A rescue cable attached to a helicopter weighs 2 lb/ft. A 190 lb man grabs the end of the rope and is pulled from the ocean into the helicopter. How much work is done by lifting the man if the helicopter is 50 ft above to water.
A) 12,000 ft lb
B) 9,600 ft lb
C) 2,690 ft lb
D) 14,500 ft lb
12000
To find the work done by lifting the man, we need to calculate the total weight that is lifted.
The weight of the rescue cable is 2 lb/ft, and the height the man is lifted is 50 ft. Therefore, the weight of the rescue cable can be calculated as:
Weight of the rescue cable = 2 lb/ft * 50 ft
Weight of the rescue cable = 100 lb
In addition to the weight of the rescue cable, we have the weight of the man, which is 190 lb.
The total weight lifted is the sum of the weight of the rescue cable and the weight of the man:
Total weight lifted = Weight of the rescue cable + Weight of the man
Total weight lifted = 100 lb + 190 lb
Total weight lifted = 290 lb
Now, we can calculate the work done by lifting the man using the formula:
Work = Force x Distance
The force can be calculated as the total weight lifted, which is 290 lb, and the distance is the height the man is lifted, which is 50 ft.
Work = 290 lb * 50 ft
Work = 14,500 ft-lb
Therefore, the work done by lifting the man into the helicopter is 14,500 ft-lb.
To calculate the work done in lifting the man from the ocean into the helicopter, we need to determine the total weight being lifted.
First, let's compute the weight of the rescue cable. We are given that the cable weighs 2 lb/ft. Since we need to find the total weight of the cable, we multiply the weight per foot by the height (assuming the cable is fully extended) the helicopter is above the water.
Weight of the cable = Weight per foot × Height
Weight of the cable = 2 lb/ft × 50 ft
Weight of the cable = 100 lb
Now, to determine the total weight being lifted, we add the weight of the man to the weight of the cable.
Total weight being lifted = Weight of the man + Weight of the cable
Total weight being lifted = 190 lb + 100 lb
Total weight being lifted = 290 lb
Lastly, we can calculate the work done by lifting the man using the formula:
Work = Force × Distance
Since force is measured in pounds and distance is measured in feet, we can multiply the total weight by the height the man is lifted.
Work = Total weight being lifted × Height
Work = 290 lb × 50 ft
Work = 14,500 ft-lb
Therefore, the work done by lifting the man from the ocean into the helicopter is 14,500 foot-pounds (ft-lb).