Since the car is moving in a circular path, it is undergoing centripetal acceleration toward the center of the circle. This acceleration is caused by a net force directed towards the center of the circle, which is the resultant force on the car. This force is known as the centripetal force.
Centripetal force is the net force that acts on an object moving in a circular path, directed towards the center of the circle. This force is responsible for the object's centripetal acceleration and is necessary to keep the object moving in a circular path.
According to Newton's second law of motion, F=ma, where F is the net force, m is the mass of the object, and a is the acceleration of the object. Since the car is experiencing centripetal acceleration, which is perpendicular to its velocity, the direction of the net force is also perpendicular to the velocity.
As a result, the direction of the net force on the car is towards the center of the circle. If the net force were to suddenly disappear, the car would move off in a straight line tangent to the circle.
Therefore, Since the net force on the car is constantly changing the direction of the car's velocity, the velocity is also changing. Specifically, the velocity is changing in direction, but not in magnitude, since the car is moving at a constant speed along the circular path. This change in the direction of the velocity is what causes the acceleration, and therefore the centripetal force.
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A block is attached to a spring and executes
simple harmonic motion according to x = 2.0
cos(50t), where x is in meters and t is in
seconds. The spring constant is k = 100 N/m.
What is the mass of the block?
Answer:
.04 kg
Explanation:
The equation for simple harmonic motion is x = A*cos(ωt), where A is the amplitude, ω is the angular frequency, and t is the time.
Comparing the given equation x = 2.0cos(50t) with the equation for simple harmonic motion, we see that A = 2.0 meters and ω = 50 radians/second.
The angular frequency is related to the spring constant and mass by the equation ω = sqrt(k/m), where sqrt denotes the square root.
Substituting the values given, we get:
50 = sqrt(100/m)
Squaring both sides and solving for m, we get:
m = 100/2500 = 0.04 kg
What is a hydrogen displacement?
A chemical process known as hydrogen displacement occurs when hydrogen gas is replaced or displaced by another element or molecule.
It results from a number of reactions, most of which involve a reactive metal or substance. A metal reacting with an acid can displace hydrogen atoms of the acid, resulting in the formation of a salt and the release of hydrogen gas as an example.
Another example is the interaction of a metal with water molecules, which displaces hydrogen atoms and results in the formation of metal hydroxide and hydrogen gas. Chemistry studies hydrogen displacement reactions in great detail because they are important for understanding the reactivity of various compounds. They shed light on the behavior of elements, how well they can replace hydrogen, and how new compounds are formed.
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1. Two resistors R₁ (12 ohm) and R₁ (24 ohm) are
connected in series across a 6.0 V battery
of negligible internal resistance.
Draw a circuit diagram (to the right) and calculate:
The total resistance of the two resistors:
The total current flowing in the circuit:
The current flowing in R₁
The current flowing in R2
The total power consumed by R₁ and R₂
11
Here's the circuit diagram:
```
+---R₁---R₂---+
| |
- -
(6V) ( )
|
|
|
|
|
|
|
( )
-
```
Calculations:
1. The total resistance of the two resistors:
R_total = R₁ + R₂
= 12 ohm + 24 ohm
= 36 ohm
Answer: 36 ohm
2. The total current flowing in the circuit:
I = V / R_total
= 6.0 V / 36 ohm
= 0.167 A
Answer: 0.167 A
3. The current flowing in R₁:
I₁ = V / R₁
= 6.0 V / 12 ohm
= 0.5 A
Answer: 0.5 A
4. The current flowing in R₂:
I₂ = V / R₂
= 6.0 V / 24 ohm
= 0.25 A
Answer: 0.25 A
5. The total power consumed by R₁ and R₂:
P = I² * R_total
= (I₁ + I₂)² * R_total
= (0.5 A + 0.25 A)² * 36 ohm
= 0.1875 * 36 ohm
= 6.75 W
Answer: 6.75 W
A blue train of mass 50 kg moves at 4 m/s toward a green train of 30 kg initially at rest. The trains collide. After the collision the green train moves with a speed of 3 m/s. What is the final momentum of the blue train?
