 kg * 3 m) / 10 kg
Simplifying:
x2 = (x_cm * 18 kg - 24 kg*m) / 10 kg
Now, we can set the y-coordinate of the center of mass equal to 4.5 m and solve for x_cm:
4.5 m = (8 kg * 3 m + 10 kg * x2) / (8 kg + 10 kg)
Simplifying:
4.5 m = (24 kg + 10 kg * x2) / 18 kg
Multiplying both sides by 18 kg:
81 kg*m = 24 kg + 10 kg * x2
Subtracting 24 kg from both sides:
10 kg * x2 = 81 kg*m - 24 kg
Dividing both sides by 10 kg:
x2 = (81 kg*m - 24 kg) / 10 kg
Simplifying:
x2 = 8.1 m - 2.4 m
x2 = 5.7 m
(brainlest?) ples:(
Answer:
the 10 kg mass should be placed at x = -2.4 m to achieve a center of mass at y = 4.5 m.
Explanation:
To find the position along the x-axis where the 10 kg mass should be placed so that the center of mass is located at y = 4.5, we can use the principle of the center of mass.
The center of mass of a system is given by the equation:
x_cm = (m1x1 + m2x2) / (m1 + m2),
where x_cm is the x-coordinate of the center of mass, m1 and m2 are the masses, and x1 and x2 are the positions along the x-axis.
Given:
m1 = 8 kg,
x1 = 3 m,
m2 = 10 kg,
y_cm = 4.5 m.
To solve for x2, we need to find the x-coordinate of the center of mass (x_cm) by using the y-coordinate:
y_cm = (m1y1 + m2y2) / (m1 + m2),
where y1 and y2 are the positions along the y-axis.
Rearranging the equation and substituting the given values:
4.5 = (83 + 10y2) / (8 + 10).
Simplifying the equation:
4.5 = (24 + 10*y2) / 18.
Multiplying both sides by 18:
81 = 24 + 10*y2.
Rearranging the equation:
10*y2 = 81 - 24,
10*y2 = 57.
Dividing both sides by 10:
y2 = 5.7.
Therefore, the y-coordinate of the 10 kg mass should be 5.7 m.
To find the x-coordinate of the 10 kg mass, we can use the equation for the center of mass:
x_cm = (m1x1 + m2x2) / (m1 + m2).
Substituting the given values:
x_cm = (83 + 10x2) / (8 + 10).
Since the center of mass is at x_cm = 0 (the origin), we can solve for x2:
0 = (83 + 10x2) / (8 + 10).
Rearranging the equation:
83 + 10x2 = 0.
24 + 10*x2 = 0.
10*x2 = -24.
Dividing both sides by 10:
x2 = -2.4.
a student practicing for a track meet ran 250 m in 30 seconds. What was her average speed?
Answer:
8.33 meters/sec.
time = 30 sec. 30 sec. = 8.33 meters/sec.
The flywheel of a steam engine begins to rotate from rest with a constant angular acceleration of 1.27 rad/s^2. It accelerates for 27.5 s, then maintains a constant angular velocity. Calculate the total angle through which the wheel has turned 66.1 s after it begins rotating.
With a constant angular acceleration of 1.27 rad/s^2 and acceleration of 27.5 s, is mathematically given as
\(\theta = 1848 radians\)
What is the total angle through which the wheel has turned 66.1 s after it begins rotating?Generally, the angular velocity is mathematically given as
w2 = 0 + 1.27*27.9
w2 = 35.43 rad/s
Therefore
\(\theta1 = 0.5*1.27*27.9*27.9\)
\(\theta2 = w2*(66.1-27.9)\\\\\ \theta = \theta1 + \theta2\)
\(\theta = 1848 radians\)
In conclusion, the total angle is
\(\theta = 1848 radians\)
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1. The diagram shows a satellite traveling in uniform circular motion around the Earth.
(a) Give the relation between radius of the orbit and the velocity of the satellite.
(b ) The satellite is kept in orbit by a force. On the diagram draw an arrow to show the
direction of this force.
