- #1
bpw91284
- 67
- 0
Problem
Sphere has ring around it. At T=70C the diameter of the sphere is 0.05% larger than the diameter of the ring. At what temp will the ring be able to come off sphere?
Attempt
D_s=1.0005*D_r at 70C
Sphere
delta_V=beta*V_o*delta_T
Ring
delta_L=alpha*L_o*delta_T
L=pi*D_r (circumference)
delta_L=alpha*(pi*D_r,o)*delta_T
Tried relating D_r and D_s with sphere volume eqn (V=4/3*pi*(D_s/2)^3) and circumference of ring eqn C=L_r=pi*D_r and I'm stuck...
Temeperature where D_r=D_s is the point when ring can come off, but I don't know how to get there.
Sphere has ring around it. At T=70C the diameter of the sphere is 0.05% larger than the diameter of the ring. At what temp will the ring be able to come off sphere?
Attempt
D_s=1.0005*D_r at 70C
Sphere
delta_V=beta*V_o*delta_T
Ring
delta_L=alpha*L_o*delta_T
L=pi*D_r (circumference)
delta_L=alpha*(pi*D_r,o)*delta_T
Tried relating D_r and D_s with sphere volume eqn (V=4/3*pi*(D_s/2)^3) and circumference of ring eqn C=L_r=pi*D_r and I'm stuck...
Temeperature where D_r=D_s is the point when ring can come off, but I don't know how to get there.