Questions 7-10 and tadius R is located on a frictionless table and pivoted at Tr

Question

Questions 7-10 and tadius R is located on a frictionless table and pivoted at Trom the disk as shown in the igure. (For a disk of mass M and A disk of mass Tm its center, and initially at rest. A point mass of m with an initial speed vo hits and s 7. What ave the conserved quantites in this collision? (a) L relative to the center of mass of the disk every point in space (c) relative to the point of collision (e) (b) 5 and L relative to the and L relativeto the point of collision (d) 8. What is the iteo e angular speed of the disk just after the collision? 9. What is the impulse transferred to the mass m during the collision? 10. If the disk were not pivoted at the beginning, what would be the center of mass velocity, vom, of the disk just after the (e) -muo3/2) (b) mvoi (e) mo(+ 3/2) (d)-2mwol(2i-i) (e) -muo- v33/4) collision? (a) (i-j) (i-j) (i-VS3/4) (e) 2 (i-3) (b) (c)?(21-j) (d)

Explanation / Answer

7.

a)

Angular momentum about a fixed axis L is conserved before and after the collision.

b)

Since there will be some reaction forces due to collision at the center of disc, which will result in net moment, p and L cannot be conserved relative to every point in space.

c)

Relative to the point of collision, both L1 and L2 will be 0. Hence, L will be conserved.

d)

For disc, linear momentum p relative to point of collision is 0 before collision and Rw after collision. For mass, p is not same before and after collision. Hence, p is not conserved.

e)

As found in part d, p is not conserved.

Therefore, option a and c are correct.

8.

Before collision, angular momentum of disc, L1disk = 0

Before collision, angular momentum of mass, L1mass = - mv0 * R/2 k

After collision, angular momentum of disc, L2disk = Iw = - MR2 / 2 * w k

After collision collision, angular momentum of mass, L2mass = - m (v0 root3 / 4) * (R root3 /2) k = - 3/8 mv0 R k

0 - mv0 * R/2 k = - MR2 / 2 * w k  - 3/8 mv0 R k

Magnitude of w = mv0 / (4MR)

9.

Impulse = Change in momentum

= m (v0 root3 / 4) j - mv0 i

= - mv0 (i - root3 j / 4)

10.

Linear momentum balance yields, mv0 i + 0 = m (v0 root3 / 4) j + M (Vx i + Vy j)

Vx = mv0 / M

Vy = - m (v0 root3 / 4) / M

Vcm = Vx i + Vy j

= (mv0 / M) i - m (v0 root3 / 4) / M j

= (mv0 / M) (i - root3 j / 4)

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

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