A. 200 kgm/s
B. 20 kgm/s
C. 110 kgm/s
D. 90 kgm/s
Answer:
C. 110 kgm/s
Explanation:
Law of Conservation of Momentum states that total momentum before the collision must equal total momentum after the collision.
Momentum = p = mv
x = final velocity of the blue train
(50 kg)(4 m/s) + (30 kg)(0 m/s) = (50 kg)(x) + (30 kg)( 3 m/s)
200 kg·m/s + 0 = (50 kg)(x) + 90 kg·m/s
50 kg(x) = 110 kg·m/s
x = (110 kg·m/s)/(50 kg) = 2.2 m/s
p-final (blue train) = (50 kg)(2.2 m/s) = 110 kg·m/s
Answer:
According to the law of conservation of momentum, the total momentum of the system before and after the interaction must be equal.
The total initial momentum of the system is:
P_initial = 50 * 4 + 30* 0 = 200kgm/s
The total final momentum of the system
let the velocity of the blue train is=v
P_final = 30* 3 + 50* v = 200
after solving v=2.2m/sec
the momentum of blue train will be= 50* 2.2=110kgm/s
A vehicle is being planned that is driven by a flywheel engine. It has to run for at least 30 minutes and develop a steady power of 500 W.
Answer:
To meet the requirements of running for at least 30 minutes and developing a steady power of 500W, the flywheel engine needs to have sufficient energy storage capacity and be capable of delivering a steady power output.
Assuming that the flywheel engine is 100% efficient (i.e., no energy losses due to friction, air resistance, or other factors), the energy storage capacity required can be calculated as follows:
Energy storage capacity = Power x Time
= 500W x 30min
= 15,000 watt-minutes or 250 watt-hours
This means that the flywheel engine needs to be capable of storing at least 250 watt-hours of mechanical energy.
estimate the work you do to mow a lawn 10m by 20m with a 50 cm wide mower. Assume you push with a force of about 15 N.
Answer:
W = 6000 Joule
Explanation:
Work is defined as force times distance
W = F * d
We know that F = 15N, we just need the distance (d)
Imagine you have a square lawn with length of 10 m and width of 20m. So, we want to know the the distance you have to travel to cover every square meter of the lawn.
The width of the mower is only 50 cm = 0.5 m.
This means that you have to go back and forth 40 times to cover 20m (lawn width), with a distance of 10 m (lawn length). So,
d = 10 (meter) * 40 (times) = 400 meter
Therefore:
W = (15) * (400) = 6000 J
5) Find the electric current of this circuit:
( ) 5 A
( ) 8.5 A
( ) 3 A
( ) 10 A
The electric current in the circuit below is 3 A And the right option is C. 3A.
What is electric current?
Electric current is the rate of flow of charge in a circuit.
To calculate the electric current in the circuit below, we use the formula:
Formula:
I = V/R'.....................Equation 1Where:
I = Electric currentV = VoltageR' = Effective resistanceFrom the question,
Given:
V = 285 VR' = (20//20)+25+25+15R' = (20/2)+25+25+15+20R' = 10+25+25+15R' = 95 ohmsSubstitute these values into equation 1
I = 285/95I = 3 AHence, the right option is C. 3A
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Simple machines make work easier. You must left a move this load of Saul for your parents. It is heavy you’re using to simple machines when you use this wheel barrow wight simple machine included in the wheelbarrow makes it easier to move the song from one place to another.
The use of the wheel barrow in this case makes it a simple machine
What is the simple machine?A wheelbarrow is an illustration of a straightforward device that can simplify labour by lowering the force needed to move a large load. The wheel and axle and the lever are two basic machines that are used.
The wheelbarrow's wheel is made of an axle and wheel. The friction between the wheel and the ground is decreased by the wheel's rotation around the axle. It can also be seen as one of the classes of the lever.
