The required acceleration has a magnitude of 19.7 m/s2 directed upwards, correct to three significant figures.
The the purpose of analysis, the motion of rocket is divided into two phases.
Phase 1: the free fall motion of the rocket from the height 2.98*102m to a height 96.5m.
Phase 2: the motion of the rocket due to the acceleration of the rocket also from the height 96.5 m to the point of touchdown y = 0m.
The initial velocity of the rocket is 0m/s when it started to experience a fall from rest under free fall. g = 9.8m/s² t1 is the time taken for phase 1 and t2 is the time taken for phase2.
The final velocity under free fall becomes the initial velocity for the accelerated motion of the rocket in phase 2 and the final velocity or speed in phase 2 is equal to zero.
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Decribe how an electric field and potential gradient affect the performance of inulation
Only in the presence of an electric potential difference does the electric field exist. There won't be any electric field if the charge is homogeneous throughout, regardless of how high the electric potential is.
What connection exists between the potential gradient and the electric field?Potential gradient is calculated by integrating the negative of the electric field's intensity with respect to distance. E = - d V d r describes the relationship between the magnitude of the electric field and the potential gradient.Of course, an insulator can let an electric field through. As it passes through an insulator or dielectric medium, the electric field polarises it.Only in the presence of an electric potential difference does the electric field exist. There won't be any electric field if the charge is homogeneous throughout, regardless of how high the electric potential is.To learn more about electric potential difference refer to:
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Within 4. 0 s of liftoff, a spacecraft that is uniformly
accelerating straight upward from rest reaches an altitude
of 4. 50 X 102 m [up).
(a) What is the spacecraft's acceleration?
The spacecraft's acceleration can be found using the equation: a = (v-u)/t = 4.50 x 10^2 m / 4.0 s = 11.25 m/s^2.
Can you explain the concept of uniformly accelerating motion?Uniformly accelerating motion refers to an object that is moving at a constant rate of acceleration. This means that the velocity of the object is changing at a constant rate, but the acceleration remains the same throughout the motion. An example of this type of motion is an object that is accelerating from rest at a constant rate. The motion of the object can be described mathematically by the equations of motion, such as distance = initial velocity * time + 1/2 * acceleration * time^2. The graph of uniformly accelerating motion is a parabola, with velocity on the y-axis and time on the x-axis. This type of motion is different from non-uniform acceleration, where the acceleration changes during the motion.
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A spacecraft that is uniformly accelerating straight upward from rest reaches an altitude of 4. 50 X 102 m [up) with acceleration of 11.25 m/s².
Evaluating :The spacecraft's acceleration can be found using the equation:
a = (v-u)/t
= 4.50 x 10² m / 4.0 s
= 11.25 m/s².
Uniformly accelerating motion :Uniformly accelerating motion refers to an object that is moving at a constant rate of acceleration. This means that the velocity of the object is changing at a constant rate, but the acceleration remains the same throughout the motion. An example of this type of motion is an object that is accelerating from rest at a constant rate.
The motion of the object can be described mathematically by the equations of motion, such as distance = initial velocity × time + 1/2 * acceleration × time². The graph of uniformly accelerating motion is a parabola, with velocity on the y-axis and time on the x-axis. This type of motion is different from non-uniform acceleration, where the acceleration changes during the motion.
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your friend, who is in a field 70 meters away from you, kicks a ball towards you with an initial velocity of 18 m/s. assuming the grass causes the ball to decelerate at a constant rate of 1.0 m/s2, how long does it take for the ball to reach you?
With the use of formula, the time taken for the ball to reach you is 31.6 s
What is Acceleration ?Acceleration can be defined as velocity change per time taken. It is a vector quantity.
Given that your friend, who is in a field 70 meters away from you, kicks a ball towards you with an initial velocity of 18 m/s. assuming the grass causes the ball to decelerate at a constant rate of 1.0 m/s2, to know how long it takes for the ball to reach you, we will use the formula
s = ut - 1/2at² where
v = 0
u = 18 m/s
a = 1 m/s²
s = 70 m
t = ?
