Answer:
The natural frequency = 50 rad/s = 7.96 Hz
Damping ratio = 0.5
Explanation:
The natural frequency is calculated in this manner
w = √(k/m)
k = spring constant = 5 N/m
m = mass = 2 g = 0.002 kg
w = √(5/0.002) = 50 rad/s
w = 2πf
50 = 2πf
f = 50/(2π) = 7.96 Hz
Damping ratio = c/[2√(mk)] = 0.1/(2 × √(5 × 0.002)) = 0.5
Kinetic and Potential Energy HistoryA roller coaster train going down hill represents merely a complex case as a body is descending an inclined plane. Newton's first two laws relate force and acceleration, which are key concepts in roller coaster physics. At amusement parks, Newton's laws can be applied to every ride. These rides range from 'The Swings' to The 'Hammer'. Newton was also one of the developers of calculus which is essential to analyzing falling bodies constrained on more complex paths than inclined planes. A roller coaster rider is in an gravitational field except with the Principle of Equivalence.Potential EnergyPotential energy is the same as stored energy. The "stored" energy is held within the gravitational field. When you lift a heavy object you exert energy which later will become kinetic energy when the object is dropped. A lift motor from a roller coaster exerts potential energy when lifting the train to the top of the hill. The higher the train is lifted by the motor the more potential energy is produced; thus, forming a greater amount if kinetic energy when the train is dropped. At the top of the hills the train has a huge amount of potential energy, but it <span>has very little kinetic energy.Kinetic Energy The word "kinetic" is derived from the Greek word meaning to move, and the word "energy" is the ability to move. Thus, "kinetic energy" is the energy of motion --it's ability to do work. The faster the body moves the more kinetic energy is produced. The greater the mass and speed of an object the more kinetic energy there will be. Hope this helped:))))</span>
The minimum stopping distance when the car is moving at 32.0 m/s is 348.3 m.
<h3>
Acceleration of the car </h3>
The acceleration of the car before stopping at the given distance is calculated as follows;
v² = u² + 2as
when the car stops, v = 0
0 = u² + 2as
0 = 15² + 2(76.5)a
0 = 225 + 153a
-a = 225/153
a = - 1.47 m/s²
<h3>Distance traveled when the speed is 32 m/s</h3>
If the same force is applied, then acceleration is constant.
v² = u² + 2as
0 = 32² + 2(-1.47)s
2.94s = 1024
s = 348.3 m
Learn more about distance here: brainly.com/question/4931057
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