Answer:
Angle = 18.41°
Explanation:
Torque = F•r•sin θ
where;
F = force
r = distance from the rotation point
θ = the angle between the force and the radius vector.
We are given;
Torque = 15 N.m
F = 95 N
r = 0.5 m
Thus, plugging in the relevant values ;
15 = 95 × 0.5 × sin θ
sin θ = 15/(95 × 0.5)
sin θ = 0.3158
θ = sin^(-1)0.3158
θ = 18.41°
As you get ready for bed, you roll up one of your socks into a tight ball and toss it into the laundry basket across the room. Then, you try to toss the other sock without rolling it up.. What effects whether or not your socks land in the basket?
Answer:
The drag (air resistance) it experiences along its flight to the basket, due to the shape and surface area of the socks, the size of the sock (weight), and the speed with which the socks is tossed.
Explanation:
The socks, like every other particle or body travelling through air is met by a resistance that impedes its motion. This resistance is due to the air molecules around, that collide with the body as it travels through them. The resistance offered by this force is proportional to the surface area of the body that collides with the air molecule, so, rolling the socks into a ball reduces the effect of air resistance on the socks, compared to the one tossed without rolling. Air resistance is also largely dependent on the relative motion of the body and the air molecules, the density of the fluid (air), and the size of the body (weight).
Therefore, whether the socks lands in the basket or not is affected by the drag (air resistance) it experiences along its flight to the basket, due to the shape and surface area of the socks, size of the socks (weight), and the speed with which the socks is tossed.
Drag force opposes motion of objects through fluid with its magnitude depending on the velocity of the object in the fluid
The single parameter that effects whether or not the socks lands in the basket is the drag force, [tex]\mathbf{F_D}[/tex] acting on the socks
[tex]F_D = \mathbf{C_D \times A \times \dfrac{\rho \times v_r^2}{2}}[/tex]
The reason that drag force is the parameter that effects the landing point of the socks is as follows:
The parameters that effects whether or not the socks land in the basket or not are;
The distance of the basket away from the thrower = The range, RThe velocity with which the socks are thrown, uThe angle of elevation with which each socks is thrown, θThe amount of drag experienced by each socks, [tex]\mathbf{F_D}[/tex]The parameters, R, u, and θ depends on the thrower, that parameter that effects the whether or not the socks lands in the basket that is independent of the thrower, is the drag, [tex]\mathbf{F_D}[/tex]
Drag is the force opposing (slows) the motion of an object in a fluid.
The drag force, [tex]\mathbf{F_D}[/tex], slowing down motion, is given by the following formula;
[tex]F_D = \mathbf{C_D \times A \times \dfrac{\rho \times v_r^2}{2}}[/tex]
Where;
[tex]v_r[/tex] = The velocity of flow of the fluid, relative to the object
ρ = The density of the fluid
[tex]C_D[/tex] = The drag coefficient
A = The cross sectional area of the fluid
Therefore, the independent parameter that effects whether or not the socks lands in the basket is the drag force on the socks
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Some runners train with parachutes that trail behind them to provide a large drag force. These parachutes are designed to have a large drag coefficient. One model expands to a square 1.8 m on a side, with a drag coefficient of 1.4. A runner completes a 200 m run at 5.0 m/s with this chute trailing behind. Part A How much thermal energy is added to the air by the drag force
Answer:
13.9 kJ
Explanation:
Given that
Length of the side, l = 1.8 m
Drag coefficient, C(d) = 1.4
Distance of run, d = 200 m
Velocity of run, v = 5 m/s
Density, ρ = 1.23
Using the Aerodynamics Drag Force formula. We have
F(d) = 1/2.ρ.A.C(d).v²
The Area, A needed is 1.8 * 1.8 = 3.24 m². So that,
F(d) = 1/2 * 1.23 * 3.24 * 1.4 * 5²
F(d) = 139.482/2
F(d) = 69.74
recall that, energy =
W = F * d
W = 69.74 * 200
W= 13948
W = 13.9kJ
Therefore, the thermal energy added to the air by the drag force is 13.9kJ
An underwater diver sees the sun at an apparent angle of 45.00 from the vertical. How far is the sun above the horizon? [n in water=1.333
Answer:
19.872 degrees
Explanation:
Mathematically;
Using Snell’s law
n1 sin A = n2 sinB
Where ;
n1 = refractive index in air = 1
n2 is refractive index in water = 1.33
A = ?
B = 45
Substituting the values in the equation;
1 sin A = 1.33 sin45
Sin A = 1.33 sin 45
A = arc sin (1.33 sin 45)
A = 70.12
Thus, the actual direction of the Sun with respect to the horizon = 90-A = 19.872 degrees
An organism has 20 chromosomes after fertilization.after meiosis, how many chromosomes would each sex cell have?
