A 100 kg roller coaster comes over the first hill at 2 m/sec (vo). The height of the first hill (h) is 20 meters. See roller diagram below.
1) Find the total energy for the roller coaster at the initial point.
2) Find the potential energy at point A using the PE formula.
3) Use the conservation of energy to find the kinetic energy (KE) at point B.
4) Find the potential energy at point C.
5) Use the conservation of energy to find the Kinetic Energy (KE) of the roller coaster at point C.
6) Use the Kinetic Energy from C, find velocity of the roller coaster at point C.
Answers
For the 100 kg roller coaster that comes over the first hill of height 20 meters at 2 m/s, we have:
1) The total energy for the roller coaster at the initial point is 19820 J
2) The potential energy at point A is 19620 J
3) The kinetic energy at point B is 10010 J
4) The potential energy at point C is zero
5) The kinetic energy at point C is 19820 J
6) The velocity of the roller coaster at point C is 19.91 m/s
1) The total energy for the roller coaster at the initial point can be found as follows:
[tex] E_{t} = KE_{i} + PE_{i} [/tex]
Where:
KE: is the kinetic energy = (1/2)mv₀²
m: is the mass of the roller coaster = 100 kg
v₀: is the initial velocity = 2 m/s
PE: is the potential energy = mgh
g: is the acceleration due to gravity = 9.81 m/s²
h: is the height = 20 m
The total energy is:
[tex] E_{t} = KE_{i} + PE_{i} = \frac{1}{2}mv_{0}^{2} + mgh = \frac{1}{2}*100 kg*(2 m/s)^{2} + 100 kg*9.81 m/s^{2}*20 m = 19820 J [/tex]
Hence, the total energy for the roller coaster at the initial point is 19820 J.
2) The potential energy at point A is:
[tex] PE_{A} = mgh_{A} = 100 kg*9.81 m/s^{2}*20 m = 19620 J [/tex]
Then, the potential energy at point A is 19620 J.
3) The kinetic energy at point B is the following:
[tex] KE_{A} + PE_{A} = KE_{B} + PE_{B} [/tex]
[tex] KE_{B} = KE_{A} + PE_{A} - PE_{B} [/tex]
Since
[tex] KE_{A} + PE_{A} = KE_{i} + PE_{i} [/tex]
we have:
[tex] KE_{B} = KE_{i} + PE_{i} - PE_{B} = 19820 J - mgh_{B} = 19820 J - 100kg*9.81m/s^{2}*10 m = 10010 J [/tex]
Hence, the kinetic energy at point B is 10010 J.
4) The potential energy at point C is zero because h = 0 meters.
[tex] PE_{C} = mgh = 100 kg*9.81 m/s^{2}*0 m = 0 J [/tex]
5) The kinetic energy of the roller coaster at point C is:
[tex] KE_{i} + PE_{i} = KE_{C} + PE_{C} [/tex]
[tex] KE_{C} = KE_{i} + PE_{i} = 19820 J [/tex]
Therefore, the kinetic energy at point C is 19820 J.
6) The velocity of the roller coaster at point C is given by:
[tex] KE_{C} = \frac{1}{2}mv_{C}^{2} [/tex]
[tex] v_{C} = \sqrt{\frac{2KE_{C}}{m}} = \sqrt{\frac{2*19820 J}{100 kg}} = 19.91 m/s [/tex]
Hence, the velocity of the roller coaster at point C is 19.91 m/s.
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Related Questions
16g 2g/cm3 what is the Volume
Answers
Answer:
V = 1.25E-7 cubic meter
A car accelerates from rest to a speed of v. Later, on a highway it accelerates from v to 2v. Which takes more energy, going from 0 to v, or from v to 2v?
Answers
Answer:
I believe 0 to V sorry if im wrong
Explanation:
A small ball is attached to one end of a spring that has an unstrained length of 0.201 m. The spring is held by the other end, and the ball is whirled around in a horizontal circle at a speed of 3.41 m/s. The spring remains nearly parallel to the ground during the motion and is observed to stretch by 0.0176 m.
Required:
By how much would the spring stretch if it were attached to the ceiling and the ball allowed to hang straight down, motionless?
Answers
The extension of the spring when the ball is allowed to hang straight down, motionless is 0.0032 m.
The given parameters;
unstrained length, l₁ = 0.201 mextension of the string, x = 0.0176 mspeed of the ball, v = 3.41 m/sThe radius of the circular path when spring is stretched is calculated as;
R = l₁ + x
R = 0.201 + 0.0176
R = 0.2186 m
The spring constant is calculated as follows;
[tex]F = ma\\\\Kx = \frac{mv^2}{R} \\\\K = \frac{mv^2}{Rx} \\\\K = \frac{(3.41)^2 m}{0.2186 \times 0.0176} \\\\K = 3,022.4 m \ N/m[/tex]
The extension of the spring when the ball is allowed to hang straight down, motionless;
[tex]F = mg\\\\Kx=mg\\\\x = \frac{mg}{K} \\\\x = \frac{9.8 m}{3022.4 m} \\\\x = 0.0032 \ m[/tex]
Thus, the extension of the spring when the ball is allowed to hang straight down, motionless is 0.0032 m.
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Two conditions must
be met for work to be done, what are they?
Answers
The two conditions are:
1) Application of-force on the body.
2) Displacement of the body in the direction of force.
Hope this helps!
You use a rope 2.00 m long to swing a 10 kg weight around your head. The tension in the rope is 20 N. In half a revolution how much work in J is done by the rope on the weight
Answers
Answer:
No work is done on the weight. :3
To solve this we must be knowing each and every concept related to work and its calculation. Therefore, 250J is the work done in joule by the rope on the weight.
What is work?Work in physics is the energy delivered to or out of an item by applying force across a displacement. It is frequently expressed in its most basic form as the combination of displacement and force.
When a force is applied, it is said to produce positive work if it has a proportion in the orientation of the movement of a site of application. Work done is positive when the direction of force acting on the object and displacement of the object both are in the same direction.
Mathematically,
Work= force ×displacement
force =20 N
displacement=2.00 m
displacement=2×3.14×2=12.5m
substituting all the given values in the above equation, we get
Work= 20 ×12.5
Work =250J
Therefore, 250J is the work done in joule by the rope on the weight.
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2. What is the period of 350 waves passing a point in 5 seconds?
Answers
Answer:
IF SHE BREATHS SHES A T.H.OT
Explanation:
Pls dont hate me its meme k ,_.
Copper is a type of metal.
A block of copper has a mass of 2.0kg.
The block of copper absorbs 12000J of thermal energy.
The specific heat capacity of copper is 385J /(kg°C).
What is the temperature rise of the copper?
A 15.6°C B 31.2°C C 46.8°C D 62.4°C
Answers
The temperature rise in the copper is. I think its 0.393
The temperature rise in the copper is. I think its 0.393. Copper is a chemical element with the symbol Cu (from Latin: cuprum) and atomic number 29.
What is Capacity of copper?The chemical element copper (Cu) is a reddish, incredibly ductile metal belonging to Periodic Group 11 (Ib) that has an exceptional ability to conduct heat and electricity.
In nature, copper can be found in its free metallic state. Neolithic (New Stone Age) humans originally utilised this local copper (about 8000 BCE) as a substitute for stone.
Around 4000 BCE, Mesopotamia saw the beginning of metallurgy as copper was cast into molds, reduced to metal from ores with fire and charcoal, and purposefully alloyed with tin to form bronze (c. 3500 BCE).
Therefore, The temperature rise in the copper is. I think its 0.393. Copper is a chemical element with the symbol Cu (from Latin: cuprum) and atomic number 29.
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A block of wood mass 0.60 kg is balanced on top of a vertical port 2.0 m high. A 10 gm
bullet is fired horizontally into the block and the embedded bullet land at a 4.0 m from
the base of the port. Find the initial velocity of the bullet.
A. 10 3 m/s B. 8.32 m/s C. 3.82 m/s D. 1.0 m/s
Answers
Answer:
m V1 = (m + M) V2 conservation of momentum
T = time to fall 2 m
2 = 9.8 / 2 T^2 initial vertical velocity zero
T^2 = 4/9.8 T = .639 sec
Sx = V2 * .639 sec distance traveled horizontally
V2 = 4 /.639 = 6.26 m/sec
V1 = (m + M) / m * 6.26 m/sec from first equation
V1 = (600 + 10) / 10 * 6.26 m/s = 382 m/s
There seems to be some confusion on units
Note that 382 m/s is a reasonable answer for speed of bullet
1100 ft/sec is reasonable for a .22 cal bullet
1100 ft/sec / 3.28 ft/m = 335 m/sec
What is a lever?....
Answers
Answer:
A lever is a simple machine in the subject "S.T.E.M"
Explanation:
Levers use the following forces in order to be used: push or pull.
examples are crow bars,shovels, brooms and ect.
Is s=[tex]\frac{Ft^{2} }{2m}[/tex] a correct conversion from a=[tex]\frac{at^{2} }{2}[/tex]?
I just substituted "a" as [tex]\frac{F}{m}[/tex]
Answers
Answer:
well your substitution method is correct but make sure to double check the original formula
6. Explain a change that you can make in your diet to further your overall health.
Answers
Answer:
“Eat more delicious whole-food plants at every meal and snack. Fruits, vegetables, whole grains, nuts and seeds are packed with nutrients and contain satisfying fiber that is good for digestion, disease prevention and sustained energy.
Explanation:
Hope this helped
Which ONE of the following pairs of physical quantities consists of one scalar and one vector quantity?
A. Distance and speed
B.Speed and acceleration C.Displacement and velocity
D. Velocity and acceleration.
Answers
Answer:
speed and acceleration
Explanation:
speed is a scalar quantity
acceleration is a vector quantity
An electric heater is rated 300W 110V. The safety fuse in the circuit can withstand 15 A of current. How many heaters can be safely operated in the circuit
Answers
The number of heaters that can safely be operated in the circuit is 5 heaters.
From the question given above, the following data were obtained:
Power of heater = 300 W
Voltage (V) = 110 V
Current (I) = 15 A
Number of heaters = ?Next, we shall determine the power that can be drawn from the circuit. This can be obtained as follow:Voltage (V) = 110 V
Current (I) = 15 A
Power (P)= ?P = IV
P = 15 × 110
P = 1650 WThus, the power that can be drawn from the circuit is 1650 W
Finally, we shall determine the number of heaters that can be operated in the circuit. This can be obtained as follow:Power of heater = 300 W
Power of Circuit = 1650 W
Number of heaters = ?[tex]Number \: of \: heaters \: = \frac{power \: of \: circuit}{power \: of \: heater} \\ \\ = \frac{1650}{300} \\ \\ = 5.5[/tex]
From the calculation made above, the number of heaters that can be operated safely in the circuit is 5 heaters.
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A ball of mass 2.0 kg is travelling at a speed of 12 m/s. It moves towards an object of mass 3.0 kg which is at rest.
The ball hits the object and sticks to it.
Which row gives the total momentum, and the speed of both objects immediately after the collision?
total momentum (kg m/s)
A- 0
B- 0
С- 24
D- 24
AND..
speed (m/s)
A- 4.8
B- 8.0
C- 4.8
D- 8.0
Answers
Please find attached photograph for your answer.
Hope it helps.
Do comment if you have any query.
The velocity for the entire trip is 0.4 m/s as It takes her 500 seconds to make the round trip and 60 kg • m/s2 = (45 kg • v) + (20 kg • 3 m/s).
Path 1 = 400 m В B. A Path 2 = 200 m Path 3 = 300 m. Thus, option C is correct.