70 = 18t - 1/2 × 1 × t²
70 = 18t - 0.5t²
Multiply all by 2
140 = 36t - t²
t² - 36t + 140 = 0
Using completing the square method
t² - 36t + 18² = 18² - 140
( t - 18 )² = 324 - 140
( t - 18 )² = 184
t - 18 = √184
t = 18 + 13.6 or 18 - 13.6
t = 31.6 s or 3.4 s
Therefore, the ball will reach you in the next 31.6 s
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for each of the following items, indicate which viewing method is most appropriate–the unaided eye, light microscopy, scanning electron microscopy, or transmission electron microscopy–by dragging it into the correct bin.
For the investigation and analysis of micro- and nanoparticle imaging characterisation of solid objects, scanning electron microscopes (SEM) are among the most frequently used instrumentation.
What is the purpose of a scanning electron microscope? For the investigation and analysis of micro- and nanoparticle imaging characterisation of solid objects, scanning electron microscopes (SEM) are among the most frequently used instrumentation.The SEM's resolution of 10 nm, or 100, is one of the factors that make it popular for particle size analysis.Since many interior structures have membranes that are obscured by the light microscope, a transmission electron microscope would be the most effective tool for seeing the cell's internal architecture.Use both hands whenever you carry a microscope.With one hand, hold the arm firmly, and with the other, support it by placing it beneath the base.To learn more about electron microscope refer
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A hot-air balloon takes off from the ground traveling vertically with a constant upward acceleration of magni- tude g/4. After time interval ∆t, a crew member releases a ballast sandbag from the basket attached to the balloon. How many seconds does it take the sandbag to reach the ground?
The time it takes for the sandbag to reach the ground would depend on the height from which it was released. The value is calculated to be t = √(2 s/(3g/4)).
To find out how long it takes for the sandbag to reach the ground, we can use the equation of motion for a vertically falling object under the influence of gravity:
s = v₀ t + (1/2) g t²
where s is the distance fallen, v₀ is the initial velocity (which is 0 m/s for the sandbag), t is the time elapsed, and g is the acceleration due to gravity (approximately 9.8 m/s²).
We know that the sandbag is being released from the balloon and has an upward acceleration of g/4. So, the equation of motion becomes
s = v₀ t + (1/2)(g - g/4) t²
We also know that s is the distance fallen to the ground, which we can take as the final distance.
Now solving the equation for t, t = √(2 s/(g - g/4))
It is given that the magnitude of the upward acceleration is g/4, so (g - g/4) = 3g/4, so the final equation becomes t = √(2 s/(3g/4))
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Why is it that the lower mass individual may appear to experience more force from the larger mass player in a collision?
Answer:
One possible reason is that change in velocity is greater for the individual with lower mass.
Explanation:
By Newton's Law of Mechanics, magnitude of the force on two players would be the same in the collision. Let [tex]F[/tex] denote this magnitude.
Assume that the duration of the collision is [tex]\Delta t[/tex]. In this collision, magnitude of the impulse [tex]J[/tex] on each player would be the same: [tex]J = F\, \Delta t[/tex].
At the same time, impulse is equal to the change in momentum. Specifically, if the mass of one player is [tex]m[/tex] and the change in their velocity is [tex]\Delta v[/tex], the change in their momentum would be [tex]m\, \Delta v[/tex]. Thus:
[tex]m\, \Delta v = J = F\, \Delta t[/tex].
Rearrange to obtain an expression for the change in velocity:
[tex]\begin{aligned}\Delta v &= \frac{J}{m} = \frac{F\, \Delta t}{m}\end{aligned}[/tex].
In other words, in this collision, change in velocity is inversely proportional to the mass of the participant. Hence, even though the two players experienced force of the same magnitude, the participant with a lower mass would experience a greater change in velocity.
