Answer:
It is called the unit function because it is the identity element for Dirichlet convolution. It may be described as the "indicator function of 1" within the set of positive integers. It is also written as u(n) (not to be confused with μ(n), which generally denotes the Möbius function).
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
If a 3.5 kg object is accelerating at 0.80 /s^2, the net force F causing this motion is ____ N.
A) 2.2
B)2.8
C)3.4
D)4.0
Answer:
The answer is option BExplanation:
To find the force acting on an object we use the formula
force = mass × accelerationFrom the question
mass = 3.5 kg
acceleration = 0.80 m/s²
We have
Force = 3.5 × 0.8
We have the final answer as
2.8 NHope this helps you
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
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
What is the Speed of child falling from tree 5.0 meters high
give at least two similarities and differences among the terrestrial planets Mars Venus and Earth
Answer:
Answer is as follow:
Explanation:
With a distance of just 6,792 km, Mars is even smaller. And again, Venus would be almost Earth's double in terms of scale. It has 81 percent of the earth 's volume, while Mars has just 10 percent of the earth 's mass. Mars and Venus have very different ecosystems, and they are both very separate from Earth.
Please help me with this.
Activity_Mass_Balance_Recycle
Sea water must be desalinated by reverse osmosis. For a feed rate of 1000 lb/h sea water containing 3.1% salt (by weight) is desalinated water with only 500 ppm salt and the brine tailings containing 5.25% salt. Part of the brine tailings is recycled and the inlet stream in the reverse osmosis cell contains 4.0% salt. Determine:
a) A brine removal taxon (ṁ3);
b) The production rate of desalinated water (ṁ2);
c) The rate of brine that is recycled (ṁR).
Answers:
ṁ1 = 1720 lb / h
ṁ2 = 409.37 lb / h
ṁ3 = 590.63 lb / h
ṁR = 720 lb / h
Answer:
m₁ = 1720
m₂ = 413.46
m₃ = 586.54
mr = 720
Explanation:
Draw a diagram. Sea water (1000 lb/h, 3.1% salt) is mixed with the recycled brine (mr, 5.25% salt) to create the inlet stream (m₁, 4.0% salt). This inlet stream is fed into the osmosis cell. The osmosis cell produces desalinated water (m₂, 500 ppm) and brine tailings. Part of the tailings is recycled (mr, 5.25% salt), and the rest is removed (m₃, 5.25%).
The mass of water is conserved, so:
1000 + mr = m₁
m₁ = mr + m₂ + m₃
The mass of salt is conserved, so:
0.031 (1000) + 0.0525 mr = 0.040 m₁
0.040 m₁ = 0.0525 mr + 0.0005 m₂ + 0.0525 m₃
Four unknown variables, and four equations. We can use the first and third to find mr and m₁.
0.031 (1000) + 0.0525 mr = 0.040 (1000 + mr)
31 + 0.0525 mr = 40 + 0.040 mr
0.0125 mr = 9
mr = 720
m₁ = 1720
Now we can use these values and the second and fourth equations to solve for the remaining variables.
1720 = 720 + m₂ + m₃
0.040 (1720) = 0.0525 (720) + 0.0005 m₂ + 0.0525 m₃
1000 = m₂ + m₃
68.8 = 37.8 + 0.0005 m₂ + 0.0525 m₃
68.8 = 37.8 + 0.0005 m₂ + 0.0525 (1000 − m₂)
68.8 = 37.8 + 0.0005 m₂ + 52.5 − 0.0525 m₂
0.052 m₂ = 21.5
m₂ = 413.46
m₃ = 586.54
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
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.
Lexington walked to her friends house.lexie walked 2miles west then 5 miles south then 3 miles east then 4 miles north then 2 miles east and finally 1 mile north what is levies distance and displacement.
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.
What type of energy transfer causes a sunburn?
A. Radiation, because particles of hot air move in space
B. Radiation, because electromagnetic waves transfer heat
C. Conduction, because hot air comes in contact with the skin
D. Conduction, because invisible light carries heat from the sun
If your right you get 100 points and a brainliest
Answer:
Hi!!
It should be A, ratation
(sorry that I didnt spell that write)
Have a great day!
To solve this we must be knowing each and every concept related to energy and its different types. Therefore, the correct option is option A among all the given options.
What is energy?In physics, energy is the capacity to accomplish work. It can be potential, kinetic, thermal, electric, chemical, radioactive, or in other forms.
