Answer:
[tex]64\; {\rm m}[/tex], assuming that the rollercoaster is not attached to the track.
Explanation:
Let [tex]r[/tex] denote the radius of the loop. The height of the top of the loop would be [tex]2\, r[/tex].
Let [tex]a[/tex] denote the acceleration of the rollercoaster. At any position in the loop, if the speed of the rollercoaster is [tex]v[/tex], the (centripetal) acceleration of the rollercoaster would be:
[tex]\displaystyle a = \frac{v^{2}}{r}[/tex].
Let [tex]m[/tex] denote the mass of the rollercoaster. The net force on the rollercoaster would then be:
[tex]\displaystyle F_\text{net} = m\, a = \frac{m\, v^{2}}{r}[/tex].
The rollercoaster would stay on the track (and goes around the loop without falling off) only if the normal force [tex]F_\text{normal}[/tex] between the track and the rollercoaster is non-negative. In other words: it is necessary that [tex]F_\text{normal} > 0[/tex] for the rollercoaster to stay on the track.
At the top of the loop, [tex]F_\text{normal}[/tex] and the weight of the rollercoaster [tex]m\, g[/tex] are in the same direction as the centripetal acceleration (downwards towards the center of the loop.) Hence:
[tex]F_\text{net} = F_\text{normal} + m\, g[/tex].
Let [tex]v_\text{top}[/tex] denote the speed of the rollercoaster at the top of the loop.
[tex]\begin{aligned} F_\text{normal} &= F_\text{net} - m\, g \\ &= \frac{m\, v_\text{top}^{2}}{r} - m\, g\end{aligned}[/tex].
If [tex]F_\text{normal} > 0[/tex] at the top of the loop, then:
[tex]\displaystyle \frac{m\, v_\text{top}^{2}}{r} - m\, g > 0[/tex].
[tex]\displaystyle v_{\text{top}}^{2} > g\, r[/tex].
At the same time, by the conservation of energy, the sum of the kinetic energy [tex]\text{KE}[/tex] and gravitational potential energy [tex]\text{GPE}[/tex] of the rollercoaster should stay the same during the entire ride. Assuming that [tex]\text{GPE}\![/tex] is [tex]0[/tex] at the bottom of the loop:
[tex]\begin{aligned}& \text{KE at the bottom}\\ &= \text{KE at the top} + \text{GPE at the top}\end{aligned}[/tex].
Let [tex]v_{0}[/tex] denote the speed of the rollercoaster at the bottom of the loop.
[tex]\begin{aligned}\text{KE at the bottom} = \frac{1}{2}\, m\, {v_{0}}^{2}\end{aligned}[/tex].
The speed of the rollercoaster at the top of the loop [tex]v_\text{top}[/tex] is at least [tex](g/r)[/tex]. Therefore:
[tex]\begin{aligned}& \text{KE at the top}= \frac{1}{2}\, m\, {v_{\text{top}}}^{2} > \frac{1}{2} \, m\, g\, r\end{aligned}[/tex].
Since the height of the loop is [tex]2\, r[/tex], the [tex]\text{GPE}[/tex] of the rollercoaster at the top of the loop would be:
[tex]\text{GPE at the top} = m\, g\, h = 2\, m\, g\, r[/tex].
Thus:
[tex]\begin{aligned} \frac{1}{2}\, m\, {v_{0}}^{2} &= \text{KE at the bottom}\\ &= \text{KE at the top} + \text{GPE at the top} \\ & > \frac{1}{2}\, m\, g\, r + \text{GPE at the top}\\ & = \frac{1}{2}\, m\, g\, r+ 2\, m\, g\, r \\ &= \frac{5}{2}\, m\, g\, r\end{aligned}[/tex].
In other words:
[tex]\displaystyle \frac{1}{2}\, m\, {v_{0}}^{2} > \frac{5}{2}\, m\, g\, r[/tex].
Rearrange and simplify to obtain a bound on [tex]r[/tex]:
[tex]\begin{aligned} r < \frac{(1/2)\, m\, {v_{0}}^{2}}{(5/2)\, m\, g}\end{aligned}[/tex].
[tex]\begin{aligned} r < \frac{{v_{0}}^{2}}{5\, g}\end{aligned}[/tex].
Given that [tex]v_{0} = 40\; {\rm m\cdot s^{-1}[/tex] and [tex]g = 10\; {\rm N \cdot kg^{-1}} = 10\; {\rm m\cdot s^{-2}[/tex]:
[tex]\begin{aligned} r & < \frac{{v_{0}}^{2}}{5\, g} \\ &= \frac{(40\; {\rm m\cdot s^{-1}})^{2}}{5 \times (10\; {\rm m\cdot s^{-2}})} \\ &= 32\; {\rm m}\end{aligned}[/tex].
Hence, the radius of this loop is at most [tex]32\; {\rm m}[/tex], such that the height of the top of this loop is at most [tex]2 \times 32\; {\rm m} = 64\; {\rm m}[/tex].
A. 15
B. 1
C. 5
D. 9
The correct answer is D (I’m pretty sure) but I don’t quite get how to read the ammeter… It would be helpful if someone can explain in a few sentences why it’s 9 :)
Question 9 of 15
6
an object is moving due north at 32m/s does this tell you the speed or the velocity of the object, or
both?
Given that the object is moving due north at 32 m/s, this simply expresses the velocity of the object.
What is a scalar quantity?This is a quantity that has magnitude but no direction. Examples include energy, work, speed, distance etc
What is a vector quantity?This is a quantity which have both magnitude and direction. Example include acceleration, velocity, moment, displacement etc
What is velocity?Velocity is the rate of change of displacement with time.
Velocity = displacement / time
Velocity can be written as 4 m/s due east
What is speed?This the distance travelled per unit time.
Speed = distance / time
Speed can be written as 4 m/s
Considering the question given above, we were told that the object is moving due north. This simply talks about the velocity.
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In a nuclear reactor a moderator is used to
Answer: A material called moderator is used to slow down the neutrons released during nuclear fission. The source's neutrons have a high speed and energy. The neutrons' speed is slowed by heavy water or graphite moderators.
Explanation:
Can someone please answer this, ill give you brainliest Would be very appreciated.
Answer:
See below ~
Explanation:
Sun - provides energy that drives the cycleprecipitation - water falling from the skyrunoff - water moving across impervious surfacesseepage - water soaking into the groundevaporation - liquid water becoming a vapor to return to the atmospherecondensation - water vapor returning to liquid formThe answers are
Sun
Provides energy that drives the circle.precipitation
water falling from skyrun off
Water moving across impervious surfacesevaporation
Liquid water becomes vapour to return to the atmosphereseapage
water soaking into the groundcondensation
water vapour returning to liquid formWhy do the north and south poles of these magnets attract each other?
Answer:
here
Explanation:
Unlike-poles attract: When a north pole and south pole point together, the arrows point in the SAME direction so the field lines can join up and the magnets pull together (attract).
A 480 g falcon reaches a speed of 75 m/s in a vertical dive. if we assume that the falcon speeds up under the influence of gravity only, what is the minimum height of the dive needed (ignore air friction) in meters.
Answer:
286.7 m
Explanation:
So we are assuming the PE of the falcon is converted to KE
KE = PE
1/2 (.480)(75)^2 = .480 (9.81)(h ) solve for h = 286.7 m
what parameters affects the inductance of a coil
Answer:
Number of Wire Turns in the Coil.
Explanation:
The greater the number of turns of wire in the coil, the greater the inductance. Fewer turns of wire in the coil results in lesser inductance. More coils of wires indicate a greater amount of magnetic field force for a given amount of coil current.
pls complete this table thankyou
Answer:
1)10 m/s
2) 20 m/s
3) 2 s
4) 500 m
5)1000 km/h
Average speed = distance travelled / time.
( note: distance must be in (m) and time in sec, if not then you convert ).
1) average speed = 20/2 = 10mls.
2) average speed = 100/5 = 20 m/s.
3) since we aren't given (time) let's call it x
so we replace the unknown time with x..
average speed = 2/x = 1
then cross multiply
you get x (the unknown time) as 2s {seconds}.
(to check if it's correct just add the time we got back into the equation and see if you would get a erage speed as 1m/s).
4) do the same, replace distance as x or any letter you want )
average speed = x/ 10 = 50
cross multiply
you get x = 500m {meters}
5) (we need to convert km to meters and time to secs because that's what we are working with).
200km = 200,000 m { to convert to meters you multiply the given by 1000, 1km = 1000m).
for 2h, we know that:
60 seconds makes 1 minute
60 minutes makes an hour.
so we multiply 60 by 60 we get 3600mins then we multiply it by 2 to get 7200 secs
so now
Average speed = 200,000/7200 = 27.77 m/s.
Here you go..
hope this helps
Good luck and ace that test.
a.5 kg model rocket launches with a thrust of 5 n in the upward direction. can it lift off of the ground? (hint: gravity is pulling it toward
the earth at 9.8 m/s2) (f=mx a) assume there is no wind resistance.
Answer:
F = F2 - F1 where F is the net force upwards
F = 5 - (.5 * 9.8) = (5 - 4.9) N = .1 N
Since there is a net force in the upwards direction the rocket should experience an upwards acceleration.
Your training partner has stopped pedaling during the spinning class you are both taking. She wants to check her exercise intensity level. You have a piece of exercise technology for this job and can continue to pedal while keeping tabs on your workout progress. Select the choice below that you would be using.
Group of answer choices
Heart rate monitor
Blood pressure monitor
Stopwatch
Pedometer
Answer:
Heart rate monitor I think
Explanation:
you would know how intense the pedaling is by knowing your heart beat rate as of the pedaling is so intense your heart beat increases and if it was not so much your pedaling is not so intense.
This works also for any other sports .
~--Hope this helped--~
Answer: it’s Heart rate monitor
Explanation:
you use a heart rate monitor to check your intensity level by seeing how fast your heart goes
name the quantity whose unit is 'newton'
The symbol most often used to describe density is?
Answer:
he density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume. The symbol most often used for density is ρ
Explanation:
A box on a spring is pushed to point A and allowed to oscillate. Describe the motion of the box at points A, B, and C. Be sure to use the words maximum velocity, minimum velocity, maximum displacement, minimum displacement, maximum acceleration, minimum acceleration, equilibrium, and restoring force where appropriate.
As the box begins to oscillate, it will have minimum velocity at maximum displacement and maximum velocity at minimum displacement.
Oscillation of the box
The force applied to box will cause a displacement of the box from equilibrium position to maximum position which increases as the applied force increases.
Therefore, as the box begins to oscillate, it will have minimum velocity at maximum displacement and maximum velocity at minimum displacement.
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In winter, your classroom is warmed by a heater. Your teacher asks you to close the window because "this will stop the cold from getting in". Explain what is actually happening to the flow of heat in this scenario.
When the window is closed the heat is trapped inside the classroom which is circulating around the room but when the window is opened, the heat is escaping so most of the heat is escaping rather than circulating the room.
In winter, your classroom is warmed by a heater. Your teacher asks you to close the window because "this will stop the cold from getting in" because of the thermal gradient present between the outside colds air and the warm air present inside the room, as the window gets closed the outside air would not able to extract the thermal energy of the warm air present inside the room.
What is thermal energy?It can be defined as the form of the energy in which heat is transferred from one body to another body due to their molecular movements, thermal energy is also known as heat energy.
Thermal energy can be produced with help of various means such as by burning fossil fuels, with the help of solar energy.
As given in the problem statement In winter, your classroom is warmed by a heater. Your teacher asks you to close the window because "this will stop the cold from getting in because when the window is closed the cold air from the outside would not be able to extract the heat from the warmed air present inside the room
Thus, the flow of heat would get obstructed by the closing of the window
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What is the change in the internal energy of a system that does 600 joules of work and absorbs 800 joules of heat?
A. -200 J
B. -1,400 J
C. 1,400 J
D. 200 J
[tex]\huge{\color{red}{\fbox{\textsf{\textbf{Answer}}}}} [/tex]
200J
Explanation:
Change in the internet energy = Heat aborsbed - work done
800 - 600
200 J
Answer:
D. 200J
Explanation:
A common brick is about 1.8 times denser than water. what is the apparent weight of a 0.20 m3 block of bricks under water?
