a) The student hypothesizes that a greater fraction of kinetic energy is lost from the system during the collision when the spee
1 answer:
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Answer:
(a) coefficient of friction = 0.451
This was calculated by the application of energy conservation principle (the total sum of energy in a closed system is conserved)
(b) No, it comes to a stop 5.35m short of point B. This is so because the spring on expanding only does a work of 43 J on the block which is not enough to meet up the workdone of 398 J against friction.
Explanation:
The detailed step by step solution to this problems can be found in the attachment below. The solution for part (a) was divided into two: the motion of the body from point A to point B and from point B to point C. The total energy in the system is gotten from the initial gravitational potential energy. This energy becomes transformed into the work done against friction and the work done in compression the spring. A work of 398J was done in overcoming friction over a distance of 6.00m. The energy used in doing so is lost as friction is not a conservative force. This leaves only 43J of energy which compresses the spring. On expansion the spring does a work of 43J back on the block is only enough to push it over a distance of 0.65m stopping short of 5.35m from point B.
Thank you for reading and I hope this is helpful to you.
The question is missing some parts. Here is the complete question.
An ideal gas is contained in a vessel at 300K. The temperature of the gas is then increased to 900K.
(i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of , (d) a factor of 1, or (e) a factor of
?
Using the same choices in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a colision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas.
Answer: (i) (b) a factor of 3;
(ii) (c) a factor of ;
(iii) (c) a factor of ;
(iv) (c) a factor of ;
(v) (e) a factor of 3;
Explanation: (i) Kinetic energy for ideal gas is calculated as:
where
n is mols
R is constant of gas
T is temperature in Kelvin
As you can see, kinetic energy and temperature are directly proportional: when tem perature increases, so does energy.
So, as temperature of an ideal gas increased 3 times, kinetic energy will increase 3 times.
For temperature and energy, the factor of change is 3.
(ii) Rms is root mean square velocity and is defined as
Calculating velocity for each temperature:
For 300K:
For 900K:
Comparing both veolcities:
For rms, factor of change is
(iii) Average momentum change of molecule depends upon velocity:
q = m.v
Since velocity has a factor of and velocity and momentum are proportional, average momentum change increase by a factor of
(iv) Collisions increase with increase in velocity, which increases with increase of temperature. So, rate of collisions also increase by a factor of .
(v) According to the Pressure-Temperature Law, also known as Gay-Lussac's Law, when the volume of an ideal gas is kept constant, pressure and temperature are directly proportional. So, when temperature increases by a factor of 3, Pressure also increases by a factor of 3.