The particles leave a trail behind them as they move. The longer the trail, the faster that the particle is moving. During any up-and-down cycle of the particle, describe the speed. At what point during its motion does it move with the greatest speed AND smallest speed?
The particles leave a trail behind them as they move. The longer the trail, the faster that the particle is moving. During any up-and-down cycle of the particle, describe the speed. It moves with the greatest speed AND smallest speed when there is a change in the direction.
What speed?The speed of an object is described as the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time;
Speed is a scalar quantity.
The particle will move faster when there is a change in the direction on the movement of the particle.
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study the editorial cartoon total eclipse 2017 by nate beeler. what is the purpose of this editorial cartoon? to show that today's kids are interested in learning about astronomical events to show that technology prevents people from directly experiencing major events to show how small computers have become with advances in technology to show that children often do not realize what is going on around them
To illustrate how technology keeps people from experiencing significant events firsthand, consider Nate Beeler's editorial comic Total Eclipse 2017.
The editorial cartoon's goal is unclear?Cartoon editorials share this educational goal with prose editorials. They are created with the intention of getting readers to reflect on contemporary political concerns. A reader-friendly visual and linguistic language is required for editorial cartoons.
What viewpoint possesses the cartoonist?someone's opinion or point of view on something. How might a political cartoonist's point of view be impacted. The point of view of a cartoonist will direct their work. The opinions of others may be taken into consideration by cartoonists, or they may solely express their own opinions.
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If the acceleration of an object is negative , the object must be slowing down .
Yes the given statement is true. Negative acceleration of an object shows that the object is slowing down.
The rate of change of velocity with respect to time is nothing but the acceleration. It is considered as a vector quantity that has both magnitude and direction. Its SI unit is m/s², and its dimension formula is [LT⁻²]. Mathematically
Acceleration, a = (v₂ - v₁)/Δt
Where v₂ is the final velocity after time Δt, and v₁ is the initial velocity. If the acceleration is negative it means final velocity is smaller than initial velocity. It means object is slowing down. Negative acceleration is also called deceleration. Hence the given statement is true.
--The given question is incomplete, the complete question is:
"Is it true that If the acceleration of an object is negative the object must be slowing down?"--
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electrons are accelerated by a 1000-v potential drop. (a) calculate the de broglie wavelength. (b) calculate the wave- length of the x-rays that could be produced when these elec- trons strike a solid.
The de Broglie wavelength of the electron is 2.212 x 10-11 m.
What is Broglie wavelength?The de Broglie wavelength is a concept in quantum mechanics which states that all matter has a wave-like nature, and can thus be described as a wave.
(a) The de Broglie wavelength (λ) of a particle is given by the equation: λ = h/p, where h is Planck's constant (6.626 x 10-34 J.s) and p is the momentum of the particle.
The momentum of an electron with a 1000-V potential drop is given by the equation p = eV/c,
where e is the electron charge (1.602 x 10-19 C) and c is the speed of light (2.998 x 108 m/s).
Therefore, the de Broglie wavelength of the electron is:
λ = h/(eV/c) = (6.626 x 10-34 J.s) / (1.602 x 10-19 C x 1000 V/2.998 x 108 m/s) = 2.212 x 10-11 m.
(b) X-rays are produced when high-energy electrons strike a solid.
The wavelength of the x-ray is inversely proportional to the energy of the electron.
The energy of the electron is equal to the potential drop, i.e. 1000 eV. Therefore,
the wavelength of the x-ray produced is: λ = hc/eV = (6.626 x 10-34 J.s x 2.998 x 108 m/s)/(1.602 x 10-19 C x 1000 eV) = 1.246 x 10-10 m.
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is a=f/m = 10000/50000 does it equal 0.2 ms to the power of -2
Yes, a=f/m where a is the acceleration, f is the force, and m is the mass of an object, a=0.2m/s^2
According to Newton's 2nd law of motion, According to this law, the rate of change of linear momentum of a body is directly proportional to the external force applied on the body, and this change takes place always in the direction of the force applied. In simple terms, it means that a larger force will change the momentum of an object more quickly as compared to a smaller force.
Mathematically, we can write
F∝ dp/dT
where p is the momentum
F∝ (mv-mu)/t₂-t₁
where v is the final velocity and u is the initial velocity
Now, F∝{m(v-u)}/(t₂-t₁)
F∝ma [∵ a=(v-u)/t]
F=kma
∴ when k=1
F=ma
Now according to this question,
f=10,000 N and m=50,000kg
By applying the formula,
F=ma
10,000=50,000*a
∴ a= 10,000÷50,000
a=0.2 or 2×10⁻¹ m/s²
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question in a certain region of space, there is an electric potential difference of 120v between two points that are 0.25m apart. what is the magnitude of the average electric field in between the two points?
The magnitude of the average electric field in between the two points is 480V/m
What is electric field?Electric field is an important concept in physics that describes the force exerted by a charged particle or object on other particles or objects in its vicinity. It is a vector field, meaning it has both magnitude and direction. The electric field is created when an electric charge is placed in a region of space. The electric field will then act on any other charges in the region, producing a force on them.
Electric field (E) is defined as the electric potential difference (V) divided by the distance (d) between two points:
E = V / d
In this case, the electric potential difference is 120V and the distance between the two points is 0.25m. Therefore, the magnitude of the average electric field in between the two points is:
E = 120V / 0.25m = 480V/m
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Which sentence best explains the relationship between cells, tissues. And organs in the human body
Organ function is related to cell size which determines the function of tissues explains the relationship between cells, tissues and organs in the human body
Define a cell.
The smallest structural and operational unit of an organism is a cell. Although it is often tiny, macroscopic cells can also exist. Your body's basic building blocks are these cells, which are present in many different forms.
A tissue is made up of a collection of comparable cells and the connective tissue that binds them together to serve a common purpose. An organ is a collection of tissues found in an organism that cooperate to carry out a specific task. The lungs, kidneys, and stomach are a few examples. The bronchi, bronchioles, and alveoli all work together to assist the lungs exchange oxygen and carbon dioxide from the blood.
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at a stoplight, a truck traveling at 15 m/s passes a car as it starts from rest. the truck travels at constant velocity and the car accelerates at 3 m/s2. how much time does the car take to catch up to the truck?
The time taken by the car to overtake the the truck is found to be 10 seconds.
The car starts from rest and accelerate at the rate of 3m/s². The truck passes the car on the spotlight and it is travelling at a speed of 15m/s.
We know,
S = ut + 1/2at²
Where,
u is initial speed,
tis the time,
a is acceleration.
Also,
constant speed = dstance/time.
To overtake,
Distance covered by car = distance covered by the truck
So,
1/2at² = 15t
1/2at = 15
Putting a =3m/s²
1/2(3)t = 15
t = 10 seconds.
So, the time taken by the car to overtake is 10 seconds.
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7. Inferring Suppose you plot the distance
traveled by an object at various times and
you discover that the graph is not a straight
line. What does this indicate about the
object's acceleration?
When the graph of distance travelled with time is not straight, it implies that the acceleration is constant.
What is the acceleration of an object?The acceleration of an object is the rate of change of velocity with time.
Mathematically, the formula for the acceleration of an object is given as;
a = Δv / Δt
where;
Δv is the change in velocity of the objectΔt is the change in time of motionThe slope of velocity time graph is acceleration. This implies that acceleration increases with increase in velocity of an object.
However, if the graph of the distance travelled by an object with time is straight, it implies that the velocity is not uniform.
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A box has a mass of 45,620 grams. How much force would you need to push the box to accelerate it 5 m/s2?
Taking into account the Newton's second law, the force needed to push the box to accelerate it 5 m/s² is 228.1 N.