Answer:
Pressure of .2 m^3 of bricks:
Pb = ρ g H = 1.8 ρw * 9.80 m/s^2 * .20 m = 1800 * 9.8 * .2 = 3530 Pascals
ρb = 1.8 ρw = 1.8 since the density of bricks is 1.8 that of water
Pw = 1 * 9.8 * 1000 * .2 = 1960 Pascals
W = P * A pressure * Area = Force
Pnet = 1570 Pascals - pressure due to bricks under water
F = 1570 N/m^2 * .2m^2 = 63 N force on pile of bricks
A stone of mass 6kg is released from a height of 30m, calculate the velocity before the impact (take gravity=10m/s)
Answer:
23,49 m/s
Explanation:
Ep= Ek
mgh=mv2/2
6×10×30=6v2/2
1800=6 v2/2
6 v2=3600
v2 =600
v=24,49 m/s
The velocity of the stone, if a stone of mass 6 kg is released from a height of 30 m, is 24.5 m/s.
What is velocity?When something is moving, its velocity shows how quickly its location is changing as seen from a certain angle and as measured by a particular unit of time.
If a point moves a certain distance along its path in a predetermined length of time, its average speed throughout that time is equal to the distance traveled divided by the travel time. For instance, a train traveling 100 km in two hours is doing it at an average speed of 50 km/h.
Given:
The mass of the stone, m = 6 kg,
The height of the release, h = 30 m,
The value of gravity, g = 10 m/s,
Calculate the velocity using energy conservation as shown below,
The kinetic energy = potential energy (Energy conservation)
1/2 × 6 × v² = 6 × 10 × 30
v² = 300 × 2
v² = 600
v = √600
v = 10√6
v = 10 × 2.45
v = 24.49 or 24.5 m/s
Thus, the velocity is 24.5 m/s.
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a car, moving at 30 m/s toward you, blows its horn at 500 Hz. if you are standing stil what frequency do you hear?
Answer:
If the engine is making sound, then the passer (like you) will be dead
ANYWAYS
but if it was silent you can hear it softly because since speed of light (the car) is lower than the speed of sound ( horn )
Explanation:
since the car is going in Miles per second if you convert it to Speed of sound that is what is equals to
c=√K^s / ρ
Write the relation between mass and weight of a body
Answer:
[tex]\text{Weight} = \text{Mass} \times \text{Gravitational acceleration}[/tex]
Explanation:
Which definition describes work?
Answer:
i would say putting effort into something
Explanation:
Answer:
put many effort into one thing or many
A small car of mass 450kg is pushing a large truck of mass 980kg due east on a level road. The car exerts a horizontal force of 1520N on the truck. What is the magnitude of the force that the truck exests on the car
F = 1520N
explanation:
by newton third law of motion every action has equal and opposite reaction so truck exert on it so F = 1520N
that's my answer
While unearthing ancient pottery in the gobi desert, an archaeologist discovers a pot containing a large amount of naturally radioactive americium-241, which experiences alpha decay.
the archaeologist needs to protect himself, but also doesn't want to overheat in the desert sun. in addition to a facemask, what is the most appropriate safety precaution that the archaeologist should take to protect against the alpha particles without overheating?
The most appropriate safety precaution that the archaeologist should take to protect against the alpha particles without overheating by wear a pair of normal leather gloves. Option D is correct.
What is radioactivity?
The act of producing radiation spontaneously is known as radioactivity. This is accomplished by an unstable atomic nucleus that want to give up some energy in order to move to a more stable form.
Radiation is being employed to assist humanity in medical, academia, and industry, as well as to generate power.
Radiation is also important in agriculture, archaeology, space exploration, law enforcement, geology a variety of other fields.
The most appropriate safety precaution that the archaeologist should take to protect against the alpha particles without overheating by wear a pair of normal leather gloves.
Hence, option D is correct.
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can some one solve this for me please
#solid in liquid
gelatin#solid in gas
Dry ice(CO2)#solid in solid
synthesized gems#solid in liquid
magma#Liquid in a gas
MethaneSelect the correct answer from each drop-down menu. a tourist bus is carrying passengers from the bottom of a hill to the top. the people, the bus, and the luggage can be analyzed as a single . the total amount of energy in the system as the bus travels. this situation happens because some of the kinetic energy changes to energy because of friction between the tires and the road.