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Toy cars of different masses accelerate as they move down a ramp as shown in the figure. A motion sensor is used to measure the speed of each car. It is found that all of the cars have the same speed at the bottom of the ramp. This graph shows how the mass of the car affects the car’s kinetic energy at the bottom of the ramp. Based on the graph, describe the relationship between the mass and the kinetic energy of the car, and then predict, in joules the kinetic energy of a car with a mass of 80 grams.
The Kinetic energy of the car with a mass of 80 grams is 0.40 joules
How do i determine the kinetic energy?From the graph given, we can see that the as the mass increase, the kinetic energy also increase. Thus, we can say that the kinetic energy and mass of the car are in direct proportionality.
Now, we shall obtain the velocity of the car. Details below:
Kinetic energy (KE) = 0.1 JMass of (m) = 20 g = 20 / 1000 = 0.02 KgVelocity (v) = ?KE = ½mv²
0.1 = ½ × 0.02 × v²
0.1 = 0.01 × v²
Divide both side by 0.01
v² = 0.1 / 0.01
Take the square root of both side
v = √(0.1 / 0.01)
v = 3.16 m/s
Finally, we shall determine the kinetic energy of the car of mass 80 grams. Details below:
Mass (m) = 80 g = 80 / 1000 = 0.08 KgVelocity (v) = 3.16 m/sKinetic energy (KE) =?KE = ½mv²
KE = ½ × 0.08 × 3.16²
Kinetic energy = 0.40 joules
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state in terms of m, u and v ,the change of momentum of the object
The change in momentum of the object in terms of its mass, initial velocity, and final velocity is 5 kg m/s.
The change in momentum of an object can be calculated using the formula:
Δp = m * (v - u)
In this case, the mass of the object is 0.5 kg, the initial velocity (u) is 0 m/s, and the final velocity (v) is 10 m/s after 3 seconds of uniform acceleration.
Substituting these values into the formula gives:
Δp = 0.5 kg * (10 m/s - 0 m/s)
Δp = 5 kg m/s
Therefore, the change in momentum of the object in terms of its mass, initial velocity, and final velocity is 5 kg m/s.
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--The complete Question is, A 0.5 kg object is initially at rest. It then accelerates uniformly for 3 seconds and reaches a velocity of 10 m/s. Calculate the change in momentum of the object in terms of its mass (m), initial velocity (u), and final velocity (v).--
A moving object of mass 0.01 kg experiences a drag force proportional to its speed square. The proportionality constant is C. If the object has an initial speed v = 10 m/s and after time T has energy 1/8 m v^2, then find C.
The proportionality constant of the moving object experiencing a drag force is 0.01875 Ns²/m².
How to calculate proportionality constant?The work-energy principle states that the work done on an object is equal to its change in kinetic energy. So, the work done by the drag force can be found as follows:
W = (1/8)mv² - (1/2)mv₀²
where m = mass of the object, v = final speed, and v₀ = initial speed.
The work done by the drag force is also given by the formula:
W = ∫F(x)dx
where F(x) = force function and x = position of the object.
In this case, the force function is F(x) = -Cv², since the drag force is in the opposite direction of motion. So:
W = ∫-Cv²dx
Since the force is proportional to v², rewrite this as:
W = -C∫v²dx
Integrating both sides with respect to x:
W = -(1/3)Cv³
So, equating the two expressions for W:
(1/8)mv² - (1/2)mv₀² = -(1/3)Cv³
Substituting m = 0.01 kg, v₀ = 10 m/s, and solving for C:
C = -(3/8) × (m/v₀³) × (v² - v₀²) = -(3/8) × (0.01/10³) × (1/8 × 10² - 10²) = 0.01875 Ns²/m²
Therefore, the proportionality constant is C = 0.01875 Ns²/m².
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6.1 Instantaneous communication. In your own words, explain why you
cannot send a message instantaneously using the mechanism of ex-
periment 6.1. If quantum mechanics were deterministic rather than
probabilistic, yet the distant atoms still always left from opposite
exits of a stern gerlach analyzer, would you then be able to send a message instantaneously?