What is velocity?A particle's settling velocity known as the rate at which is travels through a still fluid. The specific gravity of the particles, their size, and their shape all have an impact on settling velocity.
A particle in still air will gravitationally settle and reach its terminal velocity fairly quickly. A particle's terminal velocity in a still fluid is referred to as the settling velocity (also known as the "sedimentation velocity").
Understanding variations in the hydraulic regime and interactions between sediment and fluid in the surf zone depends heavily on the particle settling velocity at the foreshore region. In contrast to sedimentation, which is the end product of the settling process, settling is the movement of suspended particles through the liquid.
Therefore, Thus, option C is correct.
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A 4.6 kg bucket of water is raised from a well by a rope. The acceleration of gravity is 9.8 m/s 2 . If the upward acceleration of the bucket is 3 m/s 2 , find the force exerted by the rope on the bucket. Use g
Answers
Hi there!
If we sum the forces acting on the bucket:
∑F = T (upward) - Mg (downward)
Thus:
ma = T - mg
We can rearrange for T:
ma + mg = T
Plug in the given values:
4.6(3 + 9.8) = T = 58.88 N
SOMEONEEEE HELP ME PLEASE ILL MARK YOUR BRAINLIST !!!
Answers
This was kinda hard thinking it might be that the new force is going to 4 times bigger than the original one.
for hundreds of years scientists deny the existence of rogue waves until the presence of when was finally caught on record. when and where was the first time a rogue wave was measured?
Answers
Answer:
A rogue wave estimated at 18.3 meters (60 feet) in the Gulf Stream off of Charleston, South Carolina. At the time, surface winds were light at 15 knots.
Explanation:
Rogue, freak, or killer waves have been part of marine folklore for centuries, but have only been accepted as real by scientists over the past few decades.
Rogues, called 'extreme storm waves' by scientists, are those waves which are greater than twice the size of surrounding waves, are very unpredictable, and often come unexpectedly from directions other than prevailing wind and waves.
Most reports of extreme storm waves say they look like "walls of water." They are often steep-sided with unusually deep troughs.
Since these waves are uncommon, measurements and analysis of this phenomenon is extremely rare. Exactly how and when rogue waves form is still under investigation, but there are several known causes:
Constructive interference. Extreme waves often form because swells, while traveling across the ocean, do so at different speeds and directions. As these swells pass through one another, their crests, troughs, and lengths sometimes coincide and reinforce each other. This process can form unusually large, towering waves that quickly disappear. If the swells are travelling in the same direction, these mountainous waves may last for several minutes before subsiding.
Focusing of wave energy. When waves formed by a storm develop in a water current against the normal wave direction, an interaction can take place which results in a shortening of the wave frequency. This can cause the waves to dynamically join together, forming very big 'rogue' waves. The currents where these are sometimes seen are the Gulf Stream and Agulhas current. Extreme waves developed in this fashion tend to be longer lived.
Hope this helps, have a nice day/night! :D
On January 1st, 1995, the first accurate measurement of a rogue wave took place. It was captured by a laser detector on Statoil's Draupner oil drilling rig, which is situated 100 miles off the Norwegian coast.
What is rogue wave?
Although rogue, freak, or killer waves have been mentioned in maritime legend for many years, scientists have only recently acknowledged their existence.
Scientists refer to these waves as "rogues," or "severe storm waves," since they are more than twice as large as the waves around them, very unpredictable, and frequently arrive from directions other than the prevailing wind and waves.
Extreme storm waves are typically described as looking like "walls of water" in reports. Frequently, they have steep sides and exceptionally deep valleys.
Measurements and analyses of this phenomenon are extremely rare because these waves are not common.
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I would like to know if it would be m/s² or just m/s and explain why. thanks
Answers
It will be
[tex] {m/s}^{2} [/tex]
I am just explaining with the units only, because you want to know the accurate unit.
