Suppose the two carts have equal masses and are both moving to the right before

Question

Suppose the two carts have equal masses and are both moving to the right before the collision. The initial speed of cart 1 (on the left) is v0 and the initial speed of cart 2 (on the right) is v0/2. When the carts collide they stick together and move as one.

Part A

What is the speed of the center of mass of this system?

Express your answer in terms of v0.

Part B

What percentage of the initial kinetic energy is lost as a result of the collision?

Part C

Suppose the collision is elastic. What are the final speeds of the two carts in this case?

Express your answers in terms of v0 separated by a comma.

v0

Explanation / Answer

The speed of the COM is

vCOM = [m(vo) + m(vo/2)]/[m + m]

vCOM = 3vo / 4 [ANSWER, PART A]

********************

The initial KE is

KEi = 1/2 m vo^2 + 1/2 m(vo/2)^2

KEi = (5/8) m (vo^2)

The final KE is

KEf = 1/2 (2m) (3 vo / 4)^2

KEf = (9/16) m (vo^2)

Thus,

KElost = 1/16 m vo^2

Thus,

KElost / KEi = 0.10   or 10% [ANSWER, PART B]

******************

If the collision is elastic, the energy is now also conserved. Then, the new velocities are

v1f = vo/2

v2f = vo

Thus, you put this in as

vo/2, vo.   [ANSWER, PART C]

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.