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
7. A taxi is travelling at 15 m/s. Its driver accelerates with acceleration 3 m/s2 for 4 s. What is its new velocity
Answers
Hi there!
To solve, we can use the following equation:
vf = vi + at
vi = initial velocity (m/s)
a = acceleration (m/s²)
t = time (s)
vf = final velocity (m/s)
Plug in the given values:
vf = 15 + 3(4)
vf = 15 + 12 = 27 m/s
Answer:
[tex]\boxed {\boxed {\sf 27 \ m/s}}[/tex]
Explanation:
We are asked to find the new or final velocity of a taxi.
We will use the following kinematic equation:
[tex]v_f=v_i+at[/tex]
The car was initially traveling at 15 meters per second. It accelerated at 3 meters per second squared for 4 seconds.
[tex]v_i=[/tex]15 m/s[tex]a=[/tex]3 m/s ²t= 4 sSubstitute the values into the formula.
[tex]v_f= 15 \ m/s + (3 \ m/s^2* 4 \ s)[/tex]
Multiply the numbers in parentheses.
3 m/s/s * 4 s = 3 m/s *4 = 12 m/s[tex]v_f= 15 \ m/s +12 \ m/s[/tex]
Add.
[tex]v_f=27 \ m/s[/tex]
The new velocity of the taxi is 27 meters per second.
What does the state of matter of an object depend on?
type of molecules
size of molecules
speed of molecules
number of molecules
Answers
Explanation:
A substance's state of matter — solid, liquid, gas, or plasma — depends on how its molecules move and maintain their volume and shape.
With an average velocity of 8.3 m/s, what is the displacement (including its sign) of a sled during a straight run of 12 s?
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Answer:
this question makes no sense with out a reference point or direction.
if the amplitude of a sound wave is tripled, the intensity will:
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Answer:
Increase 9 times
Explanation:
Wind energy is the example of A) potential energy B)mechanical energy C) Kinetic energy
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Answer:
Kinetic Energy
Explanation:
Its on the internet
Alejandro Kirk is the catcher for the Blue Jays’ baseball team. He exerts a forward force on the 0.145-kg baseball to bring it to rest from a speed of 38.2 m/s. During the process, his hand recoils a distance of 0.135 m.
Determine is the acceleration of the ball.
Determine the force applied by Alejandro.
Answers
Answer:
a= -5404.6 [m/s²]; F=785.75 [N].
Explanation:
1. Determine is the acceleration of the ball:
equation of the distance (0.135m) is:
[tex]S=-\frac{at^2}{2} +v_0t,[/tex] where S=0.135[m]; a - required acceleration; t - elapsed time; v₀ - initial velocity (38.2 m/s);
also the required acceleration is:
[tex]a=\frac{v-v_0}{t}, where[/tex] V - the end velocity (0 m/s), t - elapsed time, ₀ - initial velocity (38.2 m/s).
Using the equations of reqruired acceleration and the distance it is possible to make up and solve the next system:
[tex]\left \{ {{a=-\frac{38.2}{t} } \atop {S=-\frac{at^2}{2}+38.2t }} \right. \ => \ \left \{ {{a=-\frac{38.2}{t} } \atop {0.5at^2-38.2t=0.135}} \right. \ => \ \left \{ {{a=-\frac{38.2}{t} } \atop {19.1t-38.2t=0.135}} \right. \ => \ \left \{ {{a=-5404.6} \atop {t=0.007}} \right.[/tex]
finally, a≈-5404.6 [m/s²].
2. Determine the force applied by Alejandro.
the energy is:
[tex]E=\frac{mv^2}{2}; \ or E=FS, where \ m-the \ mass; \ v-velocity; \ F-required \ force; S-distance;[/tex]
According to these two equations, the required force is:
[tex]F=\frac{E}{S}=\frac{mv^2}{2S};[/tex]
F=0.145*38.8²/2/0.135≈785.75 [N].
note, the suggested way is not the shortest one and not the only one.
P.S. if it is possible, check the arithmetic operations and the provided answers in other sources.
If someone were to be researching and studying similarities between our sun and a neighboring star, what kind of scientific investigation would they be conducting
Answers
Answer:
a
Explanation:
because there both in the solar system
There are billions of galaxies in the universe and each contains trillions of stars which are different in size, distance from the earth, brightness etc.When we scientifically investigate about this we can obtain the stars of similarity to sun in brightness and size.
What is galaxies?Galaxies are a group of stars, dust and dark matter joined together by the force of gravitation. Three trillions of stars in each galaxies. Some stars forms a group of certain size and shape and number also they are called constellations.
Sun is the closest star to earth. Thus sunlight is the major source of energy in earth. Sunlight reaches the earth surface within a time of 8 minute and 6 seconds.
The star which nearest to sun is named proximacentory which far from the earth and we can see it as spot of light in the sky. There are many more stars which are giants are more brighter than sun.