[tex] \frac{m/s}{s} \\ = \frac{m}{s} \times \frac{1}{s} \\ = \frac{m}{s \times s} \\ = \frac{m}{ {s}^{2} } \\ = {m/s}^{2} [/tex]
Hope you understood.
Do comment if you have any query.
You have a particle of length 68 nm. What is this in meters?
A. 6.8 x 10^10 m
B. 6.8 x 10^14 m
C. 6.8 x 10^-11 m
D. 6.8 x 10^-8 m
The number after "^" that symbol are exponents
Answers
Don’t pay attention to this part
what is the magnitude of the torque that the axle must apply to prevent the disk from rotating?
Answers
The required torque at the axle, is given by the difference between the
moments of the applied forces.
The torque required is 19.62 N·m counterclockwise
Reasons:
The given parameters are;
Mass of the disk, m = 5.0 kg
Location of the axle = Half the radius of the disk
Diameter of the disk, D = 40 cm = 0.4 m
Applied mass, 0.1 m from the axle = 15 kg
Applied mass, 0.3 m from the axle = 10 kg
Required:
Magnitude of torque at the axle that prevent the disk from rotating
Solution:
Torque needed = Clockwise moment - Counterclockwise moment
Clockwise moment = (10 kg × 0.3 m + 5 kg × 0.1 m) × 9.81 m/s² = 34.335 N·m
Counterclockwise moment = 15 kg × 0.1 m × 9.81 m/s² = 14.715 N·m
τ + Counterclockwise moment = Clockwise moment
τ + 14.715 N·m = 34.335 N·m
Torque required, τ = 34.335 N·m - 14.715 N·m = 19.62 N·m
Torque required, τ = 19.62 N·m counterclockwise
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The probable question drawing obtained from a similar question online is attached
What energy is used or given off by a fire?
Answers
Answer:
Heat is given off by Fire.
Explanation:
v=VyV67.2 -8.2 m/s
Part B
Now let's see if your prediction agrees with the experimental results. There isn't any data at y=-3.5 m, so you'll need to interpolate by zooming in
on the relationship between y velocity (W) and y displacement. You'll use Tracker's Data tool to help with this analysis. Follow these steps:
• Change the vy versus t graph to a vy versus y graph. (Click the t label on the horizontal axis and select y. position y-component from the
menu.)
• It's a little hard to see what's going on with this graph at y = -3.5, so zoom in. Double-click on the graph to open it up in the Data tool.
. Put your cursor on the point where the graph line intersects y = -3.5. Click and hold to read the vy at that point shown in a yellow box in the
bottom left comer).
What's the interpolated graph value of v, at y = -3.57 Comment on how well this value agrees with the value of v, that you calculated in part A of
this activity. Make a hypothesis about any notable difference.
Answers
Answer:
-3.5
Explanation:
b/c the distance is moving in to two A And B A +B or S1 +S2 that is it
Answer:
The interpolated velocity value from the graph is -8.1 meters/second. The calculated value based on the average acceleration is -8.2 meters/second. This is very good agreement.
Explanation:
How can you find the mass of an object that is broken into parts?
Find the weight of the parts, and then add those weights together.
Find the weight of the whole.
Find the mass of the whole.
Find the mass of the parts, and then add those masses together.
Answers
The mass of an object broken into parts can be determined by finding the mass of the parts, and then add those masses together.
To total mass of an object broken into parts can be determined by adding the mass of different parts together.
[tex]M_t = m_1 + m_2 +\ ---[/tex]
where;
[tex]M_t[/tex] is the total mass of the objects[tex]m_1 , \ m_2[/tex] masses of the broken partsThus, we can conclude that the mass of an object broken into parts can be determined by finding the mass of the parts, and then add those masses together.
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plzz explain how it is 66 m
i know that distance =speed × time so how it is 66 m not a
0.4 and if there us another rule plz explain like if u day that 1/2 ×speed ×time plz explain why u used 1/2 or when do I use the 1/2 rule
Answers
Hi there!
