A 34 g steel ball bounces elastically on a steel plate, always returning to the

Question

A 34 g steel ball bounces elastically on a steel plate, always returning to the same maximum height h = 19.5 m. With what speed does the ball leave the plate? What is the magnitude of the total change in momentum of the ball with each bounce? What is the magnitude of the total momentum the ball transfers to the plate at each bounce? What is the time interval between bounces? Averaged over a long time interval, what is the magnitude of the rate at which momentum is transferred to the plate? What is the magnitude of the average force exerted by the ball on the plate? What is the weight of the ball?

Explanation / Answer

(7) is the easiest, if we're to assume this happens in a terrestrial environment! W = (0.034 kg)(9.8 m/s^2) = 0.222N

(1) Again assuming a terrestrial environment, the "v-up" can be found from
2*19.5 m*9.8 m/s^2 = (v-up)^2
v-up = 19.54 m/s

(2) (0.034 kg)(19.54m/s)*2 = 1.298 kg - m/s

(3) 1.298 kg-m/s

(4) The time for JUST the falling satisfies h = (1/2)gt^2,
so the time for the rising AND falling must satisfy
t = 2*sqrt(2h/g) = 3.987 seconds

(5) 1.298 kg-m/s divided by 3.987 seconds
= 0.325 kg m/s^2

(6) 0.325 N

and I guess the "punch line" is, that that's the weight of the ball.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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