Physics: Student taking the exam received a zero for this particular question, can you answer the 2 questions?

Question

The test question below was presented on a college physics exam. The student taking the exam received a zero for this particular question. Can you answer the 2 questions?

BTW: there is no elephant in the way.

Answer 1

Part (a)
The object when comes down loses its potential energy which converts into kinetic energy. There won't be any loss in energy during conversion assuming there is no any kind of energy loss due to friction or air resistance.

So by the law of conservation of energy of the object in the above case.

Potential energy = Kinetic energy = Spring energy
=(m*g*h) = (1/2*m*v^2) = (1/2*k*x^2)

Where
m = mass of the object
g = acceleration due to gravity (almost = 10 (m/s^2))
h = height of the object
v = velocity of the object
k = spring constant expressed in (Force per unit compression displacement) ie., N/m.
x = displacement or compression of the spring in meters.

Potential energy = 3*10*5 = 150 joules
150 = 0.5*100*(x^2)
Sqrt (3) meter = x = 1.7321 m
Which is true only if the conversion of kinetic energy of the object to energy of the spring happens without any heat dissipation within spring.

Part (b)

After the object looses its energy to the spring the object looses it's velocity and comes to rest. This is when the spring starts loosing its energy (because the force of the object on the spring also becomes 0 when its velocity becomes 0 as there is no more possible deceleration) which is imparted back on to the object and assuming perfect conversion the object gains all of its kinetic energy back which converts back to potential energy without any loss and the object reaches back to the height of 5 meter.

Comments

Excellent!  A very detailed and concise explanation leading to a step by step arrival to solve both problems.

Oddly enough, the student was on the verge of the correct answer if only she would've connected her 2 equations which would satisfy the Conservation of Energy Law:  147.15 = 50 x^2, solving for: x^2 = 147.15/50, = 2.943, and  thus
x = sq rt of 2.943 = 1.72 meters.

Now, from a psychological point of view when taking an exam:  mental block = panic attack = hallucinations = an arrival of the elephant to take control and thus relieve anxiety.

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Very crisp explanation. Well done Tejas.

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Thank you :)

Answer 2

What is phase space

Comments

Phase 1

The object when comes down loses its potential energy which converts into kinetic energy. There won't be any loss in energy during conversion assuming there is no any kind of energy loss due to friction or air resistance.
So by the law of conservation of energy of the object in the above case.

Potential energy = Kinetic energy = Spring energy
=(m*g*h) = (1/2*m*v^2) = (1/2*k*x^2)

Where:
m = mass of the object
g = acceleration due to gravity (almost = 10 (m/s^2))
h = height of the object
v = velocity of the object
k = spring constant expressed in (Force per unit compression displacement) ie., N/m.
x = displacement or compression of the spring in meters.

Potential energy = 3*10*5 = 150 joules
150 = 0.5*100*(x^2)
Sqrt (3) meter = x = 1.7321 m
Which is true only if the conversion of kinetic energy of the object to energy of the spring happens without any heat dissipation within spring.

Phase 2

After the object looses its energy to the spring the object looses its velocity and comes to rest. This is when the spring starts loosing its energy (because the force of the object on the spring also becomes 0 when its velocity becomes 0 as there is no more possible deceleration) which is imparted back on to the object and assuming perfect conversion the object gains all of its kinetic energy back which converts back to potential energy without any loss and the object reaches back to the height of 5m.

Legacy

147.15 = 50 x^2, solving for: x^2 = 147.15/50, = 2.943, and thus
x = square root of 2.943 = 1.72 meters.

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In dynamical system theory, a phase space is a space in which all possible states of a system are represented, with each possible state corresponding to one unique point in the phase space. For mechanical systems, the phase space usually consists of all possible values of position and momentum variables. The concept of phase space was developed in the late 19th century by Ludwig Boltzmann, Henri Poincaré, and Josiah Willard Gibbs.