A 250 g steel ball and a 500 g steel ball each hang from 3.5 m long strings. At

Question

A 250 g steel ball and a 500 g steel ball each hang from 3.5 m long strings. At rest, the balls hang side by side, barely touching. The 250 g ball is pulled to the left until the angle between its string and vertical is 21°. The 500 g ball is pulled to a 21° angle on the right. The balls are released so as to collide at the very bottom of their swings. To what angle does each ball rebound?

I worked it out to be 15° and 32° but then determined that the sum of the final heights would be greater than the initial height. I then used the potential gravity divided into 1/3 and 2/3 and came up with 12° and 17°, also wrong.

Explanation / Answer

Height of both the balls w.r.t. initial position = R(1-cos21o) = 0.23 m

their velocities = 2gh = 2*9.8*0.23 = 2.12 m/s

conserving linear momentum =

0.25 * 2.12- 0.5*2.12 = 0.25v1+0.5v2

v1+2v2=-2.12...(1)

taking coefficient of restitution=1

1=(v2-v1)/(4.24)

v1-v2 = -4.24....(2)

v1 = 3.53m/s

v2 = 0.71m/s

h=v2/2g = R(1-cos )

for 250 g,

= 35.1o

for 500g

=6.95o

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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