The farthest that particular object will move along the x-axis in the positive direction is 0.2 m. This is the amplitude of the pendulum's motion.
What is potential energy?Potential energy in physics is the energy that an item retains as a result of its position in relation to other objects, internal tensions, electric charge, or other elements.
Since the total energy of the object is given by E = U + K, where U is the potential energy and K is the kinetic energy, and the pendulum has a small amplitude, we can assume that the kinetic energy of the object is negligible.
Therefore, we have:
E = U = [tex](1/2)kx^2[/tex]
Khere k is the spring constant of the pendulum and x is the displacement from the equilibrium position.
So, the value of x can be:
x = sqrt(2E/k)
Substituting the given values, we have:
x = sqrt(2(0.4 J)/(20 N/m)) = 0.2 m
Thus, the farthest the object moves along the x-axis in the positive direction is 0.2 m.
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sun why it that the higher you go to the becomes cold.
The temperature drops as you go higher into the atmosphere because you are moving away from the Earth's surface, where the majority of the planet's heat is generated.
What happens when we go higher?As you move higher, the air pressure and density decrease, and there is less of the Earth's atmosphere to absorb and retain heat. This results in a lower overall temperature.
Additionally, the sun's rays become more intense at higher altitudes due to the lack of air molecules to scatter the sunlight. This can cause a heating effect, but it's usually not enough to offset the cooling effect caused by the decrease in atmospheric pressure.
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When is vertical velocity zero? Select all the apply
1. when an object changes direction.
2.the moment you kick a football in the air.
3. vertical velocity is zero initially when an object is dropped from a window.
4. the moment a ball rolls off a table.
5. the moment you throw a ball in the air.
Answer:
3
Explanation:
When the projectile reaches a vertical velocity of zero, this is the maximum height of the projectile and then gravity will take over and accelerate the object downward. The horizontal displacement of the projectile is called the range of the projectile, and depends on the initial velocity of the object.
A spring with a spring constant of 2 N/m is stretched by Laura until extended by 0. 5 m. How much elastic potential energy is stored by the spring?
The spring stores 0.5 joules of elastic potential energy when stretched by 0.5 meters.
What is Potential Energy?
It is a form of energy that is stored in an object and has the potential to do work. The amount of potential energy depends on the position, shape, and orientation of the object. The most common types of potential energy are gravitational potential energy, elastic potential energy, and chemical potential energy.
The elastic potential energy stored by a spring is given by the formula:
Elastic potential energy = 1/2 * spring constant * (extension)^2
where the spring constant is measured in Newtons per meter (N/m), and the extension is measured in meters (m).
Given that the spring constant is 2 N/m and the extension is 0.5 m, we can plug these values into the formula:
Elastic potential energy = 1/2 * 2 N/m * (0.5 m)^2
= 0.5 J
Therefore, the spring stores 0.5 joules of elastic potential energy when stretched by 0.5 meters.
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Part A- Variation in the speed of sound Sound is a longitudinal wave, and its speed depends on the medium through which it propagates. In air, sound travels at 343 m/s. In an experiment, you observo a sound with a frequency of 500 Hz and a wavelength of 6.4 m. What is the speed of sound in this differont medium? Express your answer with the appropriate units. HÅ ? Value Units Submit Request Answer Sounds vary in intensity and loudness across a very wide range, and we use the logarithmic decibel scale to quantify sound. Sort and match the following sounds with their decibel level. Place each sound in the appropriate in for its decibel level. Only one sound may be placed in each bin. Reset Help Operating a lawnmower Your clothing rusting Telephone hold music A whisper across a football field Abrary with people studying -20 dB 10 dB 30 dB 60 dB 90 dB Part D- Calculating the limits of hearing In a large perfectly quiet room, at what maximum distance could you hear a bee with a power output of 1W? Recall that the threshold of hearing is 10-12 W/m² Express your answer with the appropriate units. HA ? T Value Units Submit Request Answer
The Velocity is 4270 m/s it is equal to product of frequency and wavelength.
Given: -
Frequency(f) = 700 Hz
Wavelength(λ) = 6.1m
velocity = f x λ
velocity = 700 x 6.1
velocity = 4270 m/s
Wavelength is a fundamental concept in physics, particularly in the study of waves, which includes electromagnetic radiation, light, and sound waves. It is defined as the distance between two successive points of the same phase, such as the crest or trough of a wave. This distance is usually measured in units of meters, and it is inversely proportional to the frequency of the wave.
In electromagnetic radiation, the wavelength is an important property that determines the type of radiation, such as radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Each type of radiation has a unique range of wavelengths that can be measured using instruments like a spectroscope or a radio antenna.
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When a local house was on fire, the firefighters were able to save most of it by dousing the house with water. What will happen when forensic scientists investigate this fire?.
Forensic scientists will investigate the fire by looking for clues as to what caused it and how it spread. They will collect evidence such as burn patterns and debris, and analyze the scene to determine the origin of the fire.
What is debris?
Debris is any loose material (solid or liquid) that is scattered or discarded, such as the remains of a wrecked or destroyed structure or object. Common examples of debris include rubble, broken glass, fallen tree branches, discarded plastic, scrap metal, and other discarded materials. Debris can also include materials that are the by-product of a process, such as the dust created by grinding or sawing. Debris can also be the result of natural disasters or human activities. Debris can be found in any environment and can cause environmental or safety hazards if left unchecked.
Therefore, Forensic scientists will investigate the fire by looking for clues as to what caused it and how it spread. They will collect evidence such as burn patterns and debris, and analyze the scene to determine the origin of the fire.
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Lab: Newton's Laws of Motion
Newton's law of motion
Three newton's law of motion:-
1. An object will not change its motion unless a force acts on it.
2. The force of an object is equal to its mass time its acceleration.
3. When two objects interact , they apply forces to each other of equal magnitude and opposite direction.
Newton's law of motion are three basic laws of classical mechanics that describes the relationship between the motion of an object and the forces acting on it.
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A piece of gold-alminium alloy weighs 49N. When suspended from a spring balance and submerged in water it weighs 39.2N. What is the weight of Gold in the alloy the specific gravity of gold is 19.3 and that if aluminium is 2.5?
Answer:
The mass of the water in 1 kg (9.8 N = m (9.8 m/s/s)),
Thus the volume of the water is 1000 ml.
5 = (Mau + Mal)/(Vau + Aal)
(Density = total mass to the total volume)
We know that:
19.2 = Mau/Vau and 2.5 = Mal/Val.
We have to find the volume. Therefore,
5Val + 5Vau = Mau + Mal
5(Mal/2.5) + 5(Mau/19.2) = Mau + Mal
Mal = 0.74 Mau
5 kg = M(au) + (1/.74)M(au)
=> M(au) = 2.13 kg
Weight of gold = 20.8 N
hence the weight of the gold is 20.8 N
Which of the following best describes a direct current?(1 point)
Responses
an electrical current that flows in one direction
a stationary electrical charge
an electrical current that flows in alternating directions back and forth
the flow of electric charges through a conductor
The best description of a direct current is "an electrical current that flows in one direction."
define electric current ?
Electric current is the movement of electric charges through a material, usually electrons. It is expressed in amperes (A) and is defined as the quantity of charge that passes through a point in a circuit over time. The conventional direction of current is taken as the positive charge carriers, which are in the opposite direction to the flow of electrons. Electric current is essential for the operation of numerous electrical devices and systems.
The best description of a direct current is "an electrical current that flows in one direction."
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Identify the correct sequence of events from this passage.
A. Martin Cooper invented the first cell phone.
B. AT&T discussed the concept of a wireless phone.
C. The FDA ruled that the health risks of cell phones were small.
D. Cell phone became the most common electronic device.
Answer:
The correct sequence of events is:
A. Martin Cooper invented the first cell phone.
B. AT&T discussed the concept of a wireless phone.
C. Cell phone became the most common electronic device.
D. The FDA ruled that the health risks of cell phones were small.
Using the objects around you right now as your frame of
reference, you cannot tell that the Earth is moving.
What evidence would you need to collect in order to prove
that the Earth is in motion?
EXTRA HELP
Where should you position yourself in space in order to see
the Earth spinning?
What would you use as a frame of reference?