What if the operator of the left-hand Stern-Gerlach analyzer were
somehow able to force his atom to come out of the + exit?
In Experiment 6.1, two entangled atoms are delivered to several Stern-Gerlach analyzers where the spins are detected in various orientations. Each atom's measurement result is probabilistic and arbitrary. Because there is no way to influence how the measurement on the distant atom turns out, it is impossible to use this process to convey a message instantly.
What is quantum mechanics?A fundamental area of physics called quantum mechanics examines how matter and energy behave at the atomic and subatomic scales. The behavior of particles like electrons, protons, and photons as well as their interactions are understood and described mathematically.
The idea of entanglement, which describes how two or more particles can come to be connected in such a way that their states are correlated even though they are separated by a considerable distance, is also introduced by quantum mechanics.
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The velocity of three particles of masses 20g, 30g and 50g are 2i, 10j and 10k respectively. The velocity of the centre of mass the three particle) is
Answer:
The velocity of the center of mass (Vcm) of a system of particles can be calculated using the formula:
Vcm = (m1v1 + m2v2 + m3v3 + ... + mnvn) / (m1 + m2 + m3 + ... + mn)
where m1, m2, m3, ... mn are the masses of the particles and v1, v2, v3, ... vn are their velocities.
In this problem, we have three particles with masses of 20g, 30g, and 50g and velocities of 2i, 10j, and 10k respectively. We can convert the masses to kg to make the calculations easier:
m1 = 20g = 0.02kg
m2 = 30g = 0.03kg
m3 = 50g = 0.05kg
Using the formula above, we can calculate the velocity of the center of mass:
Vcm = (m1v1 + m2v2 + m3v3) / (m1 + m2 + m3)
Vcm = (0.02kg * 2i + 0.03kg * 10j + 0.05kg * 10k) / (0.02kg + 0.03kg + 0.05kg)
Vcm = (0.04i + 0.3j + 0.5k) / 0.1kg
Vcm = 0.4i + 3j + 5k m/s
Therefore, the velocity of the center of mass of the three particles is 0.4i + 3j + 5k m/s.
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A thin beam of light falls on mirror 1 as shown in the diagram below. four P.Q.Rands are placed in front of mirror 1 and mirror 2. Mirror 2 J|||||| RE Nanda wants to find out on which tikely box in the diagram in the beam to fall after reflecting off mirrov 1 and mirrov 2 List the steps that he should Follow in the correct order.
The steps assume that the mirrors and boxes are arranged in a simple, two-dimensional configuration.
The steps to be followedThe steps to be followed are;
Determine the angle of incidence of the beam of light on mirror 1. This can be done by drawing a line perpendicular to the mirror at the point where the beam of light hits the mirror and measuring the angle between this line and the incident beam of light.Use the law of reflection to determine the angle of reflection of the beam of light from mirror 1. This angle will be equal to the angle of incidence.Use the properties of parallel lines and angles to determine the angle of incidence of the beam of light on mirror 2. This can be done by noting that mirror 2 is parallel to mirror 1 and that the angle of incidence of the beam of light on mirror 2 will be equal to the angle of reflection of the beam of light from mirror 1.Use the law of reflection again to determine the angle of reflection of the beam of light from mirror 2. This angle will be equal to the angle of incidence of the beam of light on the likely box.Use the properties of parallel lines and angles again to determine the angle of incidence of the beam of light on each of the boxes in the diagram. The box that has an angle of incidence equal to the angle of reflection of the beam of light from mirror 2 is the likely box where the beam of light will fall.Learn more on reflection of mirror here https://brainly.in/question/54972410
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78. A rocket takes off from Earth and reaches a speed of 100 m/s in 10.0 s. If the exhaust
speed is 1500 m/s and the mass of fuel burned is 100 kg, what was the initial mass of the rocket?