Answer:
EACH SEX CELL WILL HAVE 10 CHROMOSOMES BECAUSE n+n=2n
means haploid parent cells join or fuse to form diploid zygote
Answer:
10
Explanation:
A carousel has a diameter of 6.0-m and completes one rotation every 1.7s. Find the centripetal acceleration of the traveler in m / s2.
Answer:
The centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex]
Explanation:
It is given that, A carousel has a diameter of 6.0-m and completes one rotation every 1.7 s.
We need to find the centripetal acceleration of the traveler. It is given by the formula as follows :
[tex]a=\dfrac{v^2}{r}[/tex]
r is radius of carousel
[tex]v=\dfrac{2\pi r}{T}[/tex]
So,
[tex]a=\dfrac{4\pi ^2r}{T^2}[/tex]
Plugging all the values we get :
[tex]a=\dfrac{4\pi ^2\times 3}{(1.7)^2}\\\\a=40.98\ m/s^2[/tex]
So, the centripetal acceleration of the traveler is [tex]40.98\ m/s^2[/tex].
When jumping straight down, you can be seriously injured if you land stiff-legged. One way to avoid injury is to bend your knees upon landing to reduce the force of the impact. A 73.0 kg man just before contact with the ground has a speed of 6.46 m/s. In a stiff-legged landing he comes to a halt in 2.07 ms. Calculate the average net force that acts on him during this time
Answer:
Explanation:
The man comes to halt due to reaction force acting on him in opposite direction . If R be the reaction force
impulse by net force = change in momentum
Net force = R - mg , mg is weight of the man .
( R-mg ) x 2. 07 x 10⁻³ = 73 x 6.46 - 0
R - mg = 227.81 x 10³
Average net force = 227.81 x 10³ N .
The density of atmosphere (measured in kilograms/meter3) on a certain planet is found to decrease as altitude increases (as measured from the planet's surface). What type of relationship exists between the altitude and the atmospheric density, and what would the atmospheric density be at an altitude of 1,291 kilometers?
A.
inverse plot, 0.45 kilograms/meter3
B.
inverse plot, 0.51 kilograms/meter3
C.
quadratic plot, 1.05 kilograms/meter3
D.
inverse plot, 1.23 kilograms/meter3
E.
inverse plot, 0.95 kilograms/meter3
' A ' looks like the best choice.
Answer:
B. inverse plot, 0.51 kilograms/meter3
Explanation:
HELP, END OF SCHOOL YEAR, 30 POINTS Unit 9 lesson 15 astronomy unit test answers I ONLY HAVE ONE MORE DAY
1 As evidence supporting the Big Bang theory, what does the redshift of light from galaxies indicate?
The universe is mainly hydrogen.
The universe is 13.8 billion years old.
The universe is cooling off.
The universe is expanding.
2 Which evidence supports the idea that Cosmic Microwave Background radiation is a remnant of the Big Bang?(1 point)
Its temperature is uniform.
Its mass fluctuates greatly.
Its temperature fluctuates greatly.
Its mass is uniform.
3 Which of these items provide evidence supporting the Big Bang theory? Select the two correct items.(1 point)
rate of star formation
composition of matter in the universe
sizes and shapes of distant galaxies
cosmic background radiation
4 How does the change in the temperature of the universe provide evidence for universe expansion that supports the Big Bang Theory?(1 point)
The universe is warming which, according to the Big Bang Theory, is expected to happen as the cosmos disperses.
The universe is warming which, according to the Big Bang Theory, is expected to happen as the cosmos accumulates.
The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos accumulates.
The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses.
5 How does weak background radiation coming from every direction in the sky support the Big Bang Theory?(1 point)
It provides evidence of the universe's increasing mass.
It provides evidence of universe expansion.
It provides evidence of universe contraction.
It provides evidence of the universe's decreasing mass.
6 Which statements describe ways that nuclear fission is different than nuclear fusion? Select the two correct answers.(1 point)
Nuclear fission is used to produce electricity at nuclear power plants.
Nuclear fission involves one large atom splitting into two smaller atoms.
Nuclear fission takes place in the nucleus of an atom.
Nuclear fission releases a huge amount of energy.
7 Blueshift is observed when(1 point)
a distant luminous object travels rapidly away from an observer.
a distant luminous object travels rapidly towards an observer.
a luminous object travels alongside an observer.
a luminous object is stationary compared to an observer.
8 Which statements about nuclear fusion are false? Select the two correct answers.(1 point)
The fuel for nuclear fusion is often uranium.
Nuclear fusion is used to generate electricity at nuclear power plants.
Nuclear fusion releases large amounts of energy.
Nuclear fusion takes place in the cores of stars.
9 Which of the following statements provide evidence to support the big bang theory? Select the two correct answers.
The ratios of hydrogen and helium in the universe match those of the early universe.
The universe began as a very high density singularity.
Dark matter makes up the majority of matter in the galaxy.
Small spiral galaxies become larger elliptical galaxies when they collide.