The brightness and luminosity is determined based on the distance from the earth. Which can be calculated in terms of light years. Each star has an age and length of life. After that the star may die still their light energy can be seen in sky because their light takes more years to reach here.
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If you have a rocket that has a mass of 20kg and is accelerating at 25 m/s what force
would that rocket experience?
a . 20N
b . 40000N
c. 500N
d. 25N
Answers
F = (20kg) x 25
= 500N
So your answer is C :)
Always remember “FAM” In the shape of a triangle … so F will be at the top and A&M at the bottom that way you will remember that F = mass x acceleration
. The gas in a piston (defined as the system) warms and absorbs 655 J of heat. The expansion performs 344 J of work on the surroundings. What is the change in internal energy for the system
Answers
The change in the internal energy for the system is 311 J
The change in internal energy for the system will be the difference between the heat absorbed and the work expansion from the surroundings.
i.e.
ΔU = Q + W
where;
internal energy = Uheat absorbed = Qworkdone on surroundings = -WΔU = ( 655 J + ( - 344 J) )
ΔU = 311 J
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what animal that does not eat meat
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Answer:
An animal that doesn’t eat meat is called a herbivore. An few examples would be cows, rabbits, horses, and goats.
:)
List examples of how the Bill of Rights protects you:
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.
.
.
.
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guaranteeing freedom of speech, press, assembly, and exercise of religion
What do scientists call a substance that contains atoms from two or more different elements that are chemically bonded?
Atom
Compound
Element
Molecule
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A 455 kg cannon fires a 21 kg cannonball at 26 m/s. If the cannon is on wheels, at what velocity does it move backward?
Answers
Answer:
A cannon ball of mass 4.0 kg is fired from a stationary 96 kg cannon at 120 m/s. Calculate the velocity of the cannon immediately after firing.
total momentum of cannon and cannon ball before = 0 kg m/s - because neither object is moving
total momentum of cannon and cannon ball after collision = 0 kg m/s - because momentum is conserved
Momentum of cannon ball after firing = 4.0 × 120 = 480 kg m/s.
Momentum of cannon after firing = -480 kg m/s (because it recoils in the opposite direction and 480 - 480 = 0 kg m/s, the total momentum after collision).
Rearrange p = m v to find v:
v = p/m
v = 480 divided by 96
v = 5.0 m/s
Note that the forward velocity of the cannon ball was given a positive value. The negative value for the cannon's velocity shows that it moved in the opposite direction.
An object's inertia causes it to come to a rest position.
Answers
Answer:
no
Explanation:
the inertia of an object does not make it to come to rest, this is normally caused by friction
OK I have tried answering this for a while but im not very good at this so, how many waves will pass in 1 second if it has a frequency of 10 Hz?
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Answer: It's an area that's an optimal distance from the sun for potentially supporting life
true and false? When an object remains stationary, any forces acting on it must be balanced.
Answers
Answer:
Balanced forces acting on a stationary object cause the object to remain at rest. True: Forces can give energy to an object it acts on causing the object to change it state of motion. If forces acting on an object are balanced, they do not cause a change in motion.
Answer:
False
Explanation:
It is NOT possible for just three forces to be acting upon an object and they still balance each other. A free-falling object experiences a balance of forces.
A wooden block moves at a constant speed on a rough horizontal surface. Draw a free-body diagram
clearly showing all the forces applied to the block; compare their magnitudes and directions.
Answers
The weight of the block and normal reaction are equal in magnitude but opposite in direction. Also, the frictional force and applied force are equal in magnitude but opposite in direction.
The forces acting on the wooden block moving at a constant speed include the following;
weight of block acting downwards, Wnormal reaction on the block acting upwards, Napplied force on the block acting towards positive x-direction, Ffrictional force acting towards negative x-direction, [tex]F_f[/tex]The free-body diagram is presented below;
N
↑
[tex]F_f[/tex] ← ⊕ → F
↓
W
The block is moving at a constant speed, we will have the following;
[tex]W = N \\\\F = F_f[/tex]
Thus, we can conclude that the weight of the block and normal reaction are equal in magnitude but opposite in direction. Also, the frictional force and applied force are equal in magnitude but opposite in direction.
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what is the full meaning of hip
Answers
Answer:
History in Perspective (education) HIP. Health Information Professional. HIP.
Explanation:
hope this helps
The best evidence for dark matter in the milky way comes from the observation that the rotation curve
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Part IV Objects on an incline w/ Tension + Friction
1. A small 63 kg sleigh is pulled by a rein attached to horse up a 15'angle hill to the
horizontal. The tension of the rein is 510 N. The coefficient of kinetic friction is
0.25
a. What is the normal force that the sleigh exerts on the hill?
b. What are the magnitude and direction of the sleigh's acceleration?
Answers
(a) The normal force on the sleigh is 596.36 N.
(b) The magnitude and direction of acceleration of the sleigh is 3.2 m/s² upwards.
