Question

A 0.299 kg bead slides on a curved wire, start-ing from rest at point A as described below:
A: a crest (hill) 6.15 m high
b: a valley between A and C
C: a crest (hill) 1.85 m high

The acceleration of gravity is 9.8 m/s2 .
1) If the wire is frictionless, find the speed of the bead at B. Answer in units of m/s.

2)Find the speed of the bead at C. Answer in units of m/s.

Answer 1

consider energy.
PE(A)=mg*6.15
KE(A)=zero, given
total energy=mg*6.15

PE(B)=0 assuming the valley is zero height
KE(B)=totalenrgy-PE(B)=mg*6.15

PE(C)=mg*1.85
KE(C)=totalenergy-PI
= mg*6.15-mg*1.85

so to find speed from ke,
v=sqrt(2*mg(height))