Answer:
5866.9 kg
Explanation:
We can use the conservation of momentum to solve this problem. The momentum of the rocket and fuel system is conserved, so:
Initial momentum = Final momentum
The initial momentum of the system is zero since the rocket is at rest initially. The final momentum is the momentum of the rocket after burning the fuel. We can find the final momentum using the rocket equation:
Δv = ve * ln(m0 / mf)
where Δv is the change in velocity (100 m/s), ve is the exhaust speed (1500 m/s), m0 is the initial mass of the rocket and fuel system (what we want to find), and mf is the final mass of the rocket and fuel system (m0 - 100 kg).
Solving for m0, we get:
m0 = mf * exp(Δv / ve) = (m0 - 100 kg) * exp(100 / 1500)
Simplifying this equation, we get:
m0 = 100 kg / (1 - exp(100 / 1500))
m0 = 5866.9 kg (rounded to four significant figures)
Therefore, the initial mass of the rocket and fuel system was approximately 5866.9 kg.
A ball is initially at rest and travels 7.8 m. The ball travels at an acceleration of 6.4 m/s². What is the final velocity of the ball? Give your answer to 1 decimal place.
The final velocity of the ball to one decimal place is approximately 10.0 m/s.
What is the final velocity of the ball?From the third equation of motion:
v² = u² + 2as
Where v is final velocity, u is initial velocity, a is acceleration and s is the distance covered.
Given that:
Ball was initially at rest, initial velocity u = 0acceleretaion a = 6.4 m/s²distance traveled s = 7.8 mFinal velocity v = ?Plug the given values into the abovr formula and solve for the final velocity v.
v² = u² + 2as
v² = 0² + ( 2 × 6.4 m/s² × 7.8 m )
v² = 2 × 6.4 m/s² × 7.8 m
v² = 99.84 m²/s²
v = √( 99.84 m²/s² )
v = 10.0 m/s
Therefore, the final velocity is 10.0 m/s.
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what is the unit of time not based on a heavenly body
A mango hanging on a tree possesses a potential energy of 150 J.If the mass of the mango is 5kg Calculate the height of the mango from the ground take (g = = 10 m/s²
Answer: 3 meters from the ground
Explanation:
gravitational potential energy= mass*height*acceleration of free fall(g)
150=5*h*10
h=150/50
h= 3 m
. When a large truck
hits a small car, the
forces are equal.
• However, the small
.
car experiences a
much greater
change in velocity
much more rapidly
than the big truck.
Which vehicle ends up
with more damage?
Answer:
Car
Explanation:
Based on Newton 2nd law, energy are conserves. Meaning that if the Force is equal, the car with lower mass must be travelling in a much greater acceleration.
F = m.a
where,
a = Δv/Δt
When talking about energy, there are 2 factor: mass and velocity.
The change of Kinetic energy experience by the car is
ΔEk = 1/2.m.Δv²
Eventhough the car has smaller mass, notice that the velocity will be squared. In this case the velocity is the a more dominant factor. It means that energy absorbed by the car is much larger.
3-Calculate the total electric current of this circuit:
( ) 10.2 A
( ) 3.45 A
( ) 5.5 A
( ) 7.5 A
Answer :
7.5 A is the required electric currentStep-by-step explanation:
We are given with 4 resistors which are connected in parallel.
Let
R_1 =10Ω
R_2 = 12Ω
R_3 = 15Ω
R_4 = 20 Ω
First let's calculate the total resistance.