The correct answer from each drop-down menu are in this case:
systemdecreasesthermalWhat are the forms of energy conservation?In a given mechanical system, in which forms of energy related to electromagnetic or thermal phenomena are not present, it can be said that the total energy of the system is purely mechanical. Thus, the Principle of Conservation of Energy implies the conservation of mechanical energy.
This, in turn, is the sum of the amounts of kinetic energy and various forms of potential energy (gravitational and elastic among them). Although mechanical energy is always constant, the amount of each of its components can change such that the total energy remains constant.
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A 40.0 kg objects is subject to two forces, one of +18.0 N and one of -6.0 N. What is the acceleration the crate undergoes?
A. 0.3 m/s2 B. 1.67 m/s2 C. 3.3 m/s2 D. 4.0 m/s2 E. 480 m/s2
∑F=m.a
18 - 6 = 40 x a
12 = 40a
a = 0.3 m/s²
Why can you get a shock if you touch a metal doorknob after walking across a wool carpet? (1 Point) You have gained electrons; the doorknob has no electrons. You have gained neutrons; the doorknob has fewer electrons. You have lost electrons; the doorknob has many electrons. You have gained electrons; the doorknob has many electrons.
Why can you get a shock if you touch a metal doorknob after walking across a wool carpet is because you have gained neutrons; the doorknob has fewer electrons. This is further explained below.
What are electrons?Electrons can be defined as a stable subatomic particles with a negative electrical charge that is found in all atoms and serves as the major carrier of electricity in solids.
In conclusion, You have an unbalanced charge, while the doorknob is neutral. you have gained neutrons; the doorknob has fewer electrons.
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Stio
choose the true statements about magnetic fields and forces. (choose 3)
the north pole attracts the south pole of a magnet.
the north pole repels the south pole of a magnet.
forces caused by magnetic fields are weaker closer to the magnet.
forces caused by magnetic fields are weaker farther from the magnet.
magnetic forces can act on an object even if the object isn't touching the magnet.
an object must be in touching a magnet in order for a magnetic force to act on it.
3 pt
The true statements about magnetic fields and forces will be A,D and E.
What is a magnet?An iron piece,alloy, or other substance with its constituent atoms arranged in such a way that it shows magnetism qualities,
The function of the magnet is attracting other iron-containing objects or aligning itself in a magnetic field.
There are two poles of the magnet;
1. North Pole.
2. South Pole.
The same poles repel each other, while the opposite poles attract each other. In a sense, south-south and north-north repel. While the north-south and the south-north attract each other.
The correct statements are;
(A). The north pole attracts the south pole of a magnet.
(D)Forces caused by magnetic fields are weaker farther from the magnet.
(E)Magnetic forces can act on an object even if the object isn't touching the magnet.
Hence, the true statements about magnetic fields and forces will be A,D and E.
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Compare solar heating panels and solar electric panels.
pls I really need help
Answer:
We know that a solar electrical panel converts sunlight to electricity by means of solar cells and then, the electricity can be used as any electrical current.
I am not familiar with solar heating panels but assume that a liquid is heated by sunlight and then circulated thru the area that needs heating - it converts heat from sunlight to usable heat. The heat energy could also be stored and delivered at a different time (accumulated during the day and delivered at night). This is somewhat similar to a company freezing water at night when electricity is cheaper and then using the cooled water during the day for cooling.
Explain how nuclear physics works?
Answer:
Nuclear physics are the study of protons, and neutrons at the center of an atom. This study shows the interactions between atoms, including what holds them together in a small space. Nuclear physics include fission, fusion, and decay.
Identify the reactants and products in each of the following reactions: sodium +carbon > sodium hydroxide +hydrogen
Answer:
Hydrochloric acid and sodium hydroxide interact, resulting in salt and a release of heat. As we can see, the result of the interaction of two highly aggressive compounds is table salt and water – compounds that are ultimately harmless, even beneficial, to human beings.
Explanation:
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