The height of cliff is 99.225 m.
The initial speed of rock is 0, it starts from rest.
The time taken is 4.5 seconds.
The acceleration is -g, as the rock is freely falling.
Distance travelled by the rock is the height of the cliff.
Using second law of Newton,
s= ut + 0.5 a t²
where s is the distance,
u is the initial speed,
a is the acceleration,
and t is the time.
s = 0 + 0.5(9.8)(4.5)(4.5)
s = 99.225 m
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the mass of a subway car and passengers is 34,800 kg. if its acceleration as it leaves a station is 0.8 m/s2, what is the net force (in n) acting on it? (enter the magnitude.)
The net force acting on the subway car and passengers can be calculated using Newton's second law of motion:
F = ma = 34,800 kg * 0.8 m/s^2 = 27,840 N.
So the net force is 27,840 N, or 27,840 N in magnitude.
What is the acceleration of the subway car as it leaves the station?The acceleration of the subway car as it leaves the station is 0.8 m/s2. This means that every second, the subway car's velocity is increasing by 0.8 meters per second. The acceleration is a measure of how quickly the speed of an object changes and it plays an important role in determining the net force acting on the subway car and passengers. The net force is the force that drives the subway car forward and it is calculated by multiplying the mass of the subway car and passengers by the acceleration.
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A 2270kg elephant climbs a pedestal 1.2m high during a circus act. What is the elephant's potential energy
The formula for potential energy is:
PE = mgh
Where:
m = mass of the object (in kilograms)
g = acceleration due to gravity (9.8 m/[tex]s^{2}[/tex])
h = height above a reference point (in meters)
So for the elephant:
PE = 2270 kg × 9.8 m/[tex]s^{2}[/tex] × 1.2 m
PE = 27424 kg [tex]m^{2}[/tex]/[tex]s^{2}[/tex]
The elephant's potential energy is 27,424 kg [tex]m^{2}[/tex]/[tex]s^{2}[/tex].
What is potential energy?A form of energy stored in an object as a result of its position or state is called potential energy. It is determined using the object's mass, height, and gravitational force. It is the energy that an object holds due to its height, position, or tension. A stretched rubber band has potential energy because of the strain within it, whereas a rock placed at the peak of a cliff has potential energy because of its height. When the object is released or changes state, the potential energy can be converted into kinetic energy, which is the energy of motion.
Potential energy (PE) can be calculated using the formula PE = mgh.
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an object has a charge of 1 coulomb. how many excess charges does it contain? group of answer choices 6.023 x 1023 insufficient information avogrado number of charges
An object has a charge of 1 coulomb and excess charges that it contains is 6.25 x 10¹⁸.
How many excess charges does a charge of 1 coulomb contain?To illustrate the magnitude of 1 Coulomb, object would need an excess of 6.25 x 10¹⁸ electrons to have total charge of -1 C. An object with a shortage of 6.25 x 10¹⁸ electrons would have total charge of +1 C and the charge on single electron is -1.6 x 10⁻¹⁹ Coulomb.
Charge q on a body must always exist as an integral multiple of fundamental unit charge e, charge of an electron, where e=1.6×10⁻¹⁹C.
Thus, for 1 coulomb of charge the body will hold 1/1.6×10⁻¹⁹
=6.25×10¹⁸ electrons.
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consider a copper rod that is 3.14 meters long, 2 cm in diameter, and has an electrical resistivity of 2x10-6 ohm-cm. what is the electrical resistance of the rod?
Resistance is denoted by the Greek symbol omega (), which also stands for the ohm, the unit of measurement. The formula states that R Equals L / A.
What does a metal's electrical resistance mean?The difference in electric potential increases with increasing current. In contrast, a high electric resistance will result in a low current. Alternatively put, a metal with low resistance is a superior conductor. Electrons in the metal are slowed down if there is an electric resistance.
