Answer:
Explanation:
Stiffness of spring k equal to 4 lb/ft.
Unstretched length of the spring L is equal to 0.5 feet.
Weight of the collar W is 15lb
Radius of curvature of curve guide is 1 feet
length of vertical rod is 1.5 feet
Initial speed of collar when released from rest at A is 0 feet per seconds
use the energy conservation equation
[tex]P_A +K_A=P_B+K_B[/tex]
Estimate the potential energy , component as position B as below
[tex]P_A=Wh_1+\frac{1}{2} ks^2_1\\\\=5\times(1.5+1)+\frac{1}{2} \times 4 \times(1.5+1-0.5)^2\\\\=20.5lb.ft[/tex]
Estimate the kinetic energy , component as position A as below
[tex]K_A=\frac{1}{2} \frac{W}{g} V^2_1\\\\=\frac{1}{2} \frac{5}{32.2} \times0^2\\\\=0lb.ft[/tex]
Estimate the kinetic energy , component as position B as below
[tex]K_A=\frac{1}{2} \frac{W}{g} V^2_2\\\\=\frac{1}{2} \frac{5}{32.2} \times V^2_2\\\\=00777V^2_2[/tex]
Substitute 20.5lb- ft for [tex]P_A[/tex]
0.5lb-ft for [tex]P_B[/tex]
0lb -ft for [tex]K_A[/tex]
[tex]0.0777V_2^2 for K_B[/tex]
[tex]20.5+0=0.5+0.777V^2_2\\\\V^2_2=257.6\\\\V_2=16.05[/tex]
= 16.05ft/sec
