Before the development of quantum theory, Ernest Rutherford's experiments with gold atoms led him to propose the so-called Rutherford Model of atomic structure. The basic idea is that the nucleus of the atom is a very dense concentration of positive charge, and that negatively charged electrons orbit the nucleus in much the same manner as planets orbit a star. His experiments appeared to show that the average radius of an electron orbit around the gold nucleus must be about 10−1010−10 m. Stable gold has 79 protons and 118 neutrons in its nucleus.
What is the strength of the nucleus' electric field at the orbital radius of the electrons?
What is the kinetic energy of an electron in a circular orbit around the gold nucleus?
Answer:
a) F = -1.82 10⁻¹⁵ N, b) K = 9.1 10⁻¹⁶ J
Explanation:
a) To calculate the force between the nucleus and the electrons, let's use the Coulomb equation
F = k q Q / r²
as the nucleus occupies a very small volume compared to electrons, we can suppose it as punctual
let's calculate
F = 9 10⁹ (-1.6 10⁻¹⁹) (79 1.6 10⁻¹⁹) / (10⁻¹⁰)²
F = -1.82 10⁻¹⁵ N
b) they ask us for kinetic energy
let's use Newton's second law
F = m a
acceleration is centripetal
a = v² / r
we substitute
F = m v² / r
v = √ (F r / m)
v = √ (1.82 10⁻¹⁵ 10⁻¹⁰ / 9.1 10⁻³¹)
v = √ (0.2 10⁻¹⁶)
v = 0.447 10⁸ m / s
kinetic energy is
K = ½ m v²
K = ½ 9.1 10⁻³¹ (0.447 10⁸)²
K = 0.91 10⁻¹⁵ J
K = 9.1 10⁻¹⁶ J
re testing a new amusement park roller coaster with an empty car with a mass of 100 kg. One part of the track is a vertical loop with a radius of 12.0 m. At the bottom of the loop (point A) the car has a speed of 25.0 m/s and at the top of the loop (point B) it has speed of 8.00 m/s . You may want to review (Pages 203 - 212) . For related problemsolving tips and strategies, you may want to view a Video Tutor Solution of A vertical circle with friction. Part A As the car rolls from point A to point B, how much work is done by friction?
Answer:
-4530 J
Explanation:
Given that
Mass of the car, m = 100 kg
Speed of the car at point A, v1 = 25 m/s
Speed at point B, v2 = 8 m/s
Radius of the track, r = 12 m and with respect to the origin of the center of the track, we say that y1 = -12 at point A and y2 = 12 at point B
We also know that
W(total) = W(grav) + W(other) = K₂ - K₁
Work done by the gravitational force, W(grav) = -U(grav) = mgy1 - mgy2
Kinetic Energy, K = ½mv²
Adding all together, we have
½mv₁² + mgy1 + W(other) = ½mv₂² + mgy2
½ * 100 * 25² + 100 * 9.8 * -12 + W = ½ * 100 * 8² + 100 * 9.8 * 12
50 * 625 + 980 * -12 + W = 50 * 64 + 980 * 12
31250 - 11760 + W = 3200 + 11760
19490 + W = 14960
W = 14960 - 19490
W = -4530 J
Predict the magnitude of force applied on you if you push against a tree with a force of 50 and directed to the
Answer: -50N
Explanation:
Newton's 3rd law says that for every force applied, there is an opposite force with equal magnitude. The person pushing on the tree will experience a force of -50N
wheel and axle is also called a continuous lever
Explanation:
When load is connected to axle and effort is on the wheel it acts as first class lever with in fulcrum in the middle ..So wheel and axle is continuous lever
Pretty Easy question please answer only 20 minutes left:
A summary of the results of a scientific investigation is called a:
observation
research
hypothesis
conclusion
Answer:
D. Conclusion.
Explanation:
I need help with these 2 questions pls help
the measure of how many a wave passes on a certain point in a certain time is
frequency
A system of 18 electrons and 11 neutrons has a net charge of
Answer:
-28.8 × 10-19 C
An object starts from rest and accelerates at a rate of 4 m/s2 for 3 seconds. What is it's displacement from the start position?
Answer:
36m
Explanation:
a = 4 m/s^2
u = 0 ( it's starting from rest )
t = 3
a=v-u/t ....... 4=(v-0)/3, v = 12m/s
Using s=d/t,
12=d/3,
d= 36m
If an object starts from rest and accelerates at a rate of 4 m/s2 for 3 seconds, then its displacement from the start position would be 44.1 meters.
What are the three equations of motion?There are three equations of motion given by Newton
v = u + at
S = ut + 1/2 × a × t²
v² - u² = 2 × a × s
As given in the problem If an object starts from rest and accelerates at a rate of 4 m/s² for 3 seconds,
S = ut + 1/2 × a × t²
S = 0 + 0.5 × 9.8 × 3²
S = 44.1 meters
Thus, If an object starts from rest and accelerates at a rate of 4 m/s2 for 3 seconds, then its displacement from the start position would be 44.1 meters.,
To learn more about equations of motion here, refer to the link given below ;
brainly.com/question/5955789
#SPJ2
9.