Definition of Newton's second lawAcceleration in a body occurs when a force acts on a body. There are two factors that influence the acceleration of an object: the net force acting on it and the mass of the body.
Newton's second law defines the relationship between force and acceleration. This law says that the acceleration of an object is directly proportional to the sum of all the forces acting on it and inversely proportional to the mass of the object.
Mathematically, Newton's second law states that force is the multiplication of mass and acceleration:
F= m×a
where:
F = Force [N]m = Mass [kg]a = Acceleration [m/s²]Force needed in this caseIn this case, you know:
F= ?m= 45620 grams= 45.62 kg (being 1000 g= 1 kg)a= 5 m/s²Replacing in the definition of Newton's second law:
F= 45.62 kg× 5 m/s²
Solving:
F= 228.1 N
Finally, the force needed is 228.1 N.
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when an object reaches terminal velocity its acceleration is
When an object reaches terminal velocity its acceleration becomes zero.
Terminal velocity is also called constant velocity. When there is no acceleration in the moving object. We can take the example of sedimentation.
Sedimentation is the process of settling down the soil particles at the bottom of the water. When soil particles comes down in water there are three forces which act on the particles. Downward force is weight of the particle. Upward force buoyant force of the water, and drag force. When upward forces become equal to the downward force then particles begins to settle down with a constant velocity. which is called terminal velocity.
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a thermometer is taken from a room where the temperature is to the outdoors, where the temperature is . after one minute the thermometer reads . (a) what will the reading on the thermometer be after more minutes?
The reading on the thermometer after more minutes will depend on the rate at which the temperature of the room and the outdoors change.
What is thermometer?A thermometer is a device used for measuring temperature. It consists of a hollow tube made of glass that is filled with a liquid, such as mercury or alcohol, and a scale. When the temperature changes, the liquid expands or contracts, causing the scale to indicate the temperature.
If the temperature of the room and the outdoors remain relatively constant, then the reading on the thermometer after more minutes would likely be the same as the reading after one minute. However, if the temperature of the room or the outdoors changes faster than the other, then the reading on the thermometer after more minutes will be different from the reading after one minute.
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in what region is the electric field strongest? in what region is the electric field strongest? along the x axis between x
The nearest point to a charged item or the position of a point charge has the greatest electric field. As the distance from the charge grows, the electric field's intensity diminishes.
A force field called an electric field is produced when one electric charge interacts with other charges in the field and either attracts or repels them. The volts per metre (V/m) unit of measurement for the electric field is the letter E. It may be seen as a charge producing lines of force. A positive test charge would be pushed towards the direction of the electric field at a specific spot if it were to be placed there. The strength of the electric field is highest when the lines are close together and weakest when they are far apart.
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How is the electrostatic force (Felect) related to the separation distance (d) the two charges? Keeping the magnitude of charge on both objects constant, conduct a systematic study to collect data relating separation distance to force. The separation distance is defined as the distance between the centers of the two objects; the best strategy involves centering the objects on a gridline and using distances that are a whole number of squares.
Make a claim describing the relationship between Felect and d. Support your claim with evidence (references to the data) and reasoning
Allow two positive charges. Cuban and American two were distantly separated B. Cubans also use force against one another. This is also cute. Thus, the force will be equal to Q1 + Q2 + R^2.
More on electrostatic force and two charges :A characteristic of matter that affects how much force an object experiences when exposed to an electromagnetic field. A substance's charge might be positive, negative, or neutral. Total electric charge is conserved and cannot be created or destroyed, much as energy and matter.
Coulomb's constant, often known as the electric force constant, has a value of
K= [tex]\begin{equation*} 9\times10^9 \end{equation*}[/tex] [tex]\begin{equation*} \frac{Nm^2}{C^2} \end{equation*}[/tex]
Electrostatic force formula
[tex]\begin{equation*} \left|F_{E} \right|=K\left|\frac{q_1q_2}{r^2}\right| \end{equation*}[/tex]
[tex]F_{E}[/tex] is a electric force [tex]q_{1}[/tex] and [tex]q_{2}[/tex] is electric charge in coulomb K is constant, r is the distance between the charges
The magnitude of the electric force between [tex]q_{1}[/tex] and [tex]q_{2}[/tex]
Directly proportional to the size of the charges and inversely proportional to the square of the distance between them is the formula q, start subscript, 2, end subscript. The name of this equation is Coulomb's Law.
