find the work done in winding up a 175 ft cable that weighs 4.00 lb/ft?
Assuming the whole cable is just hanging there, the work required to raise it up is
∫(175-x)(4dx)[0,175]
= 4(175x - .5x^2)[0,175]
= 700x - 2x^2[0,175]
= [700*175 - 2*175^2] - [0-0]
= 61250
61250
Well, well, well... It seems we have a cable-winding conundrum on our hands! Let's calculate the work done, shall we?
First, we need to find the total weight of the cable. Since the weight is given as 4.00 lb/ft and the length is 175 ft, we can simply multiply the two values together. So, 4.00 lb/ft x 175 ft = 700 lb. That's quite a heavy load!
Now, to calculate the work done, we need to consider the formula: work = force x distance. In this case, the force is the weight of the cable and the distance is the length of the cable.
So, the work done in winding up the cable is: work = 700 lb x 175 ft = 122,500 ft-lb.
Wowza! That's one hefty amount of work just to wind up a cable. But hey, someone's gotta do it, right? Keep those muscles flexing!
To find the work done in winding up the cable, we need to calculate the total weight of the cable and then multiply it by the distance it is wound up.
Given:
Length of the cable (L) = 175 ft
Weight of the cable per foot (W) = 4.00 lb/ft
Step 1: Calculate the total weight of the cable.
Total weight = Weight per foot x Length of the cable
Total weight = 4.00 lb/ft x 175 ft
Step 2: Calculate the work done.
Work done = Total weight x Distance wound up
The distance wound up is typically not given in the problem, so we'll assume it is the full length (175 ft).
Work done = (4.00 lb/ft x 175 ft) x 175 ft
Let's calculate it now:
Work done = (4.00 lb/ft x 175 ft) x 175 ft
= 700 lb x 175 ft
= 122,500 ft.lb
Therefore, the work done in winding up the 175 ft cable is 122,500 ft.lb.
To find the work done in winding up a cable, we need two pieces of information: the weight of the cable and the distance it is being lifted.
In this case, we are given that the cable weighs 4.00 lb/ft and the length of the cable is 175 ft.
To find the total weight of the cable, we can multiply the weight per foot by the total length:
Total weight = weight per foot * total length
Total weight = 4.00 lb/ft * 175 ft
Total weight = 700 lb
Now that we have the total weight of the cable, we can calculate the work done in lifting it. The work done is given by the equation:
Work = force * distance
In this case, the force is equal to the weight of the cable, and the distance is the height it is being lifted. Since we are winding up the cable, we assume that it is being lifted vertically.
The work done in lifting the cable is:
Work = weight * height
Now, to find the work done, we need to know the height at which the cable is being lifted. If we have that information, we can multiply the weight of the cable (700 lb) by the height to get the work done.