10 Which represents a correct match between ideas related to the formation of the universe? Select the two correct answers.(1 point)
accelerating expansion — dark energy
structures forming in the early universe — dark matter
greatest percent of mass of universe — dark matter
glowing nebulae — dark energy
11 How is dark energy related to the theory of the Big Bang?(1 point)
It causes the expansion of the universe to accelerate.
It causes the universe to expand.
It seeded the formation of galaxies and star clusters.
It causes the spinning of galaxies.
Answer:
1. The Universe is Expanding
2. It’s temperature is it’s uniform
3. Cosmic background radiation
4. I will give a hint for this one, since I don’t know, the hint is the universe is cooling.
5. It provides evidence of universe expansion.
6. Sorry I don’t know the rest
Explanation:
The universe is the collection of every item in space and time as well as the contents of those items
The correct options are as follows;
1. The universe is expanding
2. Its temperature is uniform
3. Composition of matter in the universe, cosmic background radiation
4. The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses
5. It provides evidence of universe expansion
6. Nuclear fission involves one large atom splitting into two smaller atoms
Nuclear fission takes place in the nucleus of an atom
7. A distant object travels rapidly towards an observer
8. The fuel in nuclear fusion is often uranium
Nuclear fusion is used to generate electricity at nuclear power plants
9. The universe began as a very high density singularity
Dark matter makes up majority of the universe
10. Acceleration expansion — Dark energy
Structure forming in the early universe — Dark matter
11. It causes the expansion of the universe to accelerate
The reasons for selecting the above options are as follows;
1. The universe is expanding
The redshift of light from galaxies indicates that that are moving away
2. Its temperature is uniform
The uniform temperature of the microwave background suggest a common source
3. Composition of matter in the universe, cosmic background radiation
The matter present in the universe are characteristically similar in their origins
The cosmic background provides evidence of the existence of a singularity
4. The universe is cooling which, according to the Big Bang Theory, is expected to happen as the cosmos disperses
Based on the Big Bang Theory, the temperature of the universe is reducing as the universe expands, compared to the initial temperature
5. It provides evidence of universe expansion
The background radiation coming from a single source as the rest of the universe is expected to spread throughout the universe
6. Nuclear fission involves one large atom splitting into two smaller atoms
Nuclear fission takes place in the nucleus of an atom
Nuclear fusion involves the joining of small atoms to form a larger atom
7. A distant object travels rapidly towards an observer
The redshift is the opposite, indicating that the object is moving further away
8. The fuel in nuclear fusion is often uranium
Nuclear fusion is used to generate electricity at nuclear power plants
Nuclear fusion usually consists of joining small atoms together. It has not been used for commercial energy production
9. The universe began as a very high density singularity
According to the Big Bang Theory, the universe started from the dense, high temperature singularity
Dark matter makes up majority of the universe
10. Acceleration expansion — Dark energy
Dark energy causes expansion
Structure forming in the early universe — Dark matter
Dark matter is instrumental to the formation of structures in the universe
11. It causes the expansion of the universe to accelerate
Dark energy is seen as the cause of the accelerating expansion of the universe
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A corpse is discovered in a room that has its temperature held steady at 25oC. The CSI ocers ar- rive at 2pm and the temperature of the body is 33oC. at 3pm the body's temperature is 31oC. Assuming Newton's law of cooling and that the temperature of the living person was 37oC, what was the approximate time of death
Answer: Around 0:35 Pm or 12:35 Am
Explanation:
The equation that describes the cooling of objects can be written as:
T(t) = Ta + (Ti - Ta)*e^(k*t)
Where Ta is the ambient temperature, here Ta = 25°C.
Ti is the initial temperature of the body, we have Ti = 37°C.
t is the time.
k is a constant.
So our equation is:
T(t) = 25°C +12°C*e^(k*t)
at 2pm, the temperature was 33°C
at 3pm, the temperature was 31°C.
we want to find the hour where we have our t = 0, suppose this hour is X.
then we can write our times as:
2pm ---> 2 - X
3pm ----> 3 - X
and our equations are:
33°C = 25°C + 12°C*e^(k2 - k*X)
31° = 25°C + 12°C*e^(k3 - k*X)
So we have two equations and two variables, let's solve the system.
first, simplify it a bit, for the first eq:
33 - 25 = 12*e^(k2 - k*X)
8/12 = e^(k2 - k*X)
ln(8/12) = k*2 - k*X
for the second equation we have:
31 - 25 = 12*e^(k3 - k*X)
6/12 = e^(k3 - k*X)
ln(6/12) = k*3 - k*X
So our equations are:
1) ln(2/3) = 2*k - X*k
2) ln(1/2) = 3*k - X*k
First, let's isolate one of the variables in one of the equations. let's isolate k in the first equation.