How is resistance determined?By applying Ohm's Law, you can get the total resistance if you know the complete current and voltage through the entire circuit: R = One against / I. A parallel circuit, for instance, has a supply of 9 volts and a combined power of 3 amps. Total resistance (RT) is equal to 9 volts / 3 amps, or 3.
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assume the trajectory featured in figure 4.6b (p. 84 of text and reproduced below) is of a ball thrown near the surface of the earth, and the y axis points vertically upward. is the ball only under the influence of gravity?
Assuming that the ball is thrown near the surface of the Earth and the y-axis points vertically upward, then the ball is certainly under the influence of gravity.
Gravity is a force that acts on all objects with mass, and it causes objects to accelerate toward the center of the Earth. When a ball is thrown near the surface of the Earth, it experiences a downward force due to gravity that causes it to follow a parabolic trajectory.
However, other forces could also be acting on the ball depending on the specific situation. For example, if the ball is being thrown horizontally, it will experience air resistance or drag, which could affect its trajectory.
If the ball is being thrown at an angle, it will experience a combination of horizontal and vertical forces, and the trajectory will depend on the relative magnitudes and directions of those forces.In summary, while the ball is definitely under the influence of gravity, other forces could also be at play depending on the specifics of the situation.
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if a block is moving to the left at a constant velocity, what can one conclude?
Answer:
I will continue to go left untill forces such as gravity and friction act uppon it.
Explanation:
which ball (if either) has the greatest speed at the moment of impact? view available hint(s)for part a which ball (if either) has the greatest speed at the moment of impact? the ball thrown horizontally the dropped ball both balls have the same speed.
Therefore, both balls will have the same vertical speed at the moment of impact, which is the sum of their vertical and horizontal speeds.
What is moment of impact?In physics, a collision is the abrupt, powerful coming together of two bodies, such as two billiard balls, a golf club and a ball, a hammer and a nail head, two train carriages when paired together, or a falling item and a floor. Its formula equates the product of a body's mass and velocity to twice the time taken. The force created when two objects collide is known as the force of impact. The stronger the impact or hitting power of your vehicle, the faster you drive. The force of impact rises with the square of the increase in speed, according to physical rules.
Here,
Both balls have the same speed at the moment of impact. The vertical speed of the dropped ball is determined solely by its initial height and the acceleration due to gravity. The horizontal speed of the ball thrown horizontally is constant and does not change.
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when switching from a lower power objective to a higher power objective on a bright-field microscope, what happens to the amount of light that reaches the eye
When switching from a lower power objective to a higher power objective on a bright-field microscope : amount of light decreases. Higher power objective has smaller lens and so less light penetrates.
What is bright-field microscope?Bright-field microscopy is the simplest of all optical microscopy illumination techniques and sample illumination is transmitted white light, and contrast in sample is caused by attenuation of transmitted light in dense areas of sample.
Its simplicity makes it a popular technique. Appearance of bright-field microscopy image is dark sample on bright background. Light path of a bright-field microscope is extremely simple and no additional components are required beyond normal light-microscope setup.
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insulating spheres a and b are initially neutral and touching. a positively charged rod is brought near a, but not touching. the spheres are separated, and then the rod is taken away. describe the resulting net charge of each sphere.
The electrons in the spheres pull away from the rod's electrons and gather to the right. As a result, the left sphere begins to accrue a positive charge.
The rod and the two spheres are then separated. The left sphere finally reaches positive charge, while the right sphere reaches negative charge.
What distinguishes a conducting sphere from an insulating sphere?A charge is carried by an insulating sphere and is distributed evenly across its volume. The charge on a conducting sphere of the same size is the same, but it is only distributed across its surface (as it must for a conductor.)
V=ar2+b, where a and b are constants, describes how the electric potential within a charged sphere changes with distance from its center. the sphere's interior space charge distribution (r).
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a mass of 5 kg initially hangs from a pulley by a rope. the pulley itself has a mass of 20 kg and a radius of 0.5 m. if this system is released from rest, you observe the mass falls downward and the pulley rotates clockwise. what will be the angular acceleration of the pulley in rad/s2?