Scientists use the movement of pendulums to provide evidence that the Earth is rotating the moon's position in space in order to see the Earth spinning
What is the evidence of Earth's movement?The quickest observational evidence for Earth's orbital motion is the evident shift of nearby stars after six months, as the Earth moves from one side of Earth's its orbit to the other. Because of the large interval to even the nearest star, this parallax shift is to move small to be seen without a telescope.
Time subjection cameras show circular paths of star trails showing the Earth is rotating. The winds on the Earth curve evince the Earth is moving. proving the Earth is rotating.
So we can conclude that Pendulum's swing and swap direction prove the Earth is rotating.
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Newton's universal law of gravitation states that response area objects attract each other with a force response area proportional to the product of their masses and response area proportional to the square of the distance between their centers. When considering objects on the surface of the earth, the force is directly proportional to the product of the mass of the object and the response area due to response area at the earth's surface. Since the earth is response area than any object under consideration, the object is drawn response area the earth.
Newton's Law of Universal Gravitation says that every particle in the cosmos attracts every other particle with a force directly equal to the product of their masses and inversely proportional to the square of their distance.
To detect the gravitational force of attraction between any two objects, at least one of them on Earth must have an exceptionally massive mass. We cannot detect such forces because no object on Earth has an enormously big mass.
Newton's universal law of gravitation states that all objects attract each other with a force (i) away from directly proportional to the product of their masses and (ii) gravity proportional to the square of the distance between their centers. When considering objects on the surface of the Earth, the force is (iii) directly proportional to the product of the mass of the object and the (iv) acceleration due to (v) smaller at the Earth's surface. Since the Earth is (vi) larger than any object under consideration, the object is drawn (vii) towards the Earth.
The two items in a room do not move towards one other since the gravitational force of attraction between them is extremely minimal due to their modest masses. According to the universal law of gravity, every object exerts a gravitational force on every other thing. The gravitational force is directly proportional to the product of masses and inversely proportional to the square of their distances, according to the universal law of gravitation.
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Complete Question:
Fill in the blanks with the appropriate option:
Newton's universal law of gravitation states that all objects attract each other with a force (i) _____ proportional to the product of their masses and (ii) ____ proportional to the square of the distance between their centers. When considering objects on the surface of the Earth, the force is (iii) _____ proportional to the product of the mass of the object and the (iv) ____ due to (v) _____ at the Earth's surface. Since the Earth is (vi) ____ than any object under consideration, the object is drawn (vii) ______ the Earth.
Options:
acceleration, away from directly, directly, gravity, inversely, larger, smaller, some, toward.
Let E =3i^+1j^ and F =1i^−3j^.
A. Find the magnitude of E.
B. Find the magnitude of F.
C. Find the magnitude of G =E +F.
D. Find the magnitude of H =−E −2F.
The given vectors E and F are in Cartesian form. To find their magnitudes, we can use the formula:
|v| = √(vx² + vy²)
where vx and vy are the x and y components of the vector.
What is the Cartesian algebra?Cartesian algebra, also known as coordinate algebra or analytic geometry, is a branch of mathematics that deals with the use of algebraic equations to describe geometric shapes and their properties. It is named after the French philosopher and mathematician René Descartes, who developed the Cartesian coordinate system, which provides a way to describe the position of points in space using numbers.
A. Magnitude of E:
|E| = √((3i)² + (1j)²)
= √(9i² + 1j²)
= √(9 + 1)
= √(10)
Therefore, the magnitude of E is √(10).
B. Magnitude of F:
|F| = √((1i)² + (-3j)²)
= √(1 + 9)
=√(10)
Therefore, the magnitude of F is √(10).
C. Magnitude of G = E + F:
G = E + F = (3i + 1i) + (1j - 3j)
= 4i - 2j
|G| = √((4i)² + (-2j)²)
=√(16 + 4)
= √(20)
= 2√(5)
Therefore, the magnitude of G is 2√(5).
D. Magnitude of H = -E - 2F:
H = -E - 2F = (-3i - 2i) + (-1j + 6j)
= -5i + 5j
|H| = √(-5i)² + (5j)²)
= √(25 + 25)
= √(50)
= 5√(2)
Therefore, the magnitude of H is 5√(2).
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How can scientists determine whether an extinct animal gave birth on land or underwater?.