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What acceleration is produced on a mass of 200 g, when a force of 10 N is
exerted on it ?
Given parameters:
Mass of the body = 200g
Force on the body = 10N
Unknown parameters:
Acceleration produced by the force = ?
To solve this problem we must first define force in terms of mass and acceleration. This is possible due to the Newton's first law of motion.
Force = mass x acceleration
Here the unknown is acceleration and we can easily solve for it.
But we must take the mass to kilogram in order for it to cancel out.
1000g = 1 kg
200g = x kg = [tex]\frac{200}{1000}[/tex] = 0.2kg
Now input the parameters and solve;
10 = 0.2 x acceleration
Acceleration = [tex]\frac{10}{0.2}[/tex] = 50m/s²
The acceleration produced by the body is 50m/s²
As the chief design engineer for a major toy company, you are in charge of designing a loop-the-loop toy for youngsters. The idea is that a ball of mass m and radius r will roll down an inclined track and around the loop without slipping. The ball starts from rest at a height h above the tabletop that supports the whole track. The loop radius is R. Determine the minimum height h, in terms of R and r, for which the ball will remain in contact with the track during the whole of its loop-the-loop journey
Answer: h = 2.7 R - 1.7 r
Explanation:
normally, force is 0 at the top ;
-N - mg = - m v^2 / ( R - r )
-0 - mg = (- mv^2) / ( R-r )
mg = (mv^2) / (R - r)
g = v^2 / ( R - r ) ; ----------------equation 1
conservation of energy ;
ΔK + ΔP = 0 ;
1/2 I ω^2 + 1/2 m v^2 + mg ( h2 - h1 ) = 0 ;
0.5 * ( 2/5 ) m r^2 * ( v / r )^2 + 0.5 m v^2 + mg ( ( 2R - r ) -h ) = 0 ;
0.5 * ( 2/5 ) m r^2 * ( v / r )^2 + 0.5 m v^2 = mg ( - 2R + r + h ) ;
0.5 * ( 2/5 )r^2 * ( v / r )^2 + 0.5 v^2 = g ( - 2R + r + h ) ;
0.5 * ( 2/5 ) v^2 + 0.5 v^2 = g ( - 2R + r + h ) ;
[ 0.5 * ( 2/5 ) + 0.5 ] v^2 = g ( - 2R + r + h ) ;-------------equation 2
from equation 1 , v^2 = g ( R - r ), input in equation 2
[ 0.5 * ( 2/5 ) + 0.5 ] [ g ( R - r ) ] = g ( - 2R + r + h )
[ 0.5 * ( 2/5 ) + 0.5 ] [ ( R - r ) ] = ( - 2R + r + h )
0.7 ( R - r ) = h - 2R + r
0.7R - 0.7r = h - 2R + r
solve for h
h = 0.7R + 2R - 0.7r - r
h = 2.7 R - 1.7 r
a negatively charged particle is attracted to: A) all particles that are located close by B)negatively charged particles C) positively charged particles D)only particles that are large
Answer:
The answer is C) Positively charged particles
Explanation:
Particles with the same charge are repelled by one another, while particles with different charges are attracted to one another.
Answer:
positively charged particles (c)
Explanation:
I got it right on Study Island
If an object is on a 27º frictionless incline, what will be the acceleration of the object on the incline?
describe three events you cannot explain about matter and energy
Answer:
describe three events you cannot explain about matter and energy
Explanation:
as anything that has mass and takes up space. Matter is found in 3 major states; solid, liquid and gas. ... Atoms are the smallest particle of matter. They are so small that you cannot see them with your eyes or even with a standard microscope.
Hope that helped.
Answer:
1. Different kinds of balls bounce to different heights when dropped on the same floor.
2. Sugar dissolves faster in hot milk than in cold milk.
3. Plants grow more slowly when they are not near a window.
Explanation:
PLATO/edmentum
The day time temperature of Mercury is 800 F . What is Mercury’s temperature in Celsius and kelvin?
Answer:
In Celsius it is 426.667
In Kevin it is 699.817
Explanation:
Please help willing to give brainliest
Electromagnetic waves do not require a medium to travel. Which one
below is an example of an electromagnetic wave?
1.ultraviolet waves
2.sound waves
3.water waves
Answer:
sound water because sound is the most important electronic wave for water
Assume you push a 20 kg child in a little red wagon with a force of 100 N. However, the dirt and rocks below the wheels
create a frictional force of 25 N. What is the acceleration on the wagon and child?
A. 1.25 m/s2
B.3.75 m/s2
C. 5 m/s2
D. 0.2 m/s2
Answer:
a
Explanation:
If the efficiency of a machine is equal to 85% and the work input is 10.0 , what is the work output?