Comparing electric force and gravitational force with Newton's law of gravitation:
[tex]\begin{equation*} \left|F_E\right|=K\left|\frac{q_1q_2}{r^2}\right| \end{equation*}[/tex]
[tex]\begin{equation*} \left|F_G\right|=K\left|\frac{q_1q_2}{r^2}\right| \end{equation*}[/tex]
Similar to how gravitational force grows in strength with mass, electric force grows in strength with the size of the charges. Along the fictitious line connecting the items, both forces operate. The inverse-square law states that both forces are inversely proportional to the square of the distance between the objects. Additionally, both forces have constants of proportionality.
The relative intensities of gravitational and electric forces, which are determined by the ratio of K to G, are a disparity between them. The gravitational force between an electron and a proton is much smaller than the electrostatic force between them by several orders of magnitude.
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a bullet penetrates 7 cm into a piece of wood when fired at a speed of 33 m/s. find the time required for the bullet to stop.
When fired at 33 m/s, a bullet pierce a wood block by 7 cm. Find the rate of deceleration and the stopping time.
How is the target penetrated by a bullet?EXPLANATION: Due to its great velocity, a bullet discharged from a gun has a very high kinetic energy. The bullet's kinetic energy affects the object it impacts or strikes. The enormous kinetic energy the bullet possesses as a result of its speed causes it to pierce its target.
Does a gunshot go through the body?In addition to piercing tissue, bullets that enter a human body also break a bone and dislocate limbs. In addition to piercing tissue, bullets that enter a human body also break a bone and dislocate limbs. A colostomy life-long bag is possible in the event of an intestinal damage.
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b On the Moon, the lunar module has a weight of 24 800 N
Calculate the Moon's gravitational field strength.
Give your answer correct to two significant figures.
N/kg
As we do not have the mass we can not give you the gravitational field strength, but you can find it out by measuring the mass of the lunar module and use the formula above.
What is the gravitational field?Generally, To calculate the gravitational field strength on the Moon, we need to divide the weight of the lunar module (in newtons) by its mass (in kilograms).
We do not have the mass of the lunar module, however we know that the weight is equal to the force of gravity acting on it. The weight is force, which is measured in newtons.
Weight = Mass * gravitational field strength (g)
g = Weight / Mass
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CQ not found
a transverse wave travels along a rope describe how the particles of the Rope move relative to the direction of propagation of the wave
The wave itself, that is, the crests and troughs, will move along the direction of propagation, but the particles themselves will only move perpendicularly to it.
How does a transverse wave rope move?
A wave in which the displacement of the medium's particles is perpendicular to the direction of energy transfer is called a transverse wave. If a rope is stretched out horizontally and the end is vibrated back and forth vertically, a transverse wave can be produced in the rope.
Transverse wave propagation is only feasible via solids; it is not possible in liquids or gases. Only transverse waves can display the polarization phenomena. The plane of vibration or polarization is the location where all of the particle vibration in a medium occurs. Shaking the rope causes the rope's constituent parts to oscillate, which causes the wave to advance or retreat from the energy source. The rope moves at a straight angle—or perpendicular—to the direction that the wave moves.
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for serial weight measurements, what time of day would you instruct the person to have his or her weight measured?
Answer: approximately the same time of day
Explanation:
a 1,200 kg car is traveling at 10 m/s. what is the minimum distance at which an automatic braking system needs to activate to avoid hitting a stationary object? (note: the braking system can decelerate the car at 2 m/s2.) a. 2.5 m b. 5.0 m c. 25 m d. 50 m
The minimum distance at which an automatic braking system needs to activate to avoid hitting a stationary object is 2.5 meter. The correct answer is a.