The correct option is C. Position of the head of the fetus of an extinct animal that gave birth on land or underwater.
In human prenatal development, fetal development starts offevolved from the 9th week after fertilization (or eleventh week gestational age) and maintains till birth.
Prenatal improvement is a continuum, with no clear defining characteristic distinguishing an embryo from a fetus. however, a fetus is characterized by the presence of all the most important body organs, though they will now not yet be completely advanced and practical and some not but situated in their very last anatomical vicinity. An unborn offspring develops and grows within the uterus (womb) of humans and different mammals. In human beings, the fetal duration begins at 9 weeks after fertilization of an egg by using sperm and ends at the time of delivery.
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Complete Question:
1. How can scientists determine whether an extinct animal gave birth on land or underwater?
a. Location of the hind limbs of the fetus
b. Position of the nostrils
c. Position of the head of the fetus
d. Location of the fossils
Landing with a speed of 71.4 m/s and traveling due south, a jet comes to rest in 939 m
Assuming the jet slows with constant acceleration, find the magnitude of its acceleration.
(part a)
Assuming the jet slows with constant acceleration, find the direction of its acceleration.
(part b)
The acceleration is 2.7 m/s^2.
What is the acceleration?Acceleration is a measure of the rate at which an object changes its velocity. It is defined as the change in velocity per unit time and has units of meters per second squared (m/s^2). Acceleration can be positive (when an object is speeding up), negative (when it is slowing down), or zero (when its velocity is constant).
We can get the acceleration;
v^2 = u^2 - 2as
v = final velocity
u = initial velocity
a = acceleration
s = distance
Thus we have that;
v = 0 m/s thus;
u^2 = 2as
a = u^2/2s
a = (71.4)^2/2 * 939
a = 5097.96/1878
a = 2.7 m/s^2
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Which component in the circuit would most likely have the lowest resistance?
A buzzer
A capacitor
A light bulb
A wire
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
A wire should have the least resistance possible, because if there is more resistance in wires, there would be a lot of power loss when current flows through it.
Therefore, wires should have lowest resistance.
How do you calculate soil cation exchange capacity and base saturation?
To determine the cation exchange capacity (CEC), calculate the milliequivalents of H, K, Mg, and Ca per 100g of soil (meq/100g soil) by using the following formulas: H, meq/100g soil = 8 (8.00 - buffer pH) K, meq/100g soil = lbs/acre extracted K ÷ 782. Mg, meq/100g soil = lbs/acre extracted Mg ÷ 240.
To begin, multiply the total CEC by the percentage for that ion to determine the cmolc of each cation on the exchange complex. It is 0.05 * 30 cmolc/kg for hydrogen. The cmolc/kg for each ion is then converted to mass of ion per kg by multiplying by the mass of 1 cmolc.
Soil testing laboratories calculate CEC by adding the calcium, magnesium, and potassium levels measured during the soil testing procedure to an estimate of exchangeable hydrogen derived from the buffer pH. In general, CEC values obtained through this summation method will be slightly lower than those obtained through direct measurementsdirect.
The percentage of CEC occupied by bases (Ca2+, Mg2+, K+, and Na+) is represented by base saturation (BS). The%BS increases as soil pH rises (Figure 5). Ca2+, Mg2+, and K+ availability increases as %BS increases. An 80% BS soil, for example, provides cations to plants more easily than a 40% BS soil.
Base saturation is the percentage of base cations (Ca2+, Mg2+, K+, and Na+) held onto soil exchange sites divided by total CEC.
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The figure below shows a rigid 3-mass sys-
tem which can rotate about an axis perpen-
dicular to the system. The mass of each
connecting rod is negligible. Treat the masses
as particles.
The x-axis is along the horizontal direction
with the origin at the left-most mass 7 kg.
7 kg
1 kg
6 kg
5m
m.
x
*
-5m-
The masses are separated by rods of length
5 m, so that the entire length is 2 (5 m).
Determine the x-coordinate of the center of
mass for the three-mass system with respect
to the origin.
Answer in units of m. Answer in units of
The x component of the center mass is 4.64 m.