Answer:
M V R = constant angular momentum is constant because no forces act in the direction of V
Since M (mass) = constant
V R = constant
The force is directed along the gravitational force vector (towards the center of rotation)
help me get the answer in Physical Science.
Answer:
lithium
Explanation:
I took physical science 2 years ago and passed with an A
List the 6 questions you may apply to formulating a logical, reasonable perspective to any situation.
Steps to formulate a logical, reasonable perspective to any situation are: gather information, identify problem, analyze the situation, consider assumptions, generate solutions, evaluate options, consider your values, make decision and monitor and adjust
What are the 6 questions that may be applied to formulate logical, reasonable perspective to any situation?Here are the six questions that you can apply to formulating a logical, reasonable perspective to any situation:
What are the issues that should be addressed?
What are the relevant facts and data related to this problem or issue?
What assumptions am I making about the problem or issue?
What are the possible solutions or outcomes, and what are the pros and cons of each?
What are my values and priorities related to this problem or issue?
What additional information do I need to make an informed decision or come to a reasonable conclusion?
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1. Calculate the electric field due to a single +1nC point charge at a distance of lm, 2m, and 3m
Answer:
Approximately \(9.0\; \rm N \cdot C^{-1}\) at \(1\; \rm m\) from this charge, pointing away from the point charge.Approximately \(2.2\; \rm N \cdot C^{-1}\) at \(\rm 2\; \rm m\) from this charge, pointing away from the point charge.Approximately \(1.0\; \rm N \cdot C^{-1}\) at \(3\; \rm m\) from this charge, pointing away from the point charge.Assumption: there is no object between this point charge and the observer.
Explanation:
The electric field of a point charge is inversely proportional to the square of the distance from that point charge.
Let \(k\) denote Coulomb's constant (\(k \approx 8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-1}\).) Let the magnitude of that point charge be \(q\). At a distance of \(r\) from this charge, the electric field due to this charge would be:
\(\displaystyle E = \frac{k \cdot q}{r^{2}}\).
Convert the magnitude of the point charge in this question to standard units:
\(q = 1\; \rm nC = 10^{-9}\; \rm C\).
Apply that equation to find the magnitude of the electric field due to this point charge:
\(r = 1\; \rm m\):
\(\begin{aligned} E &= \frac{k \cdot q}{r^{2}} \\ &= \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times 10^{-9}\; \rm C}{(1\; \rm m)^{2}} \\ &\approx 9.0\; \rm N \cdot C^{-1}\end{aligned}\).
\(r = 2\; \rm m\):
\(\begin{aligned} E &= \frac{k \cdot q}{r^{2}} \\ &= \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times 10^{-9}\; \rm C}{(2\; \rm m)^{2}} \\ &\approx 2.2\; \rm N \cdot C^{-1}\end{aligned}\).
\(r = 3\; \rm m\):
\(\begin{aligned} E &= \frac{k \cdot q}{r^{2}} \\ &= \frac{8.98755 \times 10^{-9}\; \rm N \cdot m^{2} \cdot C^{-2} \times 10^{-9}\; \rm C}{(3\; \rm m)^{2}} \\ &\approx 1.0\; \rm N \cdot C^{-1}\end{aligned}\).
The direction of the electric field at a point is the same as the direction of a force from this field onto a positive point charge at this point.
Because the \((+1\; \rm nC)\) point charge here is positive, the electric field of this charge would repel other positive point charges. Hence, the electric field around this \((+1\; \rm nC)\!\) point charge at any point in the field would point away from this charge.
A 3250 kg car slows down from 20.0 m/s to a stop in 5.33 s. How much force would be required to stop the car?
The force required to stop the car of mass 3250 kg is -12195.12 N.
What is force?Force is the product of mass and acceleration.
