What happens when a roller coaster car moves down from the top of a hill?
Answers
Answer:
Gravitational potential energy is converted into kinetic energy
Explanation:
At the top of the hill, the roller coaster car has gravitational potential energy, which is given by:
where m is the mass of the car, g is the gravitational acceleration, h is the height of the hill.
As the car descends the hill, it gains speed (v), so it also gains kinetic energy, given by:
where v is the speed of the car.
The mechanical energy of the car is the sum of its potential energy and kinetic energy:
In absence of friction, the law of conservation of energy states that the mechanical energy of the car is constant. Therefore, since as the car moves down the hill the potential energy decreases (because the height, h, decreases), it means that the kinetic energy must increase (and this is wy the speed increases). So we can say that gravitational potential energy is converted into kinetic energy.
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The energy equation, E=12mvx2+12kx2=12kA2, is a useful alternative relationship between velocity and position, especially when energy quantities are also required. If the problem involves a relationship among position, velocity, and acceleration without reference to time, it is usually easier to use the equation for simple harmonic motion, ax=d2xdt2=−kmx (from Newton’s second law) or the energy equation above (from energy conservation) than to use the general expressions for x, vx, and ax as functions of time. Because the energy equation involves x2 and vx2, it cannot tell you the sign of x or of vx; you have to infer the sign from the situation. For instance, if the body is moving from the equilibrium position toward the point of greatest positive displacement, then x is positive and vx is positive.
IDENTIFY the relevant concepts
Energy quantities are required in this problem, therefore it is appropriate to use the energy equation for simple harmonic motion.
SET UP the problem using the following steps
Part A
The following is a list of quantities that describe specific properties of the toy. Identify which of these quantities are known in this problem.
Select all that apply.
Select all that apply.
maximum velocity vmax
amplitude A
force constant k
mass m
total energy E
potential energy U at x
kinetic energy K at x
position x from equilibrium
Part B
What is the kinetic energy of the object on the spring when the spring is compressed 5.1 cm from its equilibrium position?
Part C
What is the potential energy U of the toy when the spring is compressed 5.1 cm from its equilibrium position?
Answers
Answer:
Part A
Mass = 50g
Vmax = 3.2m/s
Amplitude= 6cm
Position x from the equilibrium= 5.1cm
Part B
Kinetic energy = 0.185J
Part C
Potential energy = 0.185J
Explanation:
Kinetic energy = 1/2mv×2
Vmax = wa
w = angular velocity= 53.33rad/s
Kinetic energy = 1/2mv^2×r^2 = 0.185J
Part c
Total energy = 1/2m×Vmax^2= 0.256J
1/2KA^2= 0.256J
K= 142.22N/m (force constant)
Potential energy = 1/2kx^2
=1/2×142.22×0.051^2
= 0.185J
Final answer:
To find the kinetic energy of the toy, we need to use the energy equation for simple harmonic motion and the relationship between velocity and position. We can then substitute the known values to calculate the kinetic energy.
Explanation:
In this problem, we are given the amplitude (A) of the oscillation and the maximum velocity (vmax) achieved by the toy. We need to find the kinetic energy (K) of the toy when the spring is compressed 5.1 cm from its equilibrium position.
To solve for the kinetic energy, we can use the energy equation for simple harmonic motion: K = 1/2mvx2, where m is the mass of the object and vx is the velocity of the object at position x. The mass of the object is given as 50 g, which is equal to 0.05 kg.
Since we know the maximum velocity (vmax = 3.2 m/s), we can use the relationship between velocity and position in simple harmonic motion to find the velocity (vx) at a displacement of 5.1 cm from the equilibrium position. The velocity and position in simple harmonic motion are related by vx = ±ω√(A2 - x2), where ω is the angular frequency of the motion.
Substituting the known values into the equations, we can calculate the kinetic energy of the toy.
Learn more about Simple Harmonic Motion here:
#SPJ3
Answers
Answer:
Movement of Galaxies away from us.
Explanation:
Big Bang theory is the most widely accepted theory which says that the universe started with a huge expansion, it was not an explosion. By that logic everything must be moving from each other even today. This was proved by observing the Redshift in the spectrum of the galaxies which means that they are moving away from us.
Answers
Answers
Answer:
190 is the average velocity.
Explanation:
Just add them together
Answers
Explanation:
The process by which atoms are arranged to form a material with a crystal shape is called crystallization.
With the help of crystallization process we can purify a solid compound.
For example, ice and snowflakes occur due to crystallization of water.
In this process, small quantity of desired solvent is added into the impure solid. Then it is heated to let the solid dissolve and after that it is cooled down so that crystals are formed. Then with the help of vacuum filtration pure solid is extracted.
Answer:
Crystallization is the correct answer.
Explanation: