Elastic and Inelastic Collisions AP Physics 1 FRQ – Exam Style Questions etc.
Elastic and Inelastic Collisions AP Physics 1 FRQ
Unit 4: Linear Momentum
Weightage : 10-15%
Exam Style Practice Questions, Elastic and Inelastic Collisions AP Physics 1 FRQ
Question
A car of known mass \(m_{1}\) will collide with a second car of known mass \(m_{2}\). The collision will be head on, and both cars will only move linearly both before and after the collision. In a clear, coherent, paragraph-length response, explain a method for determining whether the collision is perfectly elastic, perfectly inelastic, or neither. If the collision is perfectly inelastic, include at least one possible cause of energy loss.
▶️Answer/Explanation
Ans:
The defining characteristic of a perfectly elastic collision is that no kinetic energy is lost. Therefore, you must record the speeds of each car before and after the collision. Then, the equation \(\frac{1}{2}m_{1}v^{2}_{1,0}+\frac{1}{2}m_{1}v^{2}_{1,f}=\frac{1}{2}m_{2}v^{2}_{2,f}\) can be used to check whether or not it is elastic. The defining feature of a perfectly inelastic collision is that the objects stick together after the collision. This can be simply observed. If the two cars remain intact post-collision, then the collision is perfectly inelastic. If neither of the above is true, then it is neither perfectly elastic nor perfectly inelastic.
Finally, a few possible sources of energy loss would be the heat generated as metal is warped, the sound made by the crash, and even the light of any sparks generated.
Question
Two identical objects A and B of mass M move on a one-dimensional, horizontal air track. Object B initially moves to the right with speed vo. Object A initially moves to the right with speed 3vo, so that it collides
with object B. Friction is negligible. Express your answers to the following in terms of M and vo.
a. Determine the total momentum of the system of the two objects.
b. A student predicts that the collision will be totally inelastic (the objects stick together on collision). Assuming this is true, determine the following for the two objects immediately after the collision.
i. The speed
ii. The direction of motion (left or right)
When the experiment is performed, the student is surprised to observe that the objects separate after the collision and that object B subsequently moves to the right with a speed 2.5vo.
c. Determine the following for object A immediately after the collision.
i. The speed
ii. The direction of motion (left or right)
d. Determine the kinetic energy dissipated in the actual experiment.
▶️Answer/Explanation
Ans:
a) ptot = M(3vo) + (M)(vo) = 4mvo
b) i) Apply momentum conservation perfect inelastic. pbefore = pafter
4Mvo = (m1+m2)vf 4Mvo = (2M) vf vf = 2vo
ii) Since they are both moving right they would have to be moving right after
c) i) Apply momentum conservation pbefore = pafter
4Mvo = m1v1f + m2v2i 4Mvo = Mvaf + M(2.5vo) vaf = 1.5 vo
ii) As before, the would have to be moving right.
d) ∆K = Kf – Ki = (½ mavaf2 + ½ mbvbf2) – ( ½ mavai2 + ½ mbvbi2) = 4.25 Mvo2 – 5 Mvo2 = – 0.75 Mvo2