Since the resistors are connected in parallel, Total resistance will be,
[tex]{\boxed{ \implies {\sf {\dfrac{1}{R_{(total)} }= \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} + \dfrac{1}{R_4}}}}} \\ [/tex]
Plugging in the required values,
[tex]\implies \sf \dfrac{1}{R_{(total)}} = \dfrac{1}{10} + \dfrac{1}{12} + \dfrac{1}{15} + \dfrac{1}{20} \\ \\\implies \sf \dfrac{1}{R_{(total)}} = \dfrac{6 + 5 + 4 + 3}{60} \\ \\ \implies \sf \dfrac{1}{R_{(total)}} = \frac{18}{60} \\ \\ \implies \sf R_{(total)} = \frac{60}{18} \\ \\ \implies \sf R_{(total)} = 3.33 [/tex]
Hence, The total resistance is 3.33 Ω
Now,
[tex] \implies \sf I = \dfrac{V}{R}[/tex]
Where,
I is currentR is resistanceV is voltagePlugging the required values
[tex] \implies[/tex] I = 25/3.33
[tex] \implies[/tex] I = 7.5 A
Therefore, The total current in the circuit is 7.5 A
Answer:10.2
Explanation:
The 2001 World Trade Center attacks fall under which category of terrorism?
foreign-sponsored terrorism on U.S. soil
domestic-sponsored terrorism on U.S. soil
cyberwarfare and domestic terrorism
terrorism abroad that affects U.S. citizens
The 2001 World Trade Center attacks fall under which category of terrorism (a).foreign-sponsored terrorism on U.S. soil is correct option.
The 2001 World Trade Center attacks are generally considered to be an example of foreign-sponsored terrorism on U.S. soil. The attacks were carried out by a terrorist organization based in Afghanistan called Al-Qaeda, which was led by Osama bin Laden. The attackers were primarily from Saudi Arabia, but they received training and support from Al-Qaeda operatives based in Afghanistan.
Therefore, the correct option is (a).
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a student is swinging a ball attatched to a string in a vertical circle
The magnitude of the acceleration of the ball applied at the bottom of the circle can be expressed in the form of FTension-FGravity/M.
Option D is correct.
When making a vertical circle with a ball on a string?Along the string's circular and vertical paths, the tension changes. As long as the total quantity of kinetic and potential energy is constant throughout, the ball's speed can change.
Centripetal force varies as a result of motion variations.
We can determine how tight a string that is traveling in a vertical circle is using the expression below:
FC = mv2 /r.
A moving item attached to a string experiences centripetal force, which is determined by the product of the object's mass (mg) and the string tension. (T).
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Complete question:
A student swings ball of mass M on the end of a string in vertical circle of radius R,as shown in the figure below. Also shown is diagram representing all the forces exerted on the ball at the bottom of the circle where its speed is What is the magnitude of the acceleration of the ball at the bottom of the circle? FTension FGravity
A)Fi /M
B)Fc /M
C)Fr+Fg/M
D) Ft- Fg/M
An electric field of 2250 N/C is produced by a charge of 4.82 x 10^-11 C. For this field strength, what is the distance to the charge? (Kc = 8.99 x 10^9 NM^2 / C^2 )
Answer:
1.77 cm
Explanation:
The electric field strength produced by a point charge can be calculated using the equation:
E = k * Q / r^2
where E is the electric field strength, k is Coulomb's constant (k = 8.99 x 10^9 N m^2 / C^2), Q is the charge, and r is the distance between the charge and the point where the field is being measured.
Rearranging this equation to solve for r, we get:
r = sqrt(k * Q / E)
Substituting the given values, we get:
r = sqrt((8.99 x 10^9 N m^2 / C^2) * (4.82 x 10^-11 C) / (2250 N/C))
r = 0.0177 m or 1.77 cm
Therefore, the distance to the charge is 1.77 cm for this electric field strength.
This graph is a combination of atmospheric carbon dioxide measurements taken from ice cores in Antarctica and air samples atop Mauna Loa. The graph BEST shows how the atmosphere has been affected by an increase in
Responses
Industrial activity
Industrial activity
Photosynthesis
Photosynthesis
Sea Levels
Sea Levels
Ozone Layer
Which of the following is not among the uses of dimensional analysis? (a) determination of the Numerical constant (b) to convert one system of unit to another (c) to change the units of derived quantities (d) to test the correctness of an equation
To convert one system of unit to another of derived quantities is not a use of dimensional analysis.