There is also heat and work—energy inside the process of being transferred by one body to the other. Energy is always classified according to its type once it has been transmitted. As a result, heat transported could become thermal energy, whereas labor done may emerge as mechanical energy. Radiation is a t type of energy that transfer energy that causes a sunburn because particles of hot air move in space.
Therefore, the correct option is option A among all the given options.
To know more about energy, here:
brainly.com/question/29763772
#SPJ2
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 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.
PLEASE PROVIDE EXPLANATION FOR D AND E
THANK YOU!
Answer:
d) 14.1 m
e) 8.57 m/s
Explanation:
(a) There are three forces on the ball:
Normal force Fn pushing up,
Weight force Fg pulling down,
Kinetic friction Fk pushing left (resisting motion).
FBD is the correct free body diagram.
(b) Sum of forces in the y direction:
∑F = ma
Fn − Fg = 0
Fn = Fg
Sum of forces in the x direction:
∑F = ma
-Fk = ma
-Fn μk = ma
-mg μk = ma
a = -g μk
a = -(10 m/s²) (0.25)
a = -2.5 m/s²
(c) Sum of torques about the ball's center:
∑τ = Iα
Fk r = ⅖ mr² α
mg μk r = ⅖ mr² α
g μk = ⅖ r α
α = 5g μk / (2r)
α = 5 (10 m/s²) (0.25) / (2 × 0.2 m)
α = 31.25 rad/s²
(d) The velocity and angular velocity at time t is:
v = at + v₀
v = -2.5t + 12.0
ω = αt + ω₀
ω = 31.25t + 0
When the ball begins to roll without slipping, v = ωr.
-2.5t + 12.0 = (31.25t) (0.2)
-2.5t + 12.0 = 6.25t
12.0 = 8.75t
t = 1.37
The distance the ball moves is:
Δx = v₀ t + ½ at²
Δx = (12) (1.37) + ½ (-2.5) (1.37)²
Δx = 14.1 m
(e) v = at + v₀
v = (-2.5 m/s²) (1.37 s) + 12.0 m/s
v = 8.57 m/s
Answer:
a
Explanation:
on egde 2020
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
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
What is the amount of thermal energy that can be stored in an object depends on?
What determines the radiation that an electromagnetic wave emits?
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
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
A family is visiting the Statue of Liberty in New York City. One of the children accidentally drops her backpack from the top of the viewing platform which is 300 feet above the ground. At what height will the kinetic energy of the backpack be equal to it's potential energy?
In fact the actual height at which the two energies are equal can be determined only if there is a specified velocity. So by theoretically equating the energy equation we will arrive at the point that the height equal to 4.9 V².
What is kinetic energy?The kinetic energy of a body is the energy formed by virtue of its motion. It is directly proportional to the mass and velocity of the moving body and the equation is written as:
KE = 1/2 MV².
Potential energy is formed by virtue of the position of a body and it is equal to mgh. Where, g is gravitational acceleration equal to 9.8 m/s² and m is mass and h is the height from the ground.
The total of these two energy is called mechanical energy of a body and the total mechanical energy of a body is always conserved.
If the kinetic energy and potential energy are equal then the equations can be equated as:
1/2 mV² = mgh
V²/2 = gh.
=9.8 h
h = 4.9 V²
Therefore at a height of 4.9 V² the energies of the falling body will be equal where v is the velocity of the moving body.
To find more about mechanical energy, refer the link below:
https://brainly.com/question/13552918
#SPJ5
a spring scale is constructed so that each 0.10-n increment is separated by 0.50 cm. what spring constant is necessary for the scale to be accurate?
Answer:
5.00
Explanation:
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.
which theory says dreaming is an unimportant by-product of neural firing during sleep
Answer:activation-synthesis
Explanation:
a force of magnitude 30 n stretches a spring 0.83 m from equilibrium. what is the value of the spring constant?
Answer:
36 N/m
Explanation: I got the answer right on the test ight noo cap
- You travel by bus from Indianapolis to New York City which is 1100 miles away. With no stops, the trip took 11 hours. The average speed was...
Answer:
100 mph, or about 44.7 m/s
Explanation:
Average speed is [tex]\frac{distance}{time\\}[/tex].
After substitution, this is [tex]\frac{1100}{11}[/tex].
The average speed, therefore, reduces to 100 mph, or about 44.7 m/s.
A baseball player is running at a constant velocity on a level field and tosses a baseball straight up. When the ball comes back down, it will land
Answer:
]
Explanation: