A block is projected with a speed v_0 such that it strikes the point of projection after describing the path as shown by the dotted line. If friction exists for the parth of length d and the vertical circular path is smooth, assuming mu=coefficient of friction, a. Find v_0. b. What is the minimum value of v_0?

A block is projected with a speed v_0 such that it strikes the point o

1.	A block is projected with a speed v_0 such that it strikes the point of projection after describing the path as shown by the dotted line. If friction exists for the parth of length d and the vertical circular path is smooth, assuming mu=coefficient of friction, a. Find v_0. b. What is the minimum value of v_0?
Answer» Solution :a. From C to A, TIME TAKEN `t=sqrt((2[2R])/(G))=sqrt((4R)/(g))` `v_2=d/t=dsqrt((g)/(4R))` From B to C, `1/2mv_1^2=1/2mv_2^2+mg(2R)` `impliesv_1^2=v_2^2+4gR=(d^2g)/(4R)+4gR` From A to B: `v_1^2=v_0^2-2mugdimpliesv_0^2=v_1^2+2mugd` `impliesv_0=sqrt((d^2g)/(4R)+2g[mud+2R])` b. For minimum `v_0`, `v_1=sqrt(5gR)`