To calculate the force required to stop the car, we use the formula below
Formula:
F = m(v-u)/t.....................Equation 1Where:
F = Force required to stop the carm = Mass of the carv = Final speedu = Initial speedt = TimeFrom the question,
Given:
m = 3250 kgv = 0 m/su = 20 m/st = 5.33 sSubstitute these values into equation 1
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An electric iron is Mark 120 volts and 500 Watts to units consumed by it in using it for 24 hours will be
An electric iron is marked 120 volts and 500 Watts. The units consumed by it in using it for 24 hours can be calculated using the formula:Power (in watts) = Voltage (in volts) x Current (in amperes)P = V x I
Using the above formula, we can find the current drawn by the electric iron as follows:I = P/VI = 500/120I = 4.17 ATherefore, the power consumed by the electric iron in 24 hours is:P = VI x tP = 120 x 4.17 x 24P = 120 x 100.08P = 12010.56 watt-hoursTo convert watt-hours to kilowatt-hours, we divide by 1000: Energy consumed = 12010.56 / 1000Energy consumed = 12.01 kWhHence, the units consumed by the electric iron in 24 hours is 12.01 kilowatt-hours.For such more question on Voltage
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A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later. Determine the distance the ball was thrown.
The distance the ball was thrown is 52.22m by A quarterback throws a pass at an angle of 35° above the horizontal with an initial speed of 25 m/s. The ball is caught by the receiver 2.55 seconds later.
How to calculate distance?Every motion under constant acceleration is projectile motion
Angle above horizontal Ф = 35°, initial speed v1 = 25m/s , time 2.55s
Substituting value in the below equation
x=x₁ + (v₁*cosθ)(t)+1/2 *a*t²
a= 0 as acceleration in horizontal direction is zero
x= 25*cos(35)*2.55
x=52.22 m
Projectile motion is a form of motion in which object influenced when it is launched into the gravitational force from the surface of Earth along a curved path.
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Two
cars, A and B , are travelling in the same
direction
although
Car B is 186 metres behind A. The
speed car B is 24.4 m/s and the speed of car A is 18.6 m/ s. How much time does it take for car B to catch up with car A?
Answer:
SA = 18.6 * t + 186 total distance traveled by A in time t
SB = 24.4 t total distance car B must travel to catch car A
SA - SB = 0 = 18.6 t + 186 = 24.4 t
(24.4 - 18.6) t = 186
t = 186 m / 5.8 m/s = 32 s
Check 18.6 * 32 + 186 = 781 m
24.4 * 32 = 781 m
Which of the following quantitative research methods should a researcher use when trying to understand the political views held by the young population of a specific area? a.) Participant observation b.) Written surveys c.) Secondary data analysis d.) Laboratory experiments
Answer:
Options B
Explanation:
The appropriate quantitative research method for understanding political views held by the young population of a specific area is written surveys (option b). Surveys allow for the collection of data from a large number of participants, and specific questions can be asked to gather data on political views.
Participant observation (option a) involves direct observation of individuals in a natural setting, which may not be practical for studying political views.
Secondary data analysis (option c) involves analyzing data that has already been collected, and may not be specific to the young population or the area of interest.
Laboratory experiments (option d) are typically used to study cause-and-effect relationships between variables, which may not be applicable to studying political views.
Therefore, the best option for understanding the political views held by the young population of a specific area is written surveys.
To understand the political views of the young population of a specific area, a researcher can use written surveys, participant observation, and secondary data analysis as quantitative research methods.
Explanation:If a researcher is trying to understand the political views held by the young population of a specific area, they should use written surveys, participant observation, and secondary data analysis as quantitative research methods.
Written surveys: This method involves distributing survey questionnaires to gather data on political opinions from a sample of the young population in the area. Participant observation: This method involves the researcher immersing themselves in the community and directly observing and interacting with individuals to understand their political views.Secondary data analysis: This method involves analyzing existing data sources, such as census records or previous surveys, to gain insights into the political views of the young population in the area.Learn more about Quantitative Research Methods here:https://brainly.com/question/33505242
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What is Moral subjectivism?
Answer:
What Is Moral Subjectivism? Moral subjectivism is based on an individual person's perspective of what is right or wrong. An individual can decide for themselves that they approve or disapprove of a certain behavior, and that is what determines if the behavior is right or wrong.
A metal ball sits motionless on a flat surface. Which of these would make the ball move?
A. The force of gravity becomes less.
B. The force of gravity becomes greater.
C. Two equal horizontal opposing forces act upon the ball.
D. Two unequal horizontal opposing forces act upon the ball.
Answer:
D
Explanation:
Unbalanced forces move stuff. Gravity would only increase/decrease movement if the object was already in motion.