What is dimensional analysis?Checking for consistency in the dimensions on both sides of an equation entails looking at the dimensions of the physical quantities involved in a problem, such as length, mass, time, electric charge, and temperature.
The core tenet of dimensional analysis is that physical quantities, such as length, mass, and time, may be described in terms of their basic dimensions.
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All of the options listed are included in the uses of dimensional analysis.
What is dimensional analysis?Dimensional analysis is a powerful tool used in physics to:
check the correctness of equations derive new equationsconvert units from one system to anotherdetermine numerical constants that relate physical quantities.The dimensional analysis involves analyzing the dimensions of physical quantities and using them to establish relationships between them.
By using the principles of dimensional analysis, we can simplify complex physical problems and gain insights into the behavior of physical systems.
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A boy of mass 60 kg and a girl of mass 40 kg are together and at rest on a frozen pond and push each other apart. The girl moves in a negative direction with a speed of 3 m/s. What must be the total final momentum of the boy and girl combined?
A. 0 kgm/s
B. -120 kgm/s
C. 120 kgm/s
D. -100 kgm/s
Answer:
Explanation:
The total initial momentum of the system is zero since the boy and girl are at rest initially. According to the law of conservation of momentum, the total final momentum of the system must also be zero.
If the girl moves in a negative direction with a speed of 3 m/s, then she gains a momentum of -3 x 40 = -120 kgm/s in the negative direction. To conserve momentum, the boy must gain a momentum of +120 kgm/s in the positive direction, so that the total momentum of the system remains zero.
Therefore, the total final momentum of the boy and girl combined is 120 kgm/s in the positive direction. The answer is C. 120 kgm/s.
Answer:
The girl acquires a velocity of -3 x 40 = -120 kgm/s in the negative direction if she goes with a speed of 3 m/s in the opposite direction. The boy must acquire a momentum of +120 kgm/s in the positive direction to preserve and keep the system's overall momentum at zero.
Explanation:
The answer is option D
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A 1.3 kg mass is attached to the left end of a meter stick. The meter stick is then balanced on a fulcrum as shown. If the mass of the meter stick is 0.2 kg and its center of mass is located at its geometric center, how far to the left of the stick's center of mass (‘d' in the figure) should the fulcrum be placed to balance the meter stick? Provide your answer in centimeters.
The fulcrum to balance the meter stick should be placed 8.33 cm to the left of the center of mass of the meter stick, under the condition that the mass of the meter stick is 0.2 kg and its center of mass is located at its geometric center.
In order to balance the meter stick with the 1.3 kg mass placed to the left end, we have to evaluate the distance ‘d' from the center of mass of the meter stick to the fulcrum.
The given center of mass of the meter stick is found at its geometric center which is at 50 cm from either end of the stick. Then the mass of the meter stick is 0.2 kg.
We can apply the principle of moments to evaluate this problem. The principle of moments says that for an object in equilibrium, the summation of the clockwise moments about any point must be equivalent to the sum of the anticlockwise moments about that point.
Let us consider that moments about the fulcrum. The clockwise moment because of the weight of the 1.3 kg mass and is stated by (1.3 kg) x (d cm). The anticlockwise moment is because of the weight of the meter stick and is given by (0.2 kg) x (50 - d cm). Since the meter stick is balanced, these two moments should be equal.
(1.3 kg) x (d cm)
= (0.2 kg) x (50 - d cm)
Evaluating for‘d’,
d = 8.33 cm
Hence, the fulcrum should be placed 8.33 cm to the left of the center of mass of the meter stick.
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In a hydraulic lift, if the radius of the smaller piston is 2.0 cm and the radius of the larger piston is 20.0 cm.
a) What is the increase in pressure caused by the 250 N force on the small piston.
ANSWER: 2 x 10E5 Pa
^^^^^^^^^^^^^^^^^^^^^^^
b) If the larger piston moves 5 cm, how far does the smaller piston move?
