A cable that weighs 3 lb/ft. is used to lift a golf cart which weighs 700 lbs up to the deck of a boat which is 300 ft above a loading dock. Find the work done.
To find the work done, we can use the formula:
Work = force * distance
First, let's find the force required to lift the golf cart. The force can be calculated by multiplying the weight of the golf cart by the acceleration due to gravity (which is approximately 9.8 m/s^2 or 32 ft/s^2):
Force = weight * gravity
The weight of the golf cart is given as 700 lbs. So the force required to lift the golf cart is:
Force = 700 lbs * 32 ft/s^2
Next, let's find the distance that the cable needs to be lifted. The distance is given as 300 ft.
Now, let's calculate the work done:
Work = Force * Distance
Substituting the values we found:
Work = (700 lbs * 32 ft/s^2) * 300 ft
To convert the weight of the golf cart from pounds (lbs) to mass in slugs, we need to divide it by the acceleration due to gravity:
mass = weight / gravity
Substituting the values:
mass = 700 lbs / 32 ft/s^2
Since the weight per foot of the cable is given as 3 lb/ft, the mass per foot can be calculated by dividing 3 lbs/ft by the acceleration due to gravity:
mass_per_foot = weight_per_foot / gravity
Substituting the values:
mass_per_foot = 3 lbs/ft / 32 ft/s^2
Now, we can calculate the mass of the cable that needs to be lifted by multiplying the mass per foot with the distance:
mass_of_cable = mass_per_foot * distance
Substituting the values:
mass_of_cable = (3 lbs/ft / 32 ft/s^2) * 300 ft
Finally, substituting the values into the equation to find the work done:
Work = ((700 lbs * 32 ft/s^2) * 300 ft) + ((3 lbs/ft / 32 ft/s^2) * 300 ft)
Simplifying the equation will give us the final answer for the work done.