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
Block 1, of mass m1, moves across a frictionless surface with speed ui. It collides elastically with block 2, of mass m2, which is at rest (vi=0). (Figure 1)After the collision, block 1 moves with speed uf, while block 2 moves with speed vf. Assume that m1>m2, so that after the collision, the two objects move off in the direction of the first object before the collision. What is the final speed vf of block 2?
Answers
The conservation of the momentum allows to find the velocity of the second body after the elastic collision is:
[tex]v_f = \frac{2u_o}{1- \frac{m_2}{m_1} }[/tex]
the momentum is defined by the product of the mass and the velocity of the body.
p = mv
The bold letters indicate vectors, p is the moment, m the mass and v the velocity of the body.
If the system is isolated, the forces during the collision are internal and the it is conserved. Let's find the momentum is two instants.
Initial instant. Before crash.
p₀ = m₁ u₀ + 0
Final moment. After crash.
[tex]p_f = m_1 u_f + m_2 v_f[/tex]
The momentum is preserved.
p₀ = [tex]p_f[/tex]
[tex]m_1 u_o = m_1 u_f + m_2 v_f[/tex]
Since the collision is elastic, the kinetic energy is conserved.
K₀ = [tex]K_f[/tex]
½ m₁ u₀² = ½ m₁ [tex]u_f^2[/tex] + ½ m₂ [tex]v_f^2[/tex]
Let's write our system of equations.
[tex]m_1 u_o = m_1 u_f + m_2 v_f \\m_1 u_o^2 = m_1 u_f^2 + m_2 v_f^2[/tex]
Let's solve
[tex]u_f = u_o - \frac{m_2}{m_2} \ v_f \\u_f^2 = u_o^2 - \frac{m_2}{m_1} \ v_f^2[/tex]
[tex]( u_o - \frac{m_2}{m_1} v_f)^2 = u_o - \frac{m_2}{m_1} \ v_f^2 \\u_o^2 - 2 \frac{m_2}{m_1} \ u_o v_f + (\frac{m_2}{m_1} )^2 v_f^2 = u_o^2 - \frac{m_2 }{m_1} \ v_f^2[/tex]
[tex]2 \frac{m_2}{m_1} \ u_o = \frac{m_2}{m_1} v_f \ ( 1 - \frac{m_2}{m_1}) \\v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]
In conclusion, using the conservation of momentum, we can find the velocity of the second body after the elastic collision is:
[tex]v_f = \frac{2u_o}{1-\frac{m_2}{m_1} }[/tex]
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The question is fishing for "balanced force".
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2) Their function and structure is carry genetic information which is read in cells to make the RNA and proteins by which living things function.
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Formulas change from F to degree C : C = (F – 32) / 1.8
so we have (176-32) /1.8= 80 oC
Formulas change from F to degree K : K = 5 / 9 x (F – 32) + 273.15
so we have 5/9 x (176-32) + 273.15 = 353 oK
ok done. Thank to me :>
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A leak develops so that air gradually escapes from the cylinder until the air in the cylinder
is at atmospheric pressure. The pressure of the atmosphere is 1.0 x 105 Pa.
Calculate the volume of the escaped air, now at atmospheric pressure. Assume that the
temperature stays constant.
Answers
Answer:
10
Explanation:
if you put 10 your right
I will give Brainliest answer and 5 stars
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Answers
Answer:
James is traveling at 4 miles per hour.
Explanation:
3 miles per 45 minutes
x miles per 60 minutes(1 hour)
___________________
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B- 0
С- 24
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Answers
Please find attached photograph for your answer.
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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").
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In a titration, 50.00 cm3 of 0.300 mol/dm3
sodium hydroxide solution is exactly neutralized by 25.0
cm3 of a dilute solution of hydrochloric acid.
NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)
Calculate the concentration of the hydrochloric acid. Show your work out
PLS URGENT ANS
Answers
Answer:
Step 1: Calculate the amount of sodium hydroxide in moles
Volume of sodium hydroxide solution = 50.0 ÷ 1,000 = 0.05 dm3
Rearrange:
Concentration in mol/dm3 = amount of solute in molvolume in dm3
Amount of solutein mol = concentration in mol/dm3 × volume in dm3
Amount of sodium hydroxide = 0.300 × 0.05
= 0.01 5mol
Step 2: Find the amount of hydrochloric acid in moles
The balanced equation is: NaOH(aq) + HCl(aq) → NaCl(aq) + H2O(l)
So the mole ratio NaOH:HCl is 1:1
Therefore 0.015 mol of NaOH reacts with 0.015 mol of HCl
Step 3: Calculate the concentration of hydrochloric acid in mol/dm3
Volume of hydrochloric acid = 25.00 ÷ 1000 = 0.025 dm3
Concentration in mol/dm3 = amount of solute in molvolume in dm3
Concentration in mol/dm3 = 0.015/0.025
= 0.6 mol/dm3
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Relative formula mass of HCl = 1 + 35.5 = 36.5
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Answer:
Kinetic Energy
Explanation:
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Answers
The unit for momentum is equal to Kgm/s.
Given the following data:
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Mathematically, momentum is giving by this formula;
[tex]Momentum = mass \times velocity[/tex]
Substituting the given parameters into the formula, we have;
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Answers
Explanation:
follow the above attachment to get the answer.
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Answers
Answer:
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Explanation:
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Answers
Explanation:
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Answer:
sound that occurs in nature, such as those of animal, trees, people, the wind, the rain, etc. are the natural sounds. it is heard near the hill because of the echo and the reverberation of the sound
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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!
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Answers
Answer:
the electromagnetic and weak forces
Explanation:
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Answers
Answer: Physical changes only change the appearance of a substance, not its chemical composition. Chemical changes cause a substance to change into an entirely substance with a new chemical formula. Chemical changes are also known as chemical reactions.
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just give the other person brainlyest
Explanation:
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A. Diaphragm contracts, Internal intercostal would relax
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C. Internal intercostal and abdominal muscles would contract
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Answers
Answer:
C
for sure
go for it
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Answers
Answer:
it increased by 29 sorry hope this helps
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Answers
Answer:
Russia
Explanation:
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Answers
Answer:
11.1
Explanation:
2 hours 15 mins = 2 1/4 hours
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A person makes a loud sound and hears the echo of this sound 1.2s later .calculate how far the person is from the object causing the echo assume that the speed of sound is 330m/s calculate the distane
Answers
Answer:
198m
Explanation:
Distance = speed x time
. d = 330m/s x 1.2s = 396m
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Answers
If we take West to be the negative direction, then the initial velocity is -15 m/s and the acceleration (which points East) is +7.0 m/s².
After t = 4.0 s, the helicopter's velocity is
-15 m/s + (7.0 m/s²) (4.0 s) = +13 m/s
or 13 m/s [E].
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