ANSWER: 5m
^^^^^^^^^^^^^^^^^^
OR: F= 250* (20^2/2^2) =25000 N
P= 250/(area of small piston) = 7.85*10^7 Pa
h= 5*(20^2/2^2)= 500 cm
The pressure exerted on the fluid by the force applied on the small piston can be calculated using the formula:
P = F/A
where P is the pressure, F is the force, and A is the area on which the force is applied. Since the force is applied on the smaller piston, we need to use its area:
A_small = πr_small^2
where r_small is the radius of the smaller piston. Thus,
A_small = π(0.02 m)^2 = 1.2566 x 10^-3 m^2
The force applied on the small piston is 250 N. Thus,
P = F/A_small = 250 N / 1.2566 x 10^-3 m^2 = 1.989 x 10^5 Pa
Therefore, the increase in pressure caused by the 250 N force on the small piston is 1.989 x 10^5 Pa, which is approximately equal to 2 x 10^5 Pa (to two significant figures).
How far can the smaller piston moves when the larger piston moves 5 cm?b) We can use the principle of conservation of volume to determine how far the smaller piston moves when the larger piston moves 5 cm. The volume of the fluid in the hydraulic lift remains constant, so we have:
A_small × h_small = A_large × h_large
where h_small and h_large are the heights of the fluid columns above the smaller and larger pistons, respectively. Since the lift is filled with an incompressible fluid, the pressure is the same throughout the fluid. Thus,
P = F/A_small = F/A_large
Multiplying both sides of this equation by the areas of the pistons, we get:
F × A_small = F × A_large
Substituting the given values, we get:
250 N × (π(0.02 m)^2) = F × (π(0.20 m)^2)
Solving for F, we get:
F = 250 N × (0.02 m/0.20 m)^2 = 25 N
Now, we can use the force applied on the larger piston and the area of the smaller piston to calculate the force on the smaller piston:
F_small = F × (A_small/A_large) = 25 N × (1.2566 x 10^-3 m^2 / (π(0.20 m)^2)) = 0.1989 N
Using the formula for pressure, we can calculate the height of the fluid column above the smaller piston:
P = F_small/A_small = h_small × ρ × g
where ρ is the density of the fluid and g is the acceleration due to gravity. Since the density of the fluid and the acceleration due to gravity are constants, we can simplify this equation to:
h_small = F_small/(A_small × ρ × g)
Substituting the given values, we get:
h_small = 0.1989 N / (1.2566 x 10^-3 m^2 × 1000 kg/m^3 × 9.81 m/s^2) = 0.0159 m
Therefore, the smaller piston moves 0.0159 m (or approximately 1.6 cm) when the larger piston moves 5 cm.
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state the energy transfer that takes place as the ball changes shape during the contact between the racquet and the ball
When the ball hits the racquet, it gets squished, and it gains elastic energy, since it is compressed.
Case (IV)
With the suspension point 30cm from the left edge of the meter stick, hang
a 200g mass 10cm from the left edge of the stick. Calculate the mass you must hang at a point 40cm to the right of the pivot point such that the stick hangs level and write it on the sketch.
The mass to be hung at a point 40cm to the right of the pivot point such that the stick hangs level is 15 g.
How to calculate mass?To solve this problem, use the principle of moments which states that the sum of the clockwise moments about a pivot point is equal to the sum of the counterclockwise moments about the same pivot point. In this case, take the pivot point to be the suspension point of the meter stick.
Let x be the mass that needs to hang at a point 40cm to the right of the pivot point. Then, set up the following equation:
(clockwise moment) = (counterclockwise moment)
(0.2 kg) × (0.3 m) × (9.81 m/s²) = (x kg) × (0.4 m) × (9.81 m/s²) + (0.1 kg) × (0.1 m) × (9.81 m/s²)
Simplifying this equation:
0.05886 = 3.924x
x = 0.015 kg or 15 g
Therefore, we need to hang a 15 g mass at a point 40 cm to the right of the pivot point such that the stick hangs level.
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