ln(2/3)/(2-X) = k
now we can replace it in the second equation:
ln(1/2) = 3*ln(2/3)/(2 - X) - X*ln(2/3)/(2-X)
now let's solve it for X, i will take a = ln(1/2) and b = ln(2/3) so it is easier to read.
a = 3*b/(2 - X) - X*b/(2 - X)
a*(2 - X) = 3*b - X*b
2a - aX = 3b - Xb
X(a - b) = 2a - 3b
X = (2*ln(1/2) - 3*ln(2/3))/(ln(1/2) - ln(2/3)) = 0.590
now, knowing that one hour has 60 minutes, then this is:
0.59*60m = 35 minutes
So the hour of death is 0:35 Pm or 12:35 Am
A politician holds a press conference that is televised live. The sound picked up by the microphone of a TV news network is broadcast via electromagnetic waves and heard by a television viewer. This viewer is seated 2.7 m from his television set. A reporter at the press conference is located 5.5 m from the politician, and the sound of the words travels directly from the celebrity's mouth, through the air, and into the reporter's ears. The reporter hears the words exactly at the same instant that the television viewer hears them. Using a value of 343 m/s for the speed of sound, determine the maximum distance between the television set and the politician. Ignore the small distance between the politician and the microphone. In addition, assume that the only delay between what the microphone picks up and the sound being emitted by the television set is that due to the travel time of the electromagnetic waves used by the network.
Answer:
Explanation:
Time taken by sound waves to cover distance between politician and reporter = time taken by em waves to travel distance between politician and the television viewer.
5.5 / 343 = d / 3 x 10⁸ + 2.7 / 343
d is distance between politician and television set + time taken by sound to travel distance between television and its viewer.
.0160349 = d / 3 x 10⁸ + .0078717
d / 3 x 10⁸ = .0081632
d = 2448960 m
= 2448.96 km
= 2449 km .
A visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 6.01 s. What is the height of the tower
Answer:
The height of the tower is 8.96 m.
Explanation:
We have, a visitor to a lighthouse wishes to determine the height of the tower. She ties a spool of thread to a small rock to make a simple pendulum, which she hangs down the center of a spiral staircase of the tower. The period of oscillation is 6.01 s.
It is required to find the height of the tower. Let it is l. The time period of a simple pendulum is given by :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
l is length of pendulum, or height of tower
[tex]l=\dfrac{T^2g}{4\pi^2}\\\\l=\dfrac{(6.01)^2\times 9.8}{4\pi^2}\\\\l=8.96\ m[/tex]
So, the height of the tower is 8.96 m.
You are comparing a reaction that produces a chemical change and one that produces a physical change. What evidence could you use to determine which type of change is occurring?
Answer: A chemical change results from a chemical reaction, while a physical change is when matter changes forms but not chemical identity. Examples of chemical changes are burning, cooking, rusting, and rotting. Examples of physical changes are boiling, melting, freezing, and shredding. Often, physical changes can be undone, if energy is input.
Explanation: hope this helps have a good day
Answer:
If the reaction is a chemical change, new substances with different properties and identities are formed. This may be indicated by the production of an odor, a change in color or energy, or the formation of a solid.
For the parallel plates mentioned above, the DC power supply is set to 31.5 Volts and the plate on the right is at x = 14 cm. What is the magnitude of the electric field at a point on the x-axis where x = 7.0 cm? Answer with a number in the format ### in Newtons per Coulombs.
Note: The complete question is attached as a file to this solution. The parallel plate mentioned can be seen in this picture attached.
Answer:
E = 225 N/C
Explanation:
Note: At any point on the parallel plates of a capacitor, the electric field is uniform and equal.
Therefore, Electric field at x = 14 cm equals the electric field at x = 7 cm
V(x) = 31.5 Volts
x = 14 cm = 0.14 m
The magnitude of the electric field at any point between the parallel plate of the capacitor is given by the equation:
E = V(x)/d
E(x = 0.14) = 31.5/0.14
E(x=0.14) = 225 N/C
E(x=0.14) = E(x=0.07) = 225 N/C
A roller coaster car is going over the top of a 15-m-radius circular rise. The passenger in the roller coaster has a true weight of 600 N (therefore a mass of 61.2 kg). At the top of the hill, the passengers "feel light," with an apparent weight of only 360 N. How fast is the coaster moving
Answer:
v = 7.67 m/s
Explanation:
The equation for apparent weight in the situation of weightlessness is given as:
Apparent Weight = m(g - a)
where,
Apparent Weight = 360 N
m = mass passenger = 61.2 kg
a = acceleration of roller coaster
g = acceleration due to gravity = 9.8 m/s²
Therefore,
360 N = (61.2 kg)(9.8 m/s² - a)
9.8 m/s² - a = 360 N/61.2 kg
a = 9.8 m/s² - 5.88 m/s²
a = 3.92 m/s²
Since, this acceleration is due to the change in direction of velocity on a circular path. Therefore, it can b represented by centripetal acceleration and its formula is given as:
a = v²/r
where,
a = centripetal acceleration = 3.92 m/s²
v = speed of roller coaster = ?
r = radius of circular rise = 15 m
Therefore,
3.92 m/s² = v²/15 m
v² = (3.92 m.s²)(15 m)
v = √(58.8 m²/s²)
v = 7.67 m/s
A heavy copper ball of mass 2 kg is dropped from a fiftieth-floor apartment window. Another one with mass 1 kg is dropped immediately after 1 second. Air resistance is negligible. The difference between the speeds of the two balls:__________.
a. increases over time at first, but then stays constant.
b. decreases over time.
c. remains constant over time.
d. increases over time.