What is the x-coordinate of the center mass?The x component of the center mass is calculated by applying the following formula as shown below;
X_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3),
where;
m1 is mass 1 = 7 kgx1 is the position of mass 1 = 0 mm2 is the mass 2 = 1 kgx2 is the position of mass 2 = 5 mm3 is the mass 3 = 6 kgx3 is the position of mass 3 = 10 mX_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
X_cm = (7 x 0 + 1 x 5 + 10 x 6) / (7 + 1 + 6)
X_cm = 4.64 m
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A bowling ball with a mass of 7.0 kg strikes a pin that has a mass of 2.0 kg. The pin flies forward with a velocity of 7.0 m/s, and the ball continues forward at 4.0 m/s. What was the original velocity of the ball?
The original velocity of the ball was -4.0 m/s, which means it was moving in the opposite direction of the final velocity (4.0 m/s).
How to find the original velocity of the ball?
The original velocity of the ball can be found using the principle of conservation of momentum. The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act upon it. In this case, the closed system is the ball and the pin. Before the collision, the total momentum of the system was zero (since the ball was at rest). After the collision, the momentum of the system is given by the ball's momentum plus the pin's momentum.
The momentum of an object is given by the product of its mass and velocity:
p = m * v
where:
p is the momentum of the object
m is the mass of the object
v is the velocity of the object
First, let's find the total momentum of the system after the collision:
p_total = p_ball + p_pin
p_total = (m_ball * v_ball) + (m_pin * v_pin)
p_total = (7.0 kg * v_ball) + (2.0 kg * 7.0 m/s)
Now, we'll use the principle of conservation of momentum to set the total momentum of the system before the collision equal to the total momentum of the system after the collision:
p_total_before = p_total_after
0 = p_total
0 = (7.0 kg * v_ball) + (2.0 kg * 7.0 m/s)
Solving for v_ball:
v_ball = (-2.0 kg * 7.0 m/s) / 7.0 kg
v_ball = -4.0 m/s
So, the original velocity of the ball was -4.0 m/s, which means it was moving in the opposite direction of the final velocity (4.0 m/s).
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b) A hammer of weight 100 N falls freely on a nail from height 1.25 m. Find the impulse and average force of blow if impact last for 10-² S.
Answer:
Explanation:
When the hammer hits the nail it transfers this energy to the nail in order to move it 1cm (0.01m). A transfer of energy is known as "work done" and work done = force x distance. So, force = work done / distance = 25 / 0.01 = 2500N Answer: Average force = 2500 Newtons.
Calculate the distance between the center of the earth and the center of the moon at which the gravitational force exerted by the earth on an object is equal in magnitude to the force exerted by the moon on the object
( solution)
At the neutral point, the distance between the Earth's center and the Moon's center is about 399,000 kilometers, or 3.989 x 10⁸ meters.
What is the force of gravity?Planets, stars, and galaxies all move because it is one of the fundamental forces of the universe. According to Newton's law of gravitation, the distance between two objects and their masses determine the magnitude of the gravitational force
We can make use of the fact that the gravitational force between two objects is inversely proportional to the square of the distance between their centers and proportional to the product of their masses to calculate this distance. As a result, we can solve for the distance by setting the force of gravity that the Earth exerts on the object to be equal to the force of gravity that the Moon exerts on the object.
The masses of the Earth and the Moon, M_E and M_M, respectively, and the distance between their centers, d. The following factors determine the Earth's gravitational pull on the object:
F_E is equal to G × M_E × m / (d₂), where m is the mass of the object and G is the gravitational constant. The following factors determine the Moon's gravitational pull on the object:
F_M = G × M_M × m / ((R-d)²)
where R is the distance between the centers of the Earth and Moon
Setting F_E equal to F_M, we get:
G × M_E × m / (d²) = G × M_M × m / ((R-d)²)
Simplifying and solving for d, we get:
d = R × (M_E / (3 × M_M))¹/³
Values for the masses and the radius of the Earth-Moon system (R = 3.844 x 10⁸ meters), we get:
d = 3.989 x 10⁸ meters
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who suggested mutation theory
Answer:
Hugo de VriesThe mutation Theory of Evolution was proposed by Hugo de Vries.Answer:
Hugo de Vries
Explanation:
In the history of evolutionary biology, Hugo dr Vries is known as a proponent of the mutation theory of evolution, in which new species are believed to arise by single mutational events.
What are the main forces involved in a flying plane?
Answer:
There are four main forces involved in the flight of an airplane: lift, weight, thrust, and drag.
Explanation:
1. Lift: Lift is the force that opposes the weight of an aircraft and keeps it in the air. It is generated by the wings as they move through the air and is affected by factors such as the shape of the wings, the angle of attack, and the speed of the aircraft.
2. Weight: Weight is the force of gravity acting on an aircraft and pulling it downward. It is proportional to the mass of the aircraft and the acceleration due to gravity.
3. Thrust: Thrust is the forward force generated by the engines of an aircraft. It must be greater than the drag force in order to maintain forward flight.
4. Drag: Drag is the aerodynamic force that opposes the forward motion of an aircraft. It is caused by the friction of the air moving past the surface of the aircraft and is affected by factors such as the speed of the aircraft, its shape, and the altitude.
These four forces are in a constant state of balance during flight, with the pilot adjusting the thrust and angle of attack to maintain a stable flight.
How many g's of force will a nascar driver experience making a 80 m/s turn with a
radius of 200 meters?
3.2 g's
32 g's
2.5 g's
25 g's
3.27 g's of force will be applied to the driver during the turn.
What in science is a force?In science, the term "force" has a particular definition. At this time, it is appropriate to refer to a force as a push or a pull. There is no such thing as a power that something "contains" or "has in it." A force is exerted on one item by another.
We must employ the centripetal acceleration formula to resolve this issue:
a = v² / r
In this case, the velocity is 80 m/s and the radius is 200 meters, so:
a = (80 m/s)² / 200 m = 32 m/s²
To convert this to g's, we divide by the acceleration due to gravity:
32 m/s² / 9.8 m/s²/g = 3.27 g's (rounded to two decimal places)
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Use Newton's Second Law Analysis combined with torque to solve the following problem.
Three masses are attached to a uniform meter stick, as shown in the figure to your right. The mass of the meter stick is 200.0 g and the masses to the left of the fulcrum are m1 = 75.0g and m2=100.0g. Don't forget the meter stick has mass.
a) What is mass m3 that balances the system when it is attached at the right end of the stick. The resulting system is balanced.
b) What is Force the fulcrum exerts on the meter stick at point S?
5.8N. is the correct answer .
What is Torque ?
In physics and engineering, "torque" is a measure of the twisting force that can cause an object to rotate around an axis or pivot point The magnitude of torque depends on both the force being applied and the distance between the axis of rotation and the point of application of the force. The direction of the torque is determined by the right-hand rule, with the thumb pointing in the direction of the applied force and the fingers curling in the direction of rotation. Torque is a key concept in the study of mechanics and is used in a wide range of applications, such as engines, motors, and machines.
τ1=+r1w1sin90=+r1m1g(counterclockwise rotation, positive sense)
τ2=+r2w2sin90°=r2m2g(counterclockwise rotation, positive sense)
τ=+rwsin90°=+rmg(gravitational torque)
τS=rSFSsinθS=0(because S=0cm)τ3=−r3w3sin90°=−r3m3g(clockwise rotation, negative sense)
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A bicyclist is finishing his repair of a flat tire when a friend rides by with a constant speed of 4.0 m/s. Two seconds later the bicyclist hops on his bike and accelerates at 2.2 m/s2 until he catches his friend.
How much time does it take until he catches his friend (after his friend passes him)?
(part a)
How far has he traveled in this time?
(part b)
What is his speed when he catches up?
(part c)
a) It takes the bicyclist 9.09 seconds to catch up to his friend.
b) The bicyclist has traveled 40.0 meters in 9.09 seconds to catch up to his friend.
c) The bicyclist is moving at a speed of 20.0 m/s when he catches up to his friend.
The Time, Distance and Speed involveda) To find out how much time it takes for the bicyclist to catch up to his friend, we need to use the equation for motion with constant acceleration:
d = v_0 t + 0.5 a t^2
where d is the total distance traveled,
v_0 is the initial velocity (0 m/s in this case),
t is the time, and a is the acceleration (2.2 m/s^2).
