Question

A bullet of mass m = 40 g, moving horizontally with speed v, strikes a clay block of mass M=1.33 kg that is hanging on a light inextensible string of length L=0.767. The bullet becomes embedded in the block, which was originally at rest. What is the smallest value of vv which would cause the block-on-a-string to swing around and execute a complete vertical circle?

Answer 1

FONT _ Reference level Prom compervation mu = of momentum of system m +M) V E =A nee m +M Froom comervation of energy K»Eit PEi = Ki Et + PoEf Ilm+) v2 +0 = 1 (m+m) uz tom+M)g (22) > v2 = 1² + 49L - 1 room equation (i) god (11) m2u? = + 4gL (mtm)2 3 v² = m² ² - 4gL (on tom)2

FONT _ Reference level Prom compervation mu = of momentum of system m +M) V E =A nee m +M Froom comervation of energy K»Eit PEi = Ki Et + PoEf Ilm+) v2 +0 = 1 (m+m) uz tom+M)g (22) > v2 = 1² + 49L - 1 room equation (i) god (11) m2u? = + 4gL (mtm)2 3 v² = m² ² - 4gL (on tom)2

F.BD of bullet-clay system at top {m+m] 9 HT For circular motion (on tm) g +T = (mtm] vt for minimum speed, Teo .. (on+m) y = 60+m) I E 76 = 7 & m² v ² - 49L = gr M/2 = 58L ² m2u2 ontmj2 = v= m+m) 5gh substituting values v = (1.33kg +0.04 kg) 15x9.8m)5x0.767m 10.048g) Tu= 209.97 mis