Answer:
8.5
Explanation:
to find efficiency take the ratio between the output and input
85/100=output/input
What does Weber's Law about 'just noticeable differences' predict about how much someone has to change the brightness of a light before we can notice the difference? a. It depends on how bright the light was in the first place - the brighter it was, the less change is needed before we realize it. b. It depends on how long we have been looking at the light - the longer we have been looking, the more change is needed. c. It is always the same amount - 7 lux. d. It depends on how bright the light was in the first place - the brighter it was, the more change is needed before we realize it.
Answer:
answer A is the correct one
Explanation:
Weber's law states that "the smallest discernible change of a stimulus and proportional to the stimulus".
Applying this law to cases of optical intensity, the ratio must be
k = cte = ΔI / I
where ΔI is the variation of the intensity and I is the value of the intensity
In general, for humans, the constant is 0.15 for the rods and 0.015 for the cones of the retina.
When reviewing the answers, answer A is the correct one, since in order for the previous relationship to be maintained, the magnitudes must rise proportionally
if a bust starts to move and its velocity becomes 90 km after 8 seconds . calculate its acceleration answer it quick please
Answer:
a = 3.125 [m/s^2]
Explanation:
In order to solve this problem, we must use the following equation of kinematics. But first, we have to convert the speed of 90 [km/h] to meters per second.
[tex]90\frac{km}{h}*\frac{1000m}{1km}*\frac{1h}{3600s} \\= 25 \frac{m}{s}[/tex]
[tex]v_{f} =v_{i} + (a*t)[/tex]
where:
Vf = final velocity = 25 [m/s]
Vi = initial velocity = 0
a = acceleration [m/s^2]
t = time = 8 [s]
The initial speed is zero as the bus starts to koverse from rest. The positive sign of the equation means that the bus increases its speed.
25 = 0 + a*8
a = 3.125 [m/s^2]
1)
What is the velocity in meters per second of a runner who runs exactly 110 m toward the beach in 72 seconds
Answer:
1.53 m/s toward the beach
Explanation:
1.53 m/s toward the beach
Explanation:
The magnitude of the velocity of the runner is given by:
where
d is the displacement of the runner
t is the time taken
In this case, d=110 m and t=72 s, so the velocity of the runner is
Velocity is a vector, so it consists of both magnitude and direction: we already calculate the magnitude, while the direction is given by the problem, toward the beach.
What is the Speed of child falling from tree 5.0 meters high
Please help me with this.
how long will a speed boat cross a 2.o km lake with a speed of 40 km/hr
Explanation:
s=d/t
t= d/s
t= 2/40
t= 0.05 hr
What is the net force on a 1200-kg car that is accelerating at 8.5 m/s2?
Answer:
10,200 N
Explanation:
Given:
Mass of the car m = 1200 kg
Acceleration of the car a = 8.5 m/s^2
Force F=?
[tex]\because F = ma\\
\therefore F = 1200 \times 8.5\\
\therefore F = 10,200 N \\ [/tex]
What determines the radiation that an electromagnetic wave emits?
Black and splinter cleavage barely scratches glass
Answer:
oh I know that sounds good to me
The neutrons in the nucleus of an atom have-
a. a positive charge
b. a negative charge
C. both positive & negative charges
d. no charge
Answer "d' no charge
Explanation:
They are as the name says neutral. They have no charge they are electrically neutral. Just as a proton is a positively charged particle and an electron carries a negative charge.
HELP!!! HURRY!!!!! 100 POINTS!!!!!!!!!
what happens at Point C is sublimation. the increase in temperature affects the Vapour pressure soon as you can see the curve is increasing with increasing pressure there is increase in temperature that is the sublimation Curve
Answer:
what happens at Point C is sublimation. the increase in temperature affects the Vapour pressure soon as you can see the curve is increasing with increasing pressure there is increase in temperature that is the sublimation Curve.
If you want to make a strong battery, should you pair two metals with high electron affinities, low electron affinities, or a mix? Explain your answer.
In the International Space Station which orbits Earth, astronauts experience apparent weightlessness because:_________
a) the astronauts and the station are in free fall towards the center of the Earth.
b) there is no gravity in space. the station is kept in orbit by a centrifugal force that counteracts the Earth's gravity.
c) the station's high speed nullifies the effects of gravity.
d) the station is so far away from the center of the Earth.
Answer:
a) the astronauts and the station are in free fall towards the center of the Earth
Explanation:
Weightlessness is only a sensation of zero weight, a body experiences when it is in free fall towards the center of the Earth, caused by lack of contact force on such body.
Weightlessness doesn't mean the object has zero actual weight, is just a sensation of no weight due to lack of contact force to produce upward reaction on the object which gives the real sense of ones weight.
Thus, the astronauts experience apparent weightlessness because:
a) the astronauts and the station are in free fall towards the center of the Earth.