Answer:
a) 2.91 hp
b) 3.81 hp
Explanation:
As we cans ee in the diagram given below force F has same direction as velocity [tex]V_D[/tex], The power is equivalent to[tex] FV_D[/tex]
A) Uniform motion
As both bodies are in equilibrium,therefore we have following relation
By free body for C:
2T - 800 = 0
T = 400 lb
By free body for D
F + T - 600 lb = 0
F = 600 - T
= 600 - 400 = 200 lb
[tex]Fv_D = 200\times 8 = 1600 ft. lb/s[/tex]
[tex]Power = 1600 \times \frac{1}{550} = 2.91 hp[/tex]
2)
we have
[tex]a_D = 2.5 ft/s^2 [given][/tex]
[tex]a_C = -\frac{1}{2}a_D = 1.25[/tex]
from equation of motion
by free body diagram C
F = ma
[tex]800- 2T = \frac{800}{32.2}1.25[/tex]
T = 384.5 lb
by free body diagram of D
F = ma
[tex]F + T -600 = \frac{600}{32.2} (2.5)[/tex]
F =262.1 lb
[tex]FV_D = 262.1 \times 8 = 2097 ft. lb/s[/tex]
[tex]Power = (2097) \frac{1 hp}{550 ft. lb/s} = 3.81 hp[/tex]