The angular acceleration of the pulley can be determined by considering the forces acting on the system and the moment of inertia of the pulley. Based on the task, the angular acceleration of the pulley is 2.45 rad/[tex]s^{2}[/tex].
The angular acceleration of the pulley can be determined by considering the forces acting on the system and the moment of inertia of the pulley. The net force acting on the system is given by the weight of the hanging mass, which creates a tension in the rope that is transferred to the pulley. The tension in the rope produces a torque on the pulley, given by:
The tension in the rope produces a torque on the pulley, given by:
τ = T * r
where,
T = the tension in the rope
r = the radius of the pulley.
The net torque on the pulley can be used to determine its angular acceleration, given by:
α = τ / I
where,
I is the moment of inertia of the pulley, given by:
I = (1/2) * m * [tex]r^{2}[/tex] + m * [tex]r^{2}[/tex]
where m is the mass of the pulley.
Substituting the values, we get:
α = (T * r) / ((1/2) * m * [tex]r^{2}[/tex] + m * [tex]r^{2}[/tex])
= (5 * 9.8 * 0.5) / ((1/2) * 20 * [tex]0.5^{2}[/tex] + 20 * [tex]0.5^{2}[/tex])
= 49 / 20
= 2.45 rad/[tex]s^{2}[/tex]
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what resonant frequency would you expect from blowing across the top of an empty soda bottle that is 19 cm deep, if you assumed it was a closed tube?
The resonant frequency of a 19 cm deep soda bottle, if it were a closed tube, would be approximately 1798 Hz.
The resonant frequency of an air column in a closed tube can be calculated using the formula:
f = (v / 2L) * n
where:
v is the speed of sound in air (about 340 m/s)
L is the length of the air column
n is an integer representing the harmonic number (the first harmonic would be n=1, the second n=2, etc.)
For a 19 cm deep soda bottle, the length of the air column is half the length of the bottle, or L = 0.19 / 2 = 0.095 meters.
Using the formula, the first harmonic resonant frequency can be calculated as follows:
f = (340 / (2 * 0.095)) * 1 = 1798 Hz
So, the first resonant frequency of a 19 cm deep soda bottle, if it were a closed tube, would be approximately 1798 Hz.
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At what temperature does water freeze in each scale?
Water freezes at 32 degrees Fahrenheit, 0 degrees Celsius, and 273.15 Kelvin, as we have all been taught.
What range of temperatures does water freeze at?Due to the salt in seawater, it freezes at a lower temperature than fresh water—approximately 28.4 degrees Fahrenheit. However, because only the water part of seawater freezes, a very little salt is present in the ice when it is formed.
At what scale of temperatures does water freeze at 273 degrees?The Kelvin scale, which measures temperatures in Kelvin, is frequently used by scientists, particularly those who investigate what happens to things when they get extremely cold (K). The steps on this scale are the same as those on the Celsius scale, however, they are moved downward. Water freezes at 273 K and boils at 373 K on this scale.
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Protocells are precursors to modern living cells. Despite being non-living matter, protocells exhibit some characteristics of life such as reproduction. However, protocells were unable to inherit traits. Why is this so?
The reason why protocells were unable to inherit traits is because they lack genetic material.
What are protocells ?Protocells are considered precursors to modern living cells because they exhibit some basic life-like properties, such as replication. However, protocells lack a key component of living cells, which is the genetic material in the form of DNA or RNA.
Protocells are unable to inherit traits because they lack genetic material. The absence of genetic material means that protocells cannot encode information or pass it on to their offspring, so they cannot produce the proteins necessary for metabolic functions or replicate themselves in a controlled manner.
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suppose a car travels 109 km at a speed of 25.0 m/s, and uses 2.0 gal of gasoline. only 28% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (see table 7.1 for the energy content of gasoline.) what is the force exerted to keep the car moving at constant speed?
The force exerted to keep the car moving at constant speed is 7.179 x 10^-6 N.
