circular motion and gravitation \"David slew Goliath with a sling and a stone.\"

Question

circular motion and gravitation "David slew Goliath with a sling and a stone." And so we know that clever use of technology wins when matched against brute force. His sling is r = 0.7 m long, and David knows a stone of mass m = 0.25 kg will vanquish his foe as long as it hits Goliath directly in the in the head with momentum p = 13.0 kg m/n. Compare this momentum with that of the 9 mm bullet in Homework 6. (m = 7.4 grams, v = 383 m/s) How many times per second must David whirl Ills sling inorder to ensure his shot has sufficient momentum? (That is, find how many revolutions per second the sling makes. Find the centripetal force provides 1 by David's arm, and the tension in the sling required for such a shot. David misses with his first shot (the 0.25 kg stone). He then picks up another rock with mass m_2 = 3/5 m = 0.15 kg. This is the stone that slays Goliath. Find the frequency of revolution, and centripetal force for this fatal case. Compare to answers 1.b) and 1.c).

Explanation / Answer

a)

Momentum of 9mm bullet

PBullet=mV =(7,4*10-3)(383) =2.8342 m/s

So

P/Pbullet =13/2.8342 =4.5868

P/Pbullet =4.6 (approx)

c)

Velocity of the sling

V=P/m =13/0.25 =52 m/s

angular velocity

W=V/r =52/0.7 =74.3 rad/s

frequency

f=W/2pi =74.3/2pi

f=11.82 times/sec =12 times /sec (approx)

c)

Centripetal force

Fc=mV2/r =0.25*522/0.7

Fc=965.7 N

Tension in the string

T=965.7 N

d)

V=P/m =13/0.15 =86.67 m/s

angular velocuty

W=V/r =86.67/0.7 =123.8 rad/s

frequency

f=W/2pi =123.8/2pi

f=19.7 times/sec =20 times/sec (approx)

Centripetal force

F=0.15*86.672/0.7

F=1610 N

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