Answer:
[tex]\epsilon=\frac{p_{out}}{P_{in}} \\p_{in}=\frac{p_{out}}{\epsilon} \\p_{in}=\frac{32965.5}{0.65}\\ p_{in}=50716.1538 lb.ft/s\\[/tex]
In hp:
[tex]p_{in}=\frac{50716.1538}{500}\\ p_{in}=101.432 hp[/tex]
Part B:
[tex]\epsilon=\frac{p_{out}}{P_{in}} \\p_{in}=\frac{p_{out}}{\epsilon} \\p_{in}=\frac{50356.2}{0.65}\\ p_{in}=77471.07692 lb.ft/s\\[/tex]
In hp:
[tex]p_{in}=\frac{77471.07692}{500}\\ p_{in}=154.94215 hp[/tex]
Explanation:
Weight of elevator=1000-lb
Force=500 lb
s=15 ft
Force on pulley=F=3*500=1500 lb
g=[tex]32.2 ft/s^2[/tex]
According to Newton's Second law:
[tex]\sum F_y=ma_y[/tex]
According to attachment:
[tex]F-W=ma_y[/tex]
[tex]1500-1000=\frac{1000}{32.2}a_y[/tex]
[tex]a_y=16.1 ft/s^2[/tex]
According to third equation of motion:
[tex]v^2=v_o^2+2a_y(S-So)\\[/tex]
Where:
Vo is initial velocity
V is final velocity
S is final distance
So is starting distance
[tex]v^2=(0)^2+2*16.1*(15)\\v^2=483\\v=21.977 ft/s[/tex]
Output power:
[tex]P_{out}=F.v\\P_{out}=1500*21.977\\P_{out}=32965.5 lb.ft/s[/tex]
[tex]\epsilon=\frac{p_{out}}{P_{in}} \\p_{in}=\frac{p_{out}}{\epsilon} \\p_{in}=\frac{32965.5}{0.65}\\ p_{in}=50716.1538 lb.ft/s\\[/tex]
In hp:
[tex]p_{in}=\frac{50716.1538}{500}\\ p_{in}=101.432 hp[/tex]
Part B:
When S=35 ft
[tex]v^2=(0)^2+2*16.1*(35)\\v^2=1127\\v=33.5708 ft/s[/tex]
Output power:
[tex]P_{out}=F.v\\ P_{out}=1500*33.5708 \\ P_{out}=50356.2 lb.ft/s[/tex]
[tex]\epsilon=\frac{p_{out}}{P_{in}} \\p_{in}=\frac{p_{out}}{\epsilon} \\p_{in}=\frac{50356.2}{0.65}\\ p_{in}=77471.07692 lb.ft/s\\[/tex]
In hp:
[tex]p_{in}=\frac{77471.07692}{500}\\ p_{in}=154.94215 hp[/tex]
