Question

See the picture

(This is a particularly challenging problem, incorporating momentum, conservation of energy, and centripetal force. If you find yourself getting annoyed, just remember that I could have turned the block into a projectile as well :-). Consider it a bonus.) A bullet of mass m = 40 g, moving horizontally with speed u, strikes a clay block of mass M = 1.45 kg that is hanging on a light inextensible string of length L = 0.770. The bullet becomes embedded in the block, which was originally at rest. What is the smallest value of u which would cause the block-on-a-string to swing around and execute a complete vertical circle?

Answer 1

51:S1pZabokep.6 l Ozanation suv bullep M clay block merrest) Just before collision and Just collision 2.l. mut mxoa (Memul wa mv CM+m) in 0.04 - 0.04 - 1:45+0.04 149 13.9 LA TNI Y 4_ 149 0 L Let speed of block of hight point of mestical cisce alle at B) is. Yo and tension in string is T. Reference line fos grawitational Applying energy consernation at A p. otential energy (rel=o) and B (KIE) A+ (P.EJA (KE) + (p. Eg m= 481002 ug=0.04 ug an / CM+m) v² + 0 = + (MAM) V6 ²4 (+ m) g 4 2 2 - 4 g= 9.8m/gh da ya wizaugh - この物 At B, mtm v T4 CM + m) g = (M+mpy? A1 -(0)2+(p. En mau of = y0x703 kg 11htm YT T= (M+mk? -(mtmjg (tm) g To execute complete vertice cisele, Tenolon am B, Jofa TL0 = (M+m)_(M+M]820 wzgr vil_ug LZ GLS v2zSgh an ( 4 1 1 2 2 2 2 Sg L = 22 Sg Lx ( 14992 and NZ 148 159 1

for minimum v V=149 sol de Vimin = ve 149 J3x9.880.77 m/s De = 228.81 m/s av