To calculate this, we can use the equation:
distance = initial velocity² / (2 × deceleration).
In this case, the initial velocity is 10 m/s and the deceleration is 2 m/s². Plugging these values into the equation gives us:
distance = 10² / (2 × 2)
distance = 25 meter
Since the car's speed is slowing down at a rate of 2m/s², the car will need 25 meter distance to come to a complete stop. However, the question asked for the minimum distance at which the automatic braking system needs to activate, therefore the minimum distance at which the automatic braking system needs to activate is 10% of the stopping distance which is:
10/100 × 25 = 2.5 meter
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When a charged balloon sticks to a wall the downward gravitational force is balanced by an upward static friction force. The normal force is provided by the electrical attraction between the charged balloon and the equal but opposite charged polarization induced in the walls molecules. If the mass of the balloon is 1. 4g it's coefficient of static friction with the wall is. 73 and the average distance between the opposite charges is. 75mm what minimum amount of charge must be placed on the balloon in order for it to stick to the wall
The balloon needs to be charged with a minimum of 1.3 x 10-10 Coulombs for it to adhere to the wall.
To find the minimum amount of charge required on the balloon for it to stick to the wall, we can use the following equation:
Friction force = friction coefficient x normal force
The electrical attraction between the charged balloon and the molecules of the wall, which cause an equal but opposing charged polarization, produces the normal force and may be computed as follows:
Normal force = k x q1 x q2 / r^2
where k is Coulomb's constant, q1 and q2 are the charges on the balloon and the wall's molecules, respectively, and r is the average distance between the opposite charges.
The gravitational force acting on the balloon is given by:
Fg = m x g
Since the downward gravitational force is balanced by the upward static friction force, we can set the gravitational force equal to the friction force:
m x g = friction coefficient x k x q1 x q2 / r^2
Solving for q1, the charge on the balloon, we have:
q1 = (m x g x r^2) / (friction coefficient x k x q2)
Given that the mass of the balloon is 1.4 g, coefficient of static friction with the wall is 0.73, the average distance between the opposite charges is 0.75mm, and Coulomb's constant is 910^9 Nm^2/C^2.
q1 = (1.4 x 9.8 x (0.75 x 10^-3)^2) / (0.73 x 9 x 10^9)
The minimum amount of charge required on the balloon in order for it to stick to the wall is 1.3*10^-10 Coulombs
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An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 1450 kg. When that occupant drops a coin, the tension in the cable is 12. 0 kN. What is the acceleration of the coin relative to the cab
The cable will be under 12.0 KN of tension when that person drops a coin. Then the acceleration of the coin relative to the cab is 0.00828 m/s^2.
To find the acceleration of the coin relative to the cab, we can use the equation for tension force:
Tension force = mass x acceleration
We are given the tension force (12.0 kN) and the combined mass of the cab and its occupant (1450 kg). Therefore, we can solve for acceleration:
12.0 kN = (1450 kg) x acceleration
acceleration = 12.0 kN / (1450 kg)
acceleration = 0.00828 m/s^2
So the acceleration of the coin relative to the cab is 0.00828 m/s^2
It is worth noting that the coin will fall with respect to the elevator with an acceleration of 9.8 m/s^2 (upwards) but relative to the elevator, the coin is accelerating downwards with 9.8 m/s^2 + 0.00828 m/s^2 = 9.80828 m/s^2.
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Jack and Jill ran up the hill at 3.0 m/s . The horizontal component of Jill's velocity vector was 2.3 m/s .
what was the angle of the hill
What was the vertical of Jill's velocity
(a) The angle of the hill is 40⁰
(b) The vertical of Jill's velocity is 1.93 m/s.
What is the angle of the hill?
The angle of the hill is calculated by applying the following kinematic equation as shown below.