Since the friend was already moving at a constant speed of 4.0 m/s when the bicyclist started pedaling, we know that the total distance d that the bicyclist has to travel to catch up is equal to 4.0 m/s * t + 0.5 * 2.2 m/s^2 * t^2.
Setting d equal to 4.0 m/s * t, we can solve for t:
4.0 m/s * t = 4.0 m/s * t + 0.5 * 2.2 m/s^2 * t^2
0.5 * 2.2 m/s^2 * t^2 = 0
t = sqrt(0 / (0.5 * 2.2 m/s^2)) = 0 s
Since the square root of zero is zero, the time t is also zero. This means that the bicyclist starts moving at the same time as the friend, so he needs to accelerate for the entire time to catch up.
Using the equation for motion with constant acceleration, we can find the time t it takes for the bicyclist to catch up:
d = v_0 t + 0.5 a t^2
d = 4.0 m/s * t
4.0 m/s * t = 0 m/s * t + 0.5 * 2.2 m/s^2 * t^2
4.0 m/s = 0.5 * 2.2 m/s^2 * t
t = 4.0 m/s / (0.5 * 2.2 m/s^2) = 9.09 s
So it takes the bicyclist 9.09 seconds to catch up to his friend.
b) To find out how far the bicyclist has traveled in this time, we can use the equation for motion with constant acceleration again:
d = v_0 t + 0.5 a t^2
d = 0 m/s * 9.09 s + 0.5 * 2.2 m/s^2 * 9.09 s^2
d = 40.0 m
So the bicyclist has traveled 40.0 meters in 9.09 seconds to catch up to his friend.
c) To find out the bicyclist's speed when he catches up, we can use the equation for velocity:
v = v_0 + a * t
v = 0 m/s + 2.2 m/s^2 * 9.09 s
v = 20.0 m/s
So the bicyclist is moving at a speed of 20.0 m/s when he catches up to his friend.
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1. A car moves at 10m/s
a. Net Force on the car is zero
b. Force of friction is equal to the forward force applied by the engine
c. Both a and b are correct
d. a is correct but b is wrong
Answer:
d. a is correct but b is wrong.
Explanation:
A car that is moving at a constant speed of 10m/s is experiencing a net force of zero, meaning that the sum of all forces acting on the car is equal to zero. This means that the forward force applied by the engine is equal in magnitude but opposite in direction to the force of friction acting on the car.
The force of friction acts to slow down the car, but it does not equal the forward force applied by the engine. Instead, it is determined by factors such as the weight of the car, the road surface, and the tire traction. If the forward force applied by the engine is greater than the force of friction, the car will accelerate. Conversely, if the force of friction is greater than the forward force applied by the engine, the car will decelerate.
(a) A charge of -275e is uniformly distributed along a circular arc of radius 3.85 cm, which subtends an angle of 37°. What is the linear charge density along the arc?
1 C/m
(b) A charge of -275e is uniformly distributed over one face of a circular disk of radius 1.85 cm. What is the surface charge density over that face?
2 C/m2
(c) A charge of -275e is uniformly distributed over the surface of a sphere of radius 1.85 cm. What is the surface charge density over that surface?
3 C/m2
(d) A charge of -275e is uniformly spread through the volume of a sphere of radius 1.85 cm. What is the volume charge density in that sphere?
4 C/m3
Uniform distribution of charge a) [tex]-1.752 * 10^(-17) C/m[/tex] b) [tex]-4.038 * 10^(-16) C/m^2[/tex] c) [tex]-6.346 * 10^(-16) C/m^2[/tex] d) [tex]-4.580 * 10^(-13) C/m^3[/tex]
(a) To find the linear charge density along the arc, we divide total charge (-275e) by arc length. Arc length is product of radius (3.85 cm) by the angle (in radians) arc subtends. Convert angle to radians:
[tex]37 degree = (37/360) * 2\pi radians = 0.6435 radians[/tex]
The length of the arc is then:
length = radius x angle = (3.85 cm) x (0.6435) ≈ 2.477 cm
The linear charge density is then:
linear charge density = charge in total / length magnitude = (-275e) / (2.477 cm)
e: elementary charge.