The given parameters;
mass of the sleigh, m = 63 kginclination of the hill, θ = 15⁰tension on the rein, F = 510 Ncoefficient of friction, μ = 0.25The normal force on the sleigh is calculated as follows;
[tex]F_n = mg \times cos(\theta)\\\\F_n = 63 \times 9.8 \times cos(15)\\\\F_n = 596.36 \ N[/tex]
The magnitude and direction of acceleration of the sleigh is calculated as follows;
[tex]\Sigma F= ma\\\\F - mgsin(\theta) - F_f = ma\\\\F - mgsin(\theta) - \mu F_n = ma\\\\510\ - \ 63 \times 9.8 \times sin15 \ -\ 0.25\times 596.36 = 63a\\\\201 .11 = 63a\\\\a = \frac{201.11}{63} \\\\a = 3.2 \ m/s^2 \ upwards[/tex]
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Hãy giải thích sự phát âm của cái sáo khi thổi vào nó
Answers
Âm phát ra từ cái sáo khi thổi là do:
-Không khí ngoài ống sáo chuyển động và phát ra âm thanh.
-Thân sáo chuyển động và phát ra âm thanh.
-Thân sáo dao động và phát ra âm thanh.
-Cột không khí trong ống sáo dao động và phát ra âm thanh.
mars one mission essay
Answers
so bassicly Mars is a planet
Explanation:
planet
What is electromagnetic force and how does it work and what it does??
Answers
Answer:
Explanation:
The electromagnetic force, also called the Lorentz force, acts between charged particles, like negatively charged electrons and positively charged protons. Opposite charges attract one another, while like charges repel. The greater the charge, the greater the force.
the ground wire on a household circuit is typically what color
Answers
Answer:
Hey mate....
Explanation:
This is ur answer.....
Green & YellowHope it helps!
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The ground wire on a household circuit is green in color in a typical household
What is an electric charge?Charged material experiences a force when it is subjected to an electromagnetic field due to the physical property of electric charge. You can have positive or negative electric charges (commonly carried by protons and electrons respectively). opposing charges attract one another whereas similar charges repel one another. We refer to an object as neutral if it has no net charge.
The charge on one electron is -1.6 ×10⁻¹⁹ coulomb.
The ground wire is either bare or has green insulation in most residential branch circuit cables in the US.
The norm in Europe and the UK is
live, brown
neutral is blue.
stripes with green and yellow: earth.
Thus,the ground wire on a household circuit is green in color in a typical household
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Any vector can be expressed as the sum of two components, usually
referred to as what?
Answers
Two vectors can be added together to determine the result (or resultant). ... computing the vector sum of all the individual forces acting upon that object.
i hope u understand
A flea sits on the edge of a classic record album that is making 1 revolution in 0.56s. The flea is 0.20m from the center of the record
a. what is the fleas velocity?
b. What is the fleas centripetal acceleration?
Answers
Hi there!
We can begin by finding the angular velocity using dimensional analysis:
[tex]\frac{1 rev}{0.56 s} * \frac{2\pi rad}{1 rev} = 11.22 rad/sec[/tex]
(A)
Find the flea's velocity using the following relationship:
v = ωr
v = (11.22)(0.20) = 2.24 m/s
(B)
Centripetal acceleration is given by:
a = ω²r
a = (11.22²)(0.20) = 25.18 m/s²
The gravitational field strength on Mars is 3. 7 N/kg. Kai has a mass of 55 kg. What would Kai weigh on Mars? Give your answer to 1 decimal place.
Answers
Hi there!
Weight = mass × acceleration due to gravity (or gravitational field strength)
We can write this as:
W = mg
Plug in the given values:
W = 55 × 3.7
W = 203.5 N
A block with initial velocity of 3 m/s slides 9 m across a rough horizontal surface before coming to rest. What is the coefficient of kinetic
friction?
Answers
The coefficient of kinetic friction between the block and the horizontal surface is 0.051.
The given parameters;
initial velocity, u = 3 m/sdistance traveled by the block, s = 9 mThe acceleration of the block is calculated as follows;
[tex]v^2 = u^2 + 2(-a)s\\\\v^2 = u^2 - 2as\\\\a = \frac{u^2 - v^2}{2s} \\\\a = \frac{3^2 - 0^2}{2\times 9} \\\\a =0.5 \ m/s^2[/tex]
The coefficient of kinetic friction between the block and the horizontal surface is calculated as follows;
[tex]\mu_k mg = ma\\\\\mu_k = \frac{a}{g} \\\\\mu_k = \frac{0.5}{9.8} \\\\\mu_k = 0.051[/tex]
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Find the acceleration if the force is 10 N and the mass is 5000 g.
Answers
Answer:
If the force is 10N and mass is 5000G, then a=2m/s2
Explanation:
F=10N
m=5000
g=5kg
a=10N/ 5kg
and finally; a= 2m/s2