For someone to hear an echo, the sound must echo and bounce back to the person.
Thus, the sound travels TWICE the distance from the person to the wall (to the wall and back).
We know that:
d = st (distance = speed × time)
Let L = distance from person to wall
Thus:
2L = st
2L = 330 × 0.40
2L = 132
L = 66 m
What net force would be necessary to cause a block of wood with a mass of 2.5 kg to accelerate at a rate of 3.0 m/s2
Answers
Answer:
7.5 NExplanation:
The force acting on an object given it's mass and acceleration can be found by using the formula
force = mass × acceleration
From the question
mass = 2.5 kg
acceleration = 3.0 m/s²
We have
force = 2.5 × 3.0 = 7.5
We have the final answer as
7.5 NHope this helps you
ignore this i put the wrong grade sorry
Answers
Answer:
Oh its fine i am not in college but its still fine
Explanation:
The mass of the hammer is 0.454 kg. Calculate the weight of the hammer.
Answers
Explanation:
weight =0.454 × 9.8=4.4492N
Answer:
4.45 n sorry if I am wrong
Fill in the blank: In the Northern Hemisphere, June 21 has ______________ than December 21.
A. longer days and more direct sunlight
B. longer days and less direct sunlight
C. shorter days and more direct sunlight
D. shorter days and less direct sunlight
Answers
Answer:
A. longer days and more direst sunlight
Explanation:
In the Northern Hemisphere, June 21 has longer days and more direct sunlight than December 21, so option A is correct.
What is Hemisphere?Essentially, it alludes to a person's half-divisions. The Earth can be split up into many equal divisions. Latitudinal or longitudinal divisions may be used. Based on a hypothetical equator line, it can be either the northern or Southern Hemisphere, and based on the prime meridian, it can be either the eastern or western hemisphere. When viewed from a latitudinal perspective, the Northern and Southern Hemispheres are essentially hemispheres of the Earth.
The Northern Hemisphere is the region of the Earth that lies above the equator, which is an imaginary line. This hemisphere includes anything that is above this 0° line. It is the half of the planet that has the most people on the planet and more land than water.
The summer solstice falls on June 21 in the Northern Hemisphere and the winter solstice falls on June 21 in the Southern Hemisphere. The solstices are reversed around December 21 and winter officially starts in the Northern Hemisphere.
Therefore, in the Northern Hemisphere, June 21 has longer days and more direct sunlight than December 21.
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A system releases 622 kJ of heat and does 105 kJ of work on the surroundings. What is the change in internal energy of the system
Answers
Answer:
Δ-727 or -7.27x10²kJ
Explanation:
ΔV=q-w
(q)= -622
(w)= -105
(both negative because it indicate loss of energy)
ΔV= -622+(-105)
ΔV= -727 kJ
The change in internal energy of the system when it released a heat of 622 kJ and does a work of 105 kJ on the surroundings is -727 kJ.
What is change in internal energy?Internal energy is all the energy contained in an object.
To calculate the change in internal energy of the system, we use the formula below.
Formula:
ΔU = Q-W............. Equation 1Where:
ΔU = Change in internal energy of the system,W = work done by the systemQ = Heat released by the system.From the question,
Given:
Q = - 622 kJ ( released of heat)W = 105 kJ.Substitute these values into equation 1
ΔU = -622-105ΔU = -727 kJHence, the change in internal energy of the system when it released a heat of 622 kJ and does a work of 105 kJ on the surroundings is -727 kJ.
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one end of a light inextensible string is attached to a tool box of mass 2.5 kg which is lying on a horizontal table. The string passing over a smooth pulley and is tied at the other end to a bag of mass 1.4kg as shown in the diagram
a. If the toolbox on the point of sliding, find the value for μ, the coefficient of friction.
b. Supposing the coefficient of friction between the tool boxe and the table is 0.20, calculate the acceleration of the system and the tension in the string gravity as 10 m per second square
Answers
Answer:
the answer is A
Explanation: