A system that consists of a single spring stores a total elastic potential energy Ep when a load is added to the spring. Another identical spring connected in parallel is added to the system. The same load is now applied to the parallel springs.
What is the total elastic potential energy stored in the changed system?
A. Ep
B. \(\frac{{{E_p}}}{2}\)
C. \(\frac{{{E_p}}}{4}\)
D. \(\frac{{{E_p}}}{8}\)
Answer/Explanation
Markscheme
B
Let the spring constant is K
so, \(E_p=\frac{1}{2}k.x^2\)
and we connect an identical spring paralally new \(k_{eq}=(k+k)\rightarrow 2k\)
\((E_p)new=\frac{1}{2}2k.x^2\)
so the chnage is \(finel-inital\rightarrow kx^2-\frac{1}{2}kx^2\rightarrow \frac{E_p}{2}\)
Question
An object of mass 2m moving at velocity 3v collides with a stationary object of mass 4m. The objects stick together after the collision. What is the final speed and the change in total kinetic energy immediately after the collision?
| Final speed | Change in total kinetic energy |
A. | v | 3 mv 2 |
B. | v | 6 mv2 |
C. | 2v | 3 mv 2 |
D. | 2v | 6 mv 2 |
Answer/Explanation
Answer – B
\( P_{i}=P_{f} \)
\( 2m\times 3v+4m\times 0=\left ( 2m+4m \right )\times v_{new} \) ( \( v_{new}=v \) )
Change is kinetic energy= \( (\frac{6m}{2}\times v^{2}) -\left ( \frac{m}{2} \times 9v^{2}\right)=6mv^{2} \)
A ball of mass m travels horizontally with speed v before colliding with a vertical wall. The ball rebounds at speed v in a direction opposite to its initial direction. What is the magnitude of the change in momentum of the ball?
A. 0
B. \(\frac{{mv}}{2}\)
C. mv
D. 2 mv
Answer/Explanation
Markscheme
D
The impulse delivered to the ball is equal to its change in momentum. The momentum of the ball was mv before hitting the wall and m(-v) after. Therefore, the change in momentum is m(-v)-mv=-2mv, so the magnitude of the momentum change (and the impulse) is 2mv.
Question
Which aspect of thermal physics is best explained by the molecular kinetic model?
A The equation of state of ideal gases
B The difference between Celsius and Kelvin temperature
C The value of the Avogadro constant
D The existence of gaseous isotopes
Answer/Explanation
Ans: A
Ref:https://www.iitianacademy.com/ib-physics-unit-3-modelling-a-gas-notes/
The kinetic molecular theory can be used to explain each of the experimentally determined gas laws.
Any sample of a gas is made of molecules. A molecule is the smallest unit having all the chemical properties of the sample. The observed behaviour of a
gas results from the detailed behaviour of its large number of molecules. The kinetic theory of gases attempts to develop a model of the molecular behaviour
which should result in the observed behaviour of an ideal gas.