The car is travelling at the velocity 25.0 m/s and it travelled 109 km by using 2.0 gal of gasoline. First we need to find the energy consumed.
2.0 gallons = 2 x 3.785 liters/gallon = 7.57 liters of gasoline.
The total energy of this much gasoline will be = 7.57 liters x 34.0 MJ/liter = 256.38 MJ.
28% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. i.e. 256.38 MJ x 28% = 71.79 MJ.
The distance travelled is 109 km. i.e. 109 km x 1000 m/s = 10^9 m.
Now to get the force, divide the energy used by the distance traveled, which is equal to 71.79 MJ / 10^9 m = 7.179 x 10^-6 N.
The force exerted to keep the car moving at constant speed is 7.179 x 10^-6 N.
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Whenever the net force on an object is zero, its acceleration _____.(a) and velocity are the same(b) is zero(c) may be zero(d) None of the above.
Whenever the net force on an object is zero, its acceleration is zero. This means that the object is either at time-out or moving at a constant velocity. If the object was initially at rest, it will remain at rest.
What is the net force?The net force is the force acting on an object. It is the sum of all the individual forces acting on the object. Net force confines the acceleration of an object.
What if the net force is not zero?If the net force on an object is not zero, the object will experience an acceleration in the direction of the net force. The magnitude of the net force is equal to the mass of the object multiplied by its acceleration.
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if the particle has a constant horizontal velocity to the right, what is the direction of the acceleration of the particle?
The direction of acceleration of a particle is given by the direction of the change in velocity of the particle. If a particle has a constant horizontal velocity to the right, its velocity is not changing, and therefore its acceleration is zero.
Acceleration is a measure of the rate of change of velocity of an object over time. It is a vector quantity, meaning it has both magnitude and direction. In general, if an object's velocity changes, it is said to be accelerating, and the direction of acceleration is given by the direction of the change in velocity.
In physics, acceleration is defined as a vector quantity with units of meters per second squared (m/s^2), and it is often represented by the symbol "a". The acceleration vector points in the direction of the change in velocity, and its magnitude is given by the rate of change of velocity.
In the case of a particle with a constant horizontal velocity to the right, the velocity vector remains constant and unchanging, so the acceleration vector is zero. This means that there is no change in velocity, and no acceleration. The particle continues to move at a constant velocity to the right, without speeding up or slowing down.
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what is the grain fall or settling velocity? how is it determined? when does grain suspension occur?
The grain fall or settling velocity is the speed at which a single grain of sediment falls through a fluid under the influence of gravity. It is determined by the size, shape, and density of the grain, and the fluid properties such as temperature, viscosity, and fluid density.
Grain suspension occurs when the upward fluid velocity exceeds the settling velocity of the grain, causing the grain to remain suspended in the fluid and not settle to the bottom. This can occur in a variety of natural systems, such as rivers and oceans, and is an important factor in the transport of sediment in these systems.
About GravityGravity is one type of force that is affected by the force of attraction of an object to the center of the object. Therefore the notion of the gravitational force of the earth is the pulling force of an object towards the center of the earth. The force of gravity is very important for living things, including humans. We certainly cannot live on Earth without gravity. Reporting from NASA, the force of gravity keeps the Earth orbiting the Sun so that all living things can enjoy the sun's light from a comfortable distance.
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onsider a solid cylindrical rod whose ends are maintained at constant but different temperatures while the side surface is perfectly insulated. there is no heat generation. it is claimed that the temperature along the axis of the rod varies linearly during steady heat conduction. is this claim reasonable?
Yes, the claim is reasonable. In steady-state heat conduction, the temperature distribution in a solid cylindrical rod with constant temperature boundary conditions and insulated side surface will indeed be linear along the axis. This is because heat is conducted through the rod by diffusion and the rate of heat flow is proportional to the temperature gradient. In a cylinder, the temperature gradient is maximum at the boundaries and zero at the center, leading to a linear temperature distribution.
About TemperatureTemperature, or temperature is a measure of the level or degree of heat on an object. Temperature shows the level of the amount of heat energy that is in the object. Discussion: The higher the temperature of an object, the hotter it is, and the more heat energy in that object.
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Which explanation is based on scientific evidence
The evidence that supports or counters a scientific hypothesis or theory is called scientific evidence.
What is scientific evidence?Although scientists frequently utilize evidence in other ways, such as when applying ideas to real-world issues, scientific evidence is evidence that helps to either support or refute a scientific theory or hypothesis.
Such proof is anticipated to be empirical and interpretable using scientific techniques. The requirements for scientific evidence vary depending on the area of study, but they are often based on the outcomes of statistical analysis and the quality of scientific controls.
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raindrops fall 1700 m from a cloud to the ground. (a) if they were not slowed by air resistance, how fast would the drops be moving when they struck the ground? (b) would it be safe to walk outside during a rainstorm? compare the putative speed of the raindrops to the speed of a bullet traveling at 3x the speed of sound. (bonus: what happens in reality?)
(a) The raindrops would be moving at a speed of approximately 40.3 m/s if they were not slowed by air resistance.
(b) It would not be safe to walk outside during a rainstorm as the raindrops would be moving at a very high speed, much faster than a bullet traveling at 3x the speed of sound.
(Bonus) In reality, the raindrops are slowed by air resistance and their speed decreases as they fall to the ground, so the actual speed is much lower than the calculated value.
How does the speed of the raindrops compare to the speed of a bullet traveling at 3x the speed of sound?The speed of the raindrops without air resistance is much slower than a bullet traveling at 3x the speed of sound. A bullet traveling at 3x the speed of sound has a velocity of approximately 944 m/s, whereas raindrops without air resistance would have a velocity of approximately 50 m/s when they reach the ground. This significant difference in speed makes it clear that it would not be safe to walk outside during a rainstorm if the raindrops were not slowed by air resistance.
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g a motorboat is heading straight across a river (the boat points its bow straight towards the other side). due to the river's current, it will not reach the shore directly across from its starting point. the motorboat moves at a velocity of 4 m/s directly across the river (east), and the river moves at a velocity of 3 m/s (north). what is the resultant angle of the motorboat's direction of motion, relative to a line drawn directly across the river?
In relation to a line drawn exactly across the river, the angle at which the motorboat is moving, as a result, is 53.1°.
According to the question;
Finding the resulting angle between the motorboat's motion direction and a line drawn directly across the river is the solution to the problem.
The motorboat's speed may be represented by the vector (v₁) = 4 m/s in the east
The river's speed by the vector (v₂) = 3 m/s in the north.
The motorboat's final speed is determined by adding these two speeds together:
v = v₁ + v₂.
v = (3 m/s)j + (4 m/s)i
The inverse of the tangent function may be used to calculate the angle θ between the direction of the resulting velocity and a straight line across the river:
θ = tan^-1 (v₂/v₁) = tan^-1 (3/4)
⇒ θ = 0.93 radians or 53.1°
Therefore, the motorboat's direction of travel is at an angle of 53.1° with respect to a line that is drawn immediately across the river.
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a car starts from rest at a stop sign. it accelerates at 3.47 m/s2 for 5.89 seconds, coasts for 2.61 s, and then slows down at a rate of 2.18 m/s2 for the next stop sign. how far apart are the stop signs?
The distance apart are the stop signs is found to be 208.78m
What is the length of the motion?The length of the maintains close an object's starting point and its destinations dictates how far it travels. Distance is the amount of time that an object moves over time. A force is applied to an item, and the more force is applied, the farther the thing will move.
The initial velocity =0
[tex]t_1= 5.89s ; a_1 = 3.47m/s^2\\\\t_2 = 2.61s ; a_2 =0\\a_3 = -2.18m/s^2[/tex]
d1 =
[tex]ut1 + 1/2a_1\times t_1^2 ;\\ u=0 = 1/2 x 3.47 x 5.89^2 = 60.1m[/tex]
v1 =
[tex]u + a_1\timest_1 = 0 + 3.47 \times 5.89 \\= 20.4m/s[/tex]
d2
[tex]= > v_1t_2 + 1/2a2t_2^2 = 20.4 \times 2.61 + 1/2 \times 0 \times t2^2 = 53.24m[/tex]
[tex]v_f = v_1 + a_3t_3[/tex]
=0 = 20.4 + (-2.18) x t3
[tex]t_3= 9.35[/tex]
d3
[tex]20.4 \times 9.35 -1/2 \times 2.18 \times 9.35^2 = 95.44m[/tex]
The distance between two stop is
[tex]d1+ d2+d3 = 60.1+ 53.24+95.44 \\ 208.78m[/tex]
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if you are looking down over the north pole of the earth, you will see the earth rotate to___
The Earth revolves counterclockwise, and if we were to gaze down on it from just above north pole, we would notice that day and night move over our planet from east to west.
Which direction is Earth rotating when viewed from the North Pole?The Earth is moving counterclockwise, toward west to east, when seen from above the North Pole. The prograde rotation is another name for this. We observe the sun rising in the eastern and sinking in the west every day as a result of this path of revolution.
According to the South Pole, which way does the Earth spin?Earth would look to be turning counterclockwise if you were floating above the earth and gazing directly down there at North Pole. When gazing up so at South Pole from below the Earth, you would say that the rotation is clockwise.
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(a) what is the magnitude of the average acceleration of a skier who, starting from rest, reaches a speed of 12.0 m/s when going down a slope for 3.98 s? (b) how far does the skier travel in this time?
The magnitude of the average acceleration of the skier is 3.10 m/s²
The total distance traveled by the skier from the rest is 24.55 m
The initial velocity of the skier = 0 m/s
The final velocity of the skier = 12 m/s
The time taken to reach the slope = 3.98 seconds
The magnitude of the acceleration can be found using the formula,
a = (v - u) / t
where a is the acceleration
v is the final velocity
u is the initial velocity
t is the total time taken
Let us substitute the known values in the above equation, we get
a = 12 - 0 / 3.98
= 12/3.98
= 3.01 m/s²
The distance traveled by the skier can be found using the formula
s = ut + 0.5at²
= 0 x 3.98 + 0.5 x 3.10 x 3.98²
= 0.5 x 3.10 x 15.84
= 24.55 m
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a fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. the thrust of its engines is 1.80 105 n. in being launched from rest it moves through a distance of 87 m and has a kinetic energy of 4.30 107 j at lift-off. what is the work done on the jet by the catapult?
A fighter jet being launched from such an aircraft carrier using a steam-powered catapult and its own engines. Its engines produce 2.3 x 105 N of thrust.
What speed is reached when a jet fighter aircraft is fired from a slingshot on an aircraft carrier?
42 m/s On an aircraft carrier, a catapult is used to launch a jet fighter. Just at end of the sling, it takes 2 seconds to achieve velocity of 42 m/s. What is the catapult's length if the acceleration is constant?
How strong is the aircraft carrier's catapult?
Catapults A 48,000-pound aeroplane was launched 300 feet and increased in speed from 0 to 165 miles an hour in two seconds by four steam-powered catapults. On every
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John walks away from his house at a constant speed of 2 m/s for 10 seconds , he then remembers he lost his key and immediately runs back to his house at a speed of 4 m/s in 5 seconds
The acceleration of John during the entire motion is 1.2 m/s².
What is the acceleration of John?
The acceleration of John during the entire motion is calculated by applying the following formula as shown below.
a = Δv / Δt
where;
Δv is the change in velocityΔt is the change in time of motiona = ( v - u ) / ( t₂ - t₁ )
a = ( 4 m/s - - 2 m/s ) / ( 10 s - 5 s )
a = ( 6 m/s ) / ( 5 s )
a = 1.2 m/s²
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The complete question is below:
John walks away from his house at a constant speed of 2 m/s for 10 seconds , he then remembers he lost his key and immediately runs back to his house at a speed of 4 m/s in 5 seconds. find the average acceleration during the journey
what is the minimum cooking temperature for ground beef
The minimum internal cooking temperature for ground beef is 160°F (71°C) to ensure that harmful bacteria such as E. coli and Salmonella are destroyed.
At what temperature should ground beef be cooked?Ground beef should be cooked to an internal temperature of 160°F (71°C) as measured with a food thermometer to ensure that it is safe to eat. It is a versatile ingredient that can be used in a variety of dishes such as burgers, meatloaf, tacos, and spaghetti sauce
Why is it important to measure the temperature of beef?It is important to measure the temperature of ground beef in multiple places, especially for thicker cuts, to ensure that it is fully cooked and that harmful bacteria have been destroyed.
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if the energy of the (doubly charged) alpha nucleus was 5.1 mev, how close to the gold nucleus (79 protons) would it come before being deflected?
If the energy of the (double-charged) alpha nucleus is 5.1 MeV, then the gold nuclei (79 protons) before being deflected will be 4.55 x 10⁻¹⁴ m close together.
Alpha particles (named after the first letter of the Greek alphabet, α) are a highly ionizing, low-penetrating form of particle radiation. In the given problem:
Charge of alpha particle: q₁ = 2 x 1.6 x 10⁻¹⁹ CEnergy of alpha particle: KE = 5 x 10⁶ eV = 5 x 10⁶ x 1.6 x 10⁻¹⁹ JCharge of gold nucleus: q₂ = 79 x 1.6 x 10⁻¹⁹ CElectric force constant: k = 9 x 10⁹ N m²/C²KE = kq₁q₂/r
5 x 10⁶ x 1.6 x 10⁻¹⁹ = (9 x 10⁹)(2 x 1.6 x 10⁻¹⁹)(79 x 1.6 x 10⁻¹⁹)/r
r = (9 x 10⁹)(2 x 1.6 x 10⁻¹⁹)(79 x 1.6 x 10⁻¹⁹)/ 5 x 10⁶ x 1.6 x 10⁻¹⁹
r = 4.55 x 10⁻¹⁴ m
So, the distance of the gold core from the alpha particles before they are close together is 4.55 x 10⁻¹⁴ m.
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a hockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 3.0 cm before coming to a momentary stop. part a what will be the spring's maximum compression if the same puck hits it at a speed of 2v ? what will be the spring's maximum compression if the same puck hits it at a speed of 2? 3.0 cm 3.8 cm 6.0 cm 7.6 cm 10 cm
The spring's maximum compression if the same puck hits it at a speed of 2v will be 7.6 cm.
This is because the force of the impact is directly proportional to the puck's speed, so when the puck's speed doubles, the force of the impact doubles as well.
To calculate the spring's maximum compression, we can use the equation F = kx, where k is the spring constant, x is the maximum displacement, and F is the force of the impact.
Since we know the puck's speed (2v) and the maximum displacement (3 cm), we can solve for k to get k = F/x = (2v)/3. We can then use this value of k to calculate the maximum displacement at a speed of 2v, which is
x = F/k = (2v)/(2v/3) = 3*(2/3) = 2v.
Finally, we can multiply this value of x by 2 to get the spring's maximum compression for a speed of 2v, which is 7.6 cm.
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Can someone please explain in detail how to do this problem?
The gravitational force between the cars is 2.92 x 10⁻⁵ N.
What is the gravitational force between the cars?
The gravitational force between the cars is calculated by applying Newton's law of universal gravitation as shown below.
F = ( Gm₁m₂ ) / ( R² )
where;
G is universal gravitation constantm₁ is the mass of one carm₂ is the mass of the second carR is the distance between the carsF = ( 6.67 x 10⁻¹¹ x 2,565 x 4,264 ) / ( 5² )
F = 2.92 x 10⁻⁵ N
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