Answer:
b
Explanation:
a) Define the Inverse Square Law and show that the field strength, E of a single charge Q acting on a test charge Q at a distance x from it along its field is given by
(b) A circuit consists of a variable resistor R connected in series with an ammeter and a cell. A voltmeter is connected in parallel across the variable resistor R. the cell is of e.m.f E and internal resistance r. For a certain value of R, the voltmeter reads 4V and the ammeter reads 1A. When R is adjusted, the voltmeter reads 2V and the ammeter reads 2.5A. Draw the circuit diagram and calculate the values of E and r.
a. The Inverse Square Law states that the intensity or strength of a physical quantity decreases with the square of the distance from its source.
b. The values of E and r in the given circuit are: E = 4V (e.m.f. of the cell) and r = ∞
How to explain the informationa. In the context of electrostatics, the Inverse Square Law describes the relationship between the electric field strength and the distance from a charged particle.
b. For the first scenario (V = 4V and I = 1A), we have:
4V = 1A * R1,
R1 = 4Ω.
For the second scenario (V = 2V and I = 2.5A), we have:
2V = 2.5A * R2,
R2 = 0.8Ω.
Total resistance in the circuit (when ammeter reads zero current) is given by:
= R1 + R2 + r.
Since the ammeter reads zero current, we have:
E = I * R_total,
4V = 0A * R_total,
R_total = ∞ (infinity).
Therefore, we can conclude that the internal resistance r of the cell is infinite (or very high compared to the resistances in the circuit).
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150 ml
Water at 22 °C
Iron at
125 °C
What is a possible
temperature of the
system after the iron
has been added to
the beaker?
A. 147 °C
B. 52°C
C. 125 °C
D. 19 °C
The possible temperature of the system after the iron has been added to the beaker is 52°C.
option B.
What is equilibrium temperature?A system is said to be in thermal equilibrium when there is no temperature difference between system and surroundings. Temperature, as you know, measures how hot or cold a body is with respect to a standard object.
When a system ( cold and hot body) reaches thermal equilibrium or equilibrium temperature, the heat lost by the hot body will be equal to the heat gained by the cold body.
heat gained by the water = heat lost by the iron
The equilibrium temperature will be greater than the initial temperature of the cold body but less than the final temperature of the hot.
Thus, the only possible answer for the equilibrium temperature of mixture is 52⁰C.
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A(n) 1252 kg car is coasting along a level
road at 29.7 m/s. A constant braking force
is applied, such that the car is stopped in a
distance of 69.9 m.
What is the magnitude of the braking force?
Answer in units of N
The magnitude of the braking force of the car of mass 1252 kg is 265.98 N.
What is force?Force can be defined as the product of mass and acceleration.
To calculate the magnitude of the braking force, we use the formula below.
Formula:
F = m(v²-u²)/2s............. Equation 1Where:
F = Force from the brakem = Mass of carv = Final velocityu = Initial velocitys = DistanceFrom the question,
Given:
m = 1252 kgv = 0 m/su = 29.7 m/ss = 69.9 mSubstitute these values into equation 1
F = 1252(0-29.7)/(69.9×2)F = 37184.4/139.8F = 265.98 NHence, the magnitude of the braking force is 265.98 N.
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Water intake and hydration are positively correlated. This indicates that as water intake increases, hydration
a. is reduced by half
b. remains the same
c. increases
d. decreases
An electron with a velocity of 14.4 m/s in the positive y-direction enters a region where there is a uniform electric field of 201 N/C in the positive x-direction. The mass of the electron is 9.109 × 10−31 kg.
What is the y-component of the electron’s displacement 2.40 μs after entering the electric-field region if no other forces act on it in μm?
What is the x-component of the electron’s displacement 2.40 μs after entering the electric-field region if no other forces act on it in m?
1. The electron experiences acceleration and moves independently in the y-direction.
2. The y-component of the electron's displacement after 2.40 μs in the electric field is -8.11 μm.
3. The x-component of displacement remains zero.
To calculate the y-component and x-component of the electron's displacement, we need to consider the motion of the electron in the electric field. Let's break it down step by step:
1. Acceleration of the Electron:
The electric field causes a force on the electron given by the equation: F = qE, where F is the force, q is the charge of the electron, and E is the electric field.
Since the charge of an electron is -1.6 × \(10^-^1^9\) C, and the electric field is 201 N/C, we can calculate the force:
F = (-1.6 × \(10^-^1^9\)C) * (201 N/C)
= -3.216 × \(10^-^1^7\) N
Using Newton's second law, F = ma, we can find the acceleration (a) of the electron:
a = F / m
= (-3.216 × \(10^-^1^7\) N) / (9.109 ×\(10^-^3^1\) kg)
= -3.530 × \(10^1^3 m/s^2\)
2. Displacement in the y-direction:
Since no other forces act on the electron, its motion in the y-direction is independent of the electric field. The equation for displacement (y) under constant acceleration is:
y = (1/2) * a *\(t^2\)
Substituting the values, where the time (t) is 2.40 μs (2.40 ×\(10^-^6\) s), we can calculate the y-component of displacement:
y = (1/2) * (-3.530 ×\(10^1^3 m/s^2\)) * (2.40 ×\(10^-^6 s)^2\)
= -8.11 μm
Therefore, the y-component of the electron's displacement 2.40 μs after entering the electric-field region is -8.11 μm.
3. Displacement in the x-direction:
Since the electron's velocity is only in the y-direction initially, the x-component of the displacement remains zero. Without any forces acting in the x-direction, the electron continues to move in the y-direction without changing its x-position.
Hence, the x-component of the electron's displacement 2.40 μs after entering the electric-field region is 0 meters.
Please note that the calculations provided are based on the given values and the provided formulas for displacement and acceleration.
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An airplane needs to reach a forward velocity of 56.4 m/s to take off. On a 2000 meter runway, what is the minimum uniform acceleration necessary for the plane to take flight if it starts from rest? NEED WORK SHOWN!! 100 PTs
What is the displacement of the airplane?
What is the initial velocity of the airplane?
What is the final velocity of the airplane?
Write the equation you will use to solve the problem.
What was your acceleration?
1.0 m/s^2
0.95 m/s^2
0.87 m/s^2
0.80 m/s^2
Displacement of the airplane (s) = 2000 m
Initial velocity of the airplane (u) = 0 m/s (Starts from rest)
Final velocity of the airplane = 56.4 m/s
Equation used to solve the problem:
\( \boxed{ \bf{ {v}^{2} = {u}^{2} + 2as}}\)
By substituting values in the equation, we get:
\( \rm \longrightarrow {56.4}^{2} = {0}^{2} + 2 \times a \times 2000 \\ \\ \rm \longrightarrow 3180.96 = 0 + 4000a \\ \\ \rm \longrightarrow 4000a = 3180.96 \\ \\ \rm \longrightarrow \dfrac{4000a}{4000} = \dfrac{3180.96}{4000} \\ \\ \rm \longrightarrow a = 0.80 \: m {s}^{ - 2} \)
\( \therefore \) Minimum uniform acceleration necessary for the plane to take flight (a) = 0.80 m/s²
A solid cylinder of uniform density of 0.85 g/cm3 floats in a glass of water tinted light blue by food coloring.
Its circular surfaces are horizontal. What effect will the following changes, each made to the initial system, have on X, the height of the upper surface above the water? The liquids added do not mix with the water, and the cylinder never hits the bottom.
1. The cylinder is replaced with one that has the same density and diameter, but with half the height.
2. Some of the water is removed from the glass.
3. A liquid with a density of 1.06 g/cm3 is poured into the glass.
4. The cylinder is replaced with one that has the same height and diameter, but with density of 0.83 g/cm3.
5. A liquid with a density of 0.76 g/cm3 is poured into the glass.
6. The cylinder is replaced with one that has the same density and height, but 1.5× the diameter.
Options are: Increase, Decrease, No change
The buoyant force acting on the cylinder is, \(Fb = \rho Ahg\). Here A is the cross-sectional area of the cylinder, h is the height of the cylinder, ρ is the density of the cylinder, and g is the acceleration due to gravity.
This buoyant force is also equal to the volume of the fluid displaced. \(Fb = \sigma h(A-x)g\). Here σ is the density of the fluid.
Equate the above two equations and solve for x.
\(\rho Ahg = \sigma A(h-x)g\\\rho h = \sigma h - \sigma x\\x = \frac{(\sigma - \rho)h}{\sigma}\)
So, the distance x depends on the density of the fluid, density of the cylinder and the height of the cylinder.
1. The density of the cylinder is same and distance x is independent of the diameter of the cylinder. Therefor, there will be no change in the distance x. Hence, the correct answer is No change.
2. Now the height is changing keeping the density same. As the distance x is directly proportional to the height, the distance x will increase.
3. The density of the added liquid is greater than of the water and it does not mix with the water. So, the liquid will settle down and there will be no change in the distance x.
4. The density of the added liquid is less than that of the water and it does not mix with the water. So, the liquid will not settle down and the distance x will change. The change in distance x can be determined as follow:
\(\rho Agh = \sigma' Axg + \sigma A(h-x)g\\\rho h=\sigma' x + \sigma h - \sigma x\\x=(\frac{\sigma - \rho}{\sigma - \sigma'})h\)
Here, σ' is the density of the added liquid.
From the above relation it is clear, that on adding the liquid of the density less than that of water, the denominator term become small ando so the value of x will increase.
5. On removing some of the water inside the glass, the height of the water column will decrease, but the value of x does not depend on the height of the water column. So, there will be no change in the distance x.
6. The density of the new cylinder is smaller than that of the earlier one. So, the numerator term will increase. Therefore, the value of x will increase.
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(PLZ HELP) The force on a rocket car stays constant to 25,000 N. Initially the car is traveling at 125 m/s. Over the course of the next 7.50 s, the mass of the car decreases by 440 kg. What is the final velocity of the car?
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Answer is 553 m/s
By the formula of,
Vf = Vi + at
where,
Vi is initial velocity
a is acceleration due to gravity
t is time.
As we know that,
F = ma
so,
\(a = \frac{F}{m}\)
put this in the final velocity formula,
Vf = Vi + (F/m)t
Vf = 125 + (25000/440)7.5
Vf = 551.13 m/s
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A motorcycle stoop is at a traffic light, when the light turns green, the motorcycle accelerates to a speed of 78 km/h over a distance of 50 m. What is the average acceleration of the motorcycle over this distance?
The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².
To calculate the average acceleration of the motorcycle, we can use the formula:
Average acceleration = (final velocity - initial velocity) / time
First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.
Converting the final velocity:
Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s
Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:
Average acceleration = (21.67 m/s - 0 m/s) / time
To find the time taken to reach this velocity, we need to use the formula for average speed:
Average speed = total distance/time
Rearranging the formula:
time = total distance / average speed
Plugging in the values:
time = 50 m / 21.67 m/s ≈ 2.31 seconds
Now we can calculate the average acceleration:
Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²
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A plant is thrown straight
down from a balcony 7.01 m
high at 8.84 m/s. How long
does it take the plant to hit
the ground?
The time taken for the plant to hit the ground from a distance of 7.01m and at a velocity of 8.84m/s is 1.59s.
How to calculate time?The time taken for a motion to occur can be calculated using the following formula:
v² = u² - 2as
Where;
v = final velocityu = initial velocitys = distancea = acceleration8.84² = 0² + 2 × a × 7.01
78.15 = 14.02a
a = 5.57m/s²
V = u + at
8.84 = 0 + 5.57t
t = 1.59s
Therefore, the time taken for the plant to hit the ground from a distance of 7.01m and at a velocity of 8.84m/s is 1.59s.
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If a transverse wave osculates 7 times every second and the speed of the wave is 27 m/s what is the wavelength of the wave
Explanation:
formula is ˠ=vf
f=1/T
1/7
f=0.14
wavelength=27Ⅹ0.14
=3.78m
OR
7Ⅹ27
=189m