Note: Be careful to avoid roundoff errors in this problem. Gigantic pinball mach

Question

Note: Be careful to avoid roundoff errors in this problem.

Gigantic pinball machine:
A pinball (solid sphere of mass=0.1 kg, outer radius=0.1 m) is cocked back 0.7 m on a spring (k= 50 N/m), and fired onto the pinball machine surface, which is tilted.

a.) How much energy is stored in the spring initially?
12.25 J

b.) Find the maximum height the pinball rolls to (above its initial location.)
12.48 m

c.) When the pinball is 2.5 m above its initial location (on the way up), find its linear and angular speeds.
____ m/s
____ rad/s

Just need help with part C

Explanation / Answer

a) initial energy stored = 1/2 k x2 = .5*50*(0.7)2 =12.25 J

b) conserving mechanical energy, 1/2 k x2 = mgH

=> mgH= 12.25 => H=12.25/(0.1*9.81)=12.487m

c) conserving energy between initial position and the given position

1/2 kx2 = mgh + 1/2 mv2 + 1/2 Iw2 =mgh + 1/2mv2 + 1/2 *2/5mr2w2

                                                    = mgh + (7/10)mv2(for solid sphere I = 2/5 mr2 and for pure rolling v=wr)

=> 12.25= 0.1*9.81*2.5 + 7/10*0.1*v2

=>v2 =139.96

=>v=11.83 m/s

w=v/r = 11.83/0.1 = 118.3 rad/s

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

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