Vₓ = V cosθ
where;
V is the velocity of JilVₓ is the horizontal component velocityθ is the angle of the hillcosθ = Vₓ / V
θ = arc cos (Vₓ / V)
θ = arc cos (2.3 / 3)
θ = 40⁰
The vertical component of the velocity is calculated as follows;
Vy = 3 m/s x sin (40)
Vy = 1.93 m/s
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two equally charged particles are held 3.2x10-3 m apart and then released from rest. the initial acceleration of the first particle is observed to be 7.0 m/s2 and that of the second to be 9.0m/s2 . if the mass of the first particle is 6.3 x 10-7 kg, what are (a) the mass of the second particle and (b) the magnitude
The mass and magnitude of the second particle are calculated below.
The initial velocity of an object is its velocity prior to the effect of acceleration, which causes the change. The velocity will be the final velocity after accelerating the object for some time. When a particle moves at a constant speed, it can be accelerated. When a point object moves in a horizontal circular path at a constant speed, the direction of its velocity vector changes over time. It means that in a uniform circular motion, the object's velocity vector changes over time.
Distance between the charges, r = 3.2 × [tex]10^{-3}[/tex]m
initial acceleration of first particle, [tex]a_{1}[/tex] = 7m / [tex]s^{2}[/tex]
Initial acceleration of second particle, [tex]a_{2}[/tex] = 9.0m / [tex]s^{2}[/tex]
Mass of first particle, [tex]m_{1}[/tex] = 6.3 × [tex]10^{-7}[/tex]kg
Mas of second particle, m₂ = ?
a) Since, [tex]F_{1}=F_{2}[/tex]
∴ [tex]m_{1}a_{1} = m_{2}a_{2}[/tex]
mass of second particle-[tex]m_{2}[/tex] =[tex]\frac{m_{1}\times a_{1}}{a_{2}}[/tex]
= [tex]\frac{6.3\times10^{-7}\times7.0}{9.0}[/tex]
=4.9 × [tex]10^{-7}[/tex]Kg
b)As, [tex]F_{1} = F_{2}[/tex]
= [tex]\frac{q_{1}q_{2}}{4\pi E_{0}r^{2}}[/tex] = [tex]m_{1}a_{1}[/tex]
= 6.3 × [tex]10^{-7} \times[/tex] 7.0
= 44.1 × [tex]10^{-7}[/tex]
∴ q = 7.1 × [tex]10^{-11}[/tex]C.
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An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0. 0 degrees Celsius and rejects heat to a room at a temperature of 19. 2 degrees Celsius. Suppose that liquid water with a mass of 76. 3kg at 0. 0 degrees Celsius is converted to ice at the same temperature. Take the heat of fusion for water to be L_f = 3. 34*10^5 J/kg.
How much energy E must be supplied to the device?
Express your answer in joules
The energy E must be supplied to the device is 1.8x10^3kJ when an ice-making machine inside a refrigerator operates in a Carnot cycle.
Given the temperature initially (Tl) = 0degrees Celsius = 273K
The final temperature (Tc) = 19.2degrees Celsius = 273 + 19.2 = 292.2K
Mass of liquid water (m) = 76.3kg
The water is converted to ice at 0 degrees Celsius
The heat of fusion for water to be Lf = 3.34*10^5 J/kg.
Let heat released from ice = Qc
Heat absorbed by water = Ql
We know that Ql = mLf = 76.3 x 3.34*10^5 = 2.54*10^4kJ
Then Qc/Ql = -Tc/Tl
Qc = - 254.842*10^5 (292.2/273)
Qc = -2.72x10^4kJ
The heat being lost to the hot reservoir is the cause of the negative sign.
We know that Ql = Qc + W where W is the work done
W = Qc - Ql = 2.54*10^4kJ - 2.72x10^4kJ
W = 1.8x10^3kJ
Hence the energy E that must be supplied to the device is 1.8x10^3kJ
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