How do you solve problems 5 & 6? Two 1.0-kg carts are coupled together and place

Question

How do you solve problems 5 & 6?

Two 1.0-kg carts are coupled together and placed on a very long horizontal track that is at rest in the Earth frame of reference. The combination is launched so that at t = 0 it is moving to the right at speed 2.0 m/s in the Earth frame, with cart #1 in front and cart #2 in back. The coupling contains an explosive charge that is remotely ignited at time t_1 > 0, releasing 18 J of energy. Half of this released energy is dissipated into noise, thermal energy, and minor damage to each cart. Assume zero friction between the carts and the track in the questions below. Which choice best represents the initial (t = 0) velocity of the center-of-mass of the 2-cart system in the Earth reference frame? Which choice best represents the final velocity (after the explosion, time t > t_1) of cart #2 in the center-of-mass (CM of the 2 cart system) reference frame? Which choice best represents the final kinetic energy of the 2-cart system in the Earth reference frame?

Explanation / Answer

5) In the centre of mass frame,

initial velocity of both carts = 0. (hence initial momentum also = 0)

After the explosion, both carts will move in opposite direction with equal speed so that momentum is conserved.

Initial KE in this frame = 0/

Final KE = 9.

Thus, 1/2 x 2m x v2 = 9

thus, v = 3 m/s for both carts in this frame.

As cart 2 is in back it will move to left with velocity = 3m/s and cart 1 to front.

6) Final KE = Initial KE + energy of explosion

Final KE = 4 + 9 = 13 J.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

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