Using charge value:
linear charge density = [tex]-1.752 * 10^(-17) C/m[/tex]
Therefore, linear charge density along the arc is [tex]-1.752 * 10^(-17) C/m.[/tex]
(b) To find the surface charge density over the face of the circular disk, we need to divide the total charge (-275e) by area of disk. Area of face of disk is [tex]\pi[/tex] times radius squared
area =[tex]\pi * (1.85 cm)^2 = 10.78 cm^2[/tex]
The surface charge density is then:
surface charge density = total value of charge / area magnitude = [tex](-275e) / (10.78 cm^2)[/tex]
e: elementary charge.
Using charge value:
surface charge density = [tex]-4.038 * 10^(-16) C/m^2[/tex]
Surface charge density over the face of the circular disk is [tex]-4.038 * 10^(-16) C/m^2[/tex].
(c) To get surface charge density over sphere surface, we divide total charge (-275e) by sphere surface area:
surface area = [tex]4\pi * (radius)^2[/tex]
The surface charge density:
surface charge density = total charge / surface area =[tex](-275e) / [4\pi * (1.85 cm)^2][/tex]
where e is the elementary charge.
Use charge value:
surface charge density ≈ [tex]-6.346 * 10^(-16) C/m^2[/tex]
Surface charge density over sphere is[tex]-6.346 * 10^(-16) C/m^2.[/tex]
(d) To get volume charge density in the sphere, we divide the total charge (-275e) by the volume of the sphere.
volume = [tex](4/3)\pi * (radius)^3[/tex]
The volume charge density is then:
volume charge density = total charge / volume = [tex](-275e) / [(4/3)\pi * (1.85 cm)^3][/tex]
e: elementary charge
Using value of the elementary charge:
volume charge density = [tex]-4.580 * 10^(-13) C/m^3[/tex]
Therefore, the volume charge density in the sphere is [tex]-4.580 * 10^(-13) C/m^3[/tex]
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a) calculate the magnitude of the force parallel to surface 1 b) calculate the magnitude of the force parallel to surface 2
A force can make a body at rest to move. The magnitude of force parallel to surface 1 is 5.04 N and the magnitude of the force parallel to surface 2 is 4.02 N.
What is Force?The force can be defined as the quantity which is expressed as the product of mass (m) and acceleration (a). It is known as the push or pull on an object which produces acceleration in the body on which it acts.
The equation which is used to calculate the force is given as:
F = ma
a) F₁ = m₁ g sin40
= 0.800 kg × 9.81 m/s² × 0.64
= 5.04 N
b) F₂ = m₂ g sin55
= 0.500 kg × 9.81 m/s² × 0.82
= 4.02 N
Thus the magnitude of the force parallel to surface 1 is 5.04 N and the magnitude of the force parallel to surface 2 is 4.02 N.
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The diagram below shows three cubes of the same material and density. If the cubes all start out at 80°C, which cube will cool the most slowly?
Answer:
the cube that will slowly cool is 2
The cube 2 will cool the most slowly.
What is meant by cooling ?The removal of heat from a system is known as cooling, and it usually leads to a decrease in temperature or a change in phase.
Here,
Three cubes of same material and density are given in the diagram. They all are said to be cooling starting from 80°C.
The three cubes have different volumes.
We know that, as the volume of the cube increases, the surface area of the cube decreases accordingly. That means, the volume of a cube is inversely proportional to its surface area.
V ∝ 1/A
According to the principle of cooling, the rate of cooling is directly proportional to the surface area. That means, the rate of cooling is higher for objects with higher surface area and slower for those with lower surface area.
So, the cube 2 is having the lowest volume among the three cubes and thus the highest surface area.
Therefore, it will take more time to cool down.
Hence,
The cube 2 will cool the most slowly.
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In the 2nd lab you were studying water squirting out from a hole in a cylinder filled with water into a tub. Just as a falling ball converts potential energy to kinetic energy, water pressure pushed water out of the hole by converting potential energy per unit volume (density x g x height) to kinetic energy per unit volume (density x velocity^2/2). Assume you have a 20 cm head of water above the hole and that the hole is 40 cm above ground.
How long after your release the finger holding the hole (in seconds) will it take the water to reach the ground (think mechanics)?