Answer:
C
Explanation:
Because everything on Earth falls at the same speed, the masses of the balls do not matter. Since the acceleration due to gravity is constant, their speeds will both be increasing at the same rate, and therefore the difference in speeds would remain constant until they hit the ground. Hope this helps!
You are helping your friend prepare for the next skateboard exhibition by determining if the planned program will work. Your friend will take a running start and then jump onto a heavy-duty 13-lb stationary skateboard. The skateboard will glide in a straight line along a short, level section of track, then up a curved concrete wall. The goal is to reach a height of at least 10 feet above the starting point before coming back down the slope. Your friend's maximum running speed to safely jump on the skateboard is 24 feet/second. Your friend weighs 155-lbs. What is the height hf that your friend will reach according to his plan?
Answer:
8.3 feet
Explanation:
The kinetic energy of the system on the ground is ...
KE = Σ(1/2)(mv^2) = (1/2)(155)(24^2) +(1/2)(13)(0^2) = 44640 lb·ft²/s²
The potential energy at the highest point is the same:
PE = mgh
44640 = (155 +13)(32)h
h = 44640/5376 = 8.30 . . . . feet
_____
We haven't worried too much about the conversion between pounds mass and pounds force. Whatever factor may be involved will divide out when computing the maximum height. We have used g=32 ft/s².
__
To achieve a 10 ft height, the running speed would need to be 26.34 ft/s, about 10% higher.
A single loop of wire with an area of 0.0820 m2 is in a uniform magnetic field that has an initial value of 3.80 T, is perpendicular to the plane of the loop, and is decreasing at a constant rate of 0.220 T/s .
Required:
a. What emf is induced in this loop?
b. If the loop has a resistance of 0.600Ω, find the current induced in the loop.
Answer:
a) emf = 0.01804 V
b) I = 0.03 A
Explanation:
a) The emf is calculated by using the following formula:
[tex]|emf|=|\frac{d\Phi_B}{dt}|=|\frac{d(A\cdot B)}{dt}|[/tex] [tex]=A|\frac{dB}{dt}|[/tex]
A: area of the loop = 0.0820m^2
B: magnitude of the magnetic field
dB/dt: change of the magnetic field, in time: 0.220 T/s
Where ФB is the magnetic flux, the surface vector and magnetic vector are perpendicular between them, and the area A is constant.
You replace the values of A and dB/dt in the equation (1):
[tex]|emf|=(0.082m^2)(0.220T/s)=0.01804V[/tex]
b) The current in the loop is:
[tex]I=\frac{emf}{R}[/tex]
R: resistance of the loop = 0.600Ω
[tex]I=\frac{0.01804V}{0.600\Omega}=0.03A=30mA[/tex]
a. The emf induced in this loop is 18.04mV.
b. The current induced in the loop is 30.06mA.
a. We know that,
[tex]flux(\phi)=B*A[/tex]
Where B is magnetic field and A is the area.
[tex]emf=\frac{d\phi}{dt}=A*\frac{dB}{dt}[/tex]
Given that, Area , [tex]A=0.0820m^{2},B=3.80T,\frac{dB}{dt}=0.220T/s[/tex]
Substituting all values in above equation.
[tex]emf=0.0820*0.220=0.01804V=18.04mV[/tex]
b. Resistance, [tex]R=0.600ohm[/tex]
Current induced in the loop is,
[tex]I=\frac{emf}{R}=18.04/0.6=30.06mA[/tex]
Hence, the emf induced in this loop is 18.04mV.
The current induced in the loop is 30.06mA.
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someone please help me out thanks
Answer:
The answer is D)Theory
Explanation:
This is due because a theory is a scientific term and is a testable model that scientists seek to explain a phenomenon. You can also find out the answer by the process of elimination it can't be data because that would be something they already know and something they use to prove not explain. It can't be law because it isn't testable but can be used to explain. So that leaves you with two answers hypothesis and theory which are very similar but it isn't hypothesis because it isn't used to explain it to help the scientists come up with a theory and accumulate what might happen.
Which symbol is used to show vector quantities
Answer: arrows
Explanation:
A vector quantity is usually represented by an arrow, with the direction of the vector being the direction in which the arrow points and the length of the arrow representing the vector's magnitude.
What is the vector quantity unit?
The meter is the only fundamental SI unit that is a vector. The rest are all scalars. Derived quantities might be scalar or vector, but all vector quantities require meters as part of their definition and measurement.
The term "vector quantities" refers to physical quantities whose magnitude and direction are well specified.
Arrows are used to depict vectors. An arrow has a direction and a magnitude (how long it is) (the direction in which it points).
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Which statement best describes one way that the molecules differ from atoms? a. A molecule can contain a nucleus about which its electrons orbit b. A molecule can contain two atoms of the same element. C. Only a molecule can be the smallest particle of a certain element. d. Only a molecule can be broken down into two or more different elements.
B and D are both true statements. I'm not comfortable saying that either one is better than the other one.
The statement that best describes one way that molecules differ from atoms is a molecule can contain two atoms of the same element, and only a molecule can be broken down into two or more different elements. The correct options are b and d.
What are atoms and molecules?According to science, an atom is the smallest component of an element that can exist freely or not. A molecule, on the other hand, is the smallest component of a chemical and is made up of a group of atoms linked together by a bond.
A molecule is the smallest component of a substance that has the chemical properties of the compound.
The term "independent molecule" is not commonly used to refer to atoms and complexes linked by non-covalent interactions such as hydrogen or ionic bonds. Molecules are common constituents of matter.
Therefore, the correct options are b and d.
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When you ride a bicycle, in what direction is the angular velocity of the wheels? When you ride a bicycle, in what direction is the angular velocity of the wheels? to your right forwards up to your left backwards g
When you ride a bicycle, the direction of the angular velocity of the wheels is; Option A; to your left
Complete question is;
When you ride a bicycle, in what direction is the angular velocity of the wheels? A) to your left B) to your right C) forwards D) backwards
While an object rotates, each particle will have a different velocity:
the 'Speed' component will vary with radius while the 'Direction' component will vary with angle.
Now, all of the velocity vectors are aligned in the same plane and as such we can be solve this by choosing a single vector normal to ALL of the possible velocity vectors of the rotating object in that plane.
The convention that will be used to answer this question is known as "Right-hand rule". The angular velocity vector points along the wheel's axle.
For instance, if you Imagine wrapping your right hand around the axle so that your fingers point in the direction of rotation, with your thumb sticking out. You will notice that your thumb points to the left.
Thus;
In conclusion, by right-hand rule, a wheel rotating on a forward - moving bicycle has an angular velocity vector pointing to the rider's left.
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A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 592 N. As the elevator later stops, the scale reading is 400 N. Assume the magnitude of the acceleration is the same during starting and stopping. (a) Determine the weight of the person. N (b) Determine the person's mass. kg (c) Determine the magnitude of acceleration of the elevator. m/s2
Answer:
a) 496Nb) 50.56kgc) 1.90m/s²Explanation:
According to newton's secomd law, ∑F = ma
∑F is the summation of the force acting on the body
m is the mass of the body
a is the acceleration
Given the normal force when the elevator starts N1 = 592N
Normal force after the elevator stopped N2 = 400N
When the elevator starts, its moves upward, the sum of force ∑F = Normal (N)force on the elevator - weight of the person( Fg)
When moving up;
N1 - Fg = ma
N1 = ma + Fg ...(1)
Stopping motion of the elevator occurs after the elevator has accelerates down. The sum of forces in this case will give;
N2 - Fg = -ma
N2 = -ma+Fg ...(2)
Adding equation 1 and 2 we will have;
N1+N2 = 2Fg
592N + 400N = 2Fg
992N 2Fg
Fg = 992/2
Fg = 496N
The weight of the person is 496N
\b) To get the person mass, we will use the relationship Fg = mg
g = 9.81m/s
496 = 9.81m
mass m = 496/9.81
mass = 50.56kg
c) To get the magnitude of acceleration of the elevator, we will subtract equation 1 from 2 to have;
N1-N2 = 2ma
592-400 = 2(50.56)a
192 = 101.12a
a = 192/101.12
a = 1.90m/s²
Two carts undergo an inelastic collision where they stick together. Cart A has an initial velocity v0, and the second cart B is initially at rest. After the collision, it is observed that the ratio of the final kinetic energy system to its initial kinetic energy is KfK0= 1/6. Determine the ratio of the carts' masses, mBmA. (Assume the track is frictionless.)
Answer:
Explanation:
Initial kinetic energy of the system = 1/2 mA v0²
If Vf be the final velocity of both the carts
applying conservation of momentum
final velocity
Vf = mAvo / ( mA +mB)
kinetic energy ( final ) = 1/2 (mA +mB)mA²vo² / ( mA +mB)²
= mA²vo² / 2( mA +mB)
Given 1/2 mA v0² / mA²vo² / 2( mA +mB) = 6
mA v0² x ( mA +mB) / mA²vo² = 6
( mA +mB) / mA = 6
mA + mB = 6 mA
5 mA = mB
mB / mA = 5 .
A uniform rod of mass 2.30 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 5.30 kg is attached to one end and a second mass m2 = 3.50 kg is attached to the other end of the rod. Treat the two masses as point particles.
A) What is the moment of inertia of the system?B) If the rod rotates with an angular speed of 2.00 rad/s, how much kinetic energy does the system have?C) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined?D) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.00 rad/s?
Answer:
Explanation:
Moment of inertia of the rod = 1/12 m L²
m is mass of the rod and L is its length
= 1/2 x 2.3 x 2 x 2
= 4.6 kg m²
Moment of inertia of masses attached with the rod
= m₁ d² + m₂ d²
m₁ and m₂ are masses attached , and d is their distance from the axis of rotation
= 5.3 x 1² + 3.5 x 1²
= 8.8 kg m²
Total moment of inertia = 13.4 kg m²
B )
Rotational kinetic energy = 1/2 I ω²
I is total moment of inertia and ω is angular velocity
= .5 x 13.4 x 2²
= 26.8 J .
C )
when mass of rod is negligible , moment of inertia will be due to masses only
Total moment of inertia of masses
= 8.8 kg m²
D )
kinetic energy of the system
= .5 x 8.8 x 2²
= 17.6 J .
(A) Total moment of inertia is 13.4 kgm²
(B) Total kinetic energy is 26.8J
(C) Moment of inertia is 8.8 kgm²
(D) Kinetic energy is 17.6J
Rotational motion:
(A) The moment of inertia of the rod is given by:
I = 1/12 mL²
where m is the mass of the rod
and L is the length
So,
I = (1/12) × 2.3 × 2²
I = 4.6 kgm²
Now, the moment of inertia of masses attached to the rod is given by:
I' = m₁ d² + m₂d²
where m₁ and m₂ are masses
and d is their distance from the axis of rotation
I' = 5.3 × 1² + 3.5 × 1²
I' = 8.8 kgm²
The total moment of inertia of the system is given by:
I(tot) = I + I'
I(tot) = 13.4 kgm²
(B) The rotational kinetic energy of an object with a moment of inertia I and angular velocity ω is given by:
KE = 1/2 I(tot)ω²
KE = 0.5 × 13.4 × 2²
KE = 26.8J
(C) If the mass of the rod is negligible, then the moment of inertia of the rod will be zero. So the total moment of inertia will be
I(tot) = I' = 8.8 kgm²
(D) the kinetic energy of the system when the mass of the rod is negligible and the angular speed is 2 rad/s is given by:
KE = 1/2 I'ω²
KE = 0.5 × 8.8 × 2²
KE = 17.6J
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A 18-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 30 N. Starting from rest, the sled attains a speed of 2.0 m/s in 8.5 m. Find the coefficient of kinetic friction between the runners of the sled and the snow. Num
Answer:
Coefficient of kinetic friction = 0.146
Explanation:
Given:
Mass of sled (m) = 18 kg
Horizontal force (F) = 30 N
FInal speed (v) = 2 m/s
Distance (s) = 8.5 m
Find:
Coefficient of kinetic friction.
Computation:
Initial speed (u) = 0 m/s
v² - u² = 2as
2(8.5)a = 2² - 0²
a = 0.2352 m/s²
Nweton's law of :
F (net) = ma
30N - μf = 18 (0.2352)
30 - 4.2336 = μ(mg)
25.7664 = μ(18)(9.8)
μ = 0.146
Coefficient of kinetic friction = 0.146
Nuclear fusion in our Sun happens when
- hydrogen atoms combine to make helium atoms and release energy
- uranium atoms break apart and release energy
- hydrogen atoms are burned and release energy
- helium atoms break apart and release energy
Answer:
A
Explanation:
Fussion occurs when elements of lower atomic mass combines to form that of a larger atomic mass, releasing energy in the process .
Hydrogen has a lower atomic mass than Helium.
One end of an insulated metal rod is maintained at 100c and the other end is maintained at 0.00 c by an ice–water mixture. The rod has a length of 75.0cm and a cross-sectional area of 1.25cm . The heat conducted by the rod melts a mass of 6.15g of ice in a time of 10.0 min .find the thermal conductivity k of the metal?k=............ W/(m.K)
Answer:
The thermal conductivity of the insulated metal rod is [tex]202.92\,\frac{W}{m\cdot K}[/tex].
Explanation:
This is a situation of one-dimensional thermal conduction of a metal rod in a temperature gradient. The heat transfer rate through the metal rod is calculated by this expression:
[tex]\dot Q = \frac{k_{rod}\cdot A_{c, rod}}{L_{rod}}\cdot \Delta T[/tex]
Where:
[tex]\dot Q[/tex] - Heat transfer due to conduction, measured in watts.
[tex]L_{rod}[/tex] - Length of the metal rod, measured in meters.
[tex]A_{c,rod}[/tex] - Cross section area of the metal rod, measured in meters.
[tex]k_{rod}[/tex] - Thermal conductivity, measured in [tex]\frac{W}{m\cdot K}[/tex].
Let assume that heat conducted to melt some ice was transfered at constant rate, so that definition of power can be translated as:
[tex]\dot Q = \frac{Q}{\Delta t}[/tex]
Where Q is the latent heat required to melt the ice, whose formula is:
[tex]Q = m_{ice}\cdot L_{f}[/tex]
Where:
[tex]m_{ice}[/tex] - Mass of ice, measured in kilograms.
[tex]L_{f}[/tex] - Latent heat of fussion, measured in joules per gram.
The latent heat of fussion of water is equal to [tex]330000\,\frac{J}{g}[/tex]. Hence, the total heat received by the ice is:
[tex]Q = (6.15\,g)\cdot \left(330\,\frac{J}{g} \right)[/tex]
[tex]Q = 2029.5\,J[/tex]
Now, the heat transfer rate is:
[tex]\dot Q = \frac{2029.5\,J}{(10\,min)\cdot \left(60\,\frac{s}{min} \right)}[/tex]
[tex]\dot Q = 3.382\,W[/tex]
Turning to the thermal conduction equation, thermal conductivity is cleared and computed after replacing remaining variables: ([tex]L_{rod} = 0.75\,m[/tex], [tex]A_{c,rod} = 1.25\times 10^{-4}\,m^{2}[/tex], [tex]\Delta T = 100\,K[/tex], [tex]\dot Q = 3.382\,W[/tex])
[tex]\dot Q = \frac{k_{rod}\cdot A_{c, rod}}{L_{rod}}\cdot \Delta T[/tex]
[tex]k_{rod} = \frac{\dot Q \cdot L_{rod}}{A_{c,rod}\cdot \Delta T}[/tex]
[tex]k_{rod} = \frac{(3.382\,W)\cdot (0.75\,m)}{(1.25\times 10^{-4}\,m^{2})\cdot (100\,K)}[/tex]
[tex]k_{rod} = 202.92\,\frac{W}{m\cdot K}[/tex]
The thermal conductivity of the insulated metal rod is [tex]202.92\,\frac{W}{m\cdot K}[/tex].
Archimedes and Heron are playing on a seesaw. Archimedes weighs 75 kg and Heron weighs 150 kg. If Heron is sitting 2 meters from the fulcrum, how many meters does Archimedes need to sit from the fulcrum?
Answer:
4metresExplanation:
Using the principle of moment to solve the problem. The principle states that the sum of clockwise moments is equal to the sum of anticlockwise moment.
Moment = force *perpendicular distance
Moment of Archimedes about the fulcrum = 75 * x ... 1
x is the distance of Archimedes from the fulcrum
Moment of Heron about the fulcrum = 150 * 2 = 300kgm... 2
Equation 1 and 2 according to principle of moment to get x we have;
75x = 300
x = 300/75
x = 4metres
Archimedes need to sit 4m from the fulcrum
Assuming 100% efficient energy conversion, how much water stored behind a 50 centimetre high hydroelectric dam would be required to charge battery
Complete question is;
Assuming 100% efficient energy conversion how much water stored behind a 50 centimeter high hydroelectric dam would be required to charge the battery with power rating, 12 V, 50 Ampere-minutes
Answer:
Amount of water required to charge the battery = 7.35 m³
Explanation:
The formula for Potential energy of the water at that height = mgh
Where;
m = mass of the water
g = acceleration due to gravity = 9.8 m/s²
H = height of water = 50 cm = 0.5 m
We know that in density, m = ρV
Where;
ρ = density of water = 1000 kg/m³
V = volume of water
So, potential energy is now given as;
Potential energy = ρVgH = 1000 × V × 9.8 × 0.5 = (4900V) J
Now, formula for energy of the battery is given as;
E = qV
We are given;
q = 50 A.min = 50 × 60 = 3,000 C
V = 12 V
Thus;
qV = 3,000 × 12 = 36,000 J
E = 36,000 J
At a 100% conversion rate, the energy of the water totally powers the battery.
Thus;
(4900V) = (36,000)
4900V = 36,000
V = 36,000/4900
V = 7.35 m³
A pendulum on a planet, where gravitational acceleration is unknown, oscillates with a time period 5 sec. If the mass is increased six times, what is the time period of the pendulum?
Explanation:
We have, a pendulum on a planet, oscillates with a time period 5 sec. The formula used to find the time period is given by :
[tex]T=2\pi \sqrt{\dfrac{l}{g}}[/tex]
l is length of the pendulum
g is acceleration due to gravity on which it is placed
It is clear that, the time period of pendulum is independent of the mass. Hence, if the mass is increased six times, its time period remains the same.
