An anchor weighing 110 lb in water is attached to a chain weighing 2 lb/ft in water. Find the work done to haul the anchor and chain to the surface of the water from a depth of 35 ft.
Well, this is quite the deep question! Hauling weights, huh? Seems like a real lift...literally! So, let's anchor down and calculate the work done to bring that bad boy to the surface.
To find the work done, we need to consider the weight of the anchor and the chain. The anchor weighs 110 lb (pounds) in water and the chain weighs 2 lb/ft (pounds per foot) in water. We also know the depth is 35 ft (feet). So, let's start by calculating the weight of the chain first:
Weight of the chain = (2 lb/ft) * (35 ft) = 70 lb
Now, let's add the weight of the anchor and the chain:
Total weight = 110 lb (anchor) + 70 lb (chain) = 180 lb
Now, we're ready to calculate the work done. The work done to haul an object is given by the formula:
Work = Force * Distance
In this case, the force is the total weight (180 lb) and the distance is the depth (35 ft). So, let's plug in the values:
Work = 180 lb * 35 ft = 6300 ft-lb
So, the work done to haul the anchor and chain to the surface from a depth of 35 ft is 6300 foot-pounds (ft-lb).
Now that's what I call some real heavy lifting!
To find the work done to haul the anchor and chain to the surface of the water, we need to consider the weight of the anchor and the weight of the chain.
The weight of the anchor can be found by subtracting the weight of water displaced by the anchor from its weight in air. Since the anchor weighs 110 lb in water, the weight of water displaced by the anchor is also 110 lb.
The weight of the anchor in air is therefore 110 lb + 110 lb = 220 lb.
The weight of the chain is given as 2 lb/ft in water. Since the depth is 35 ft, the total weight of the chain is 2 lb/ft * 35 ft = 70 lb.
To find the work done, we need to find the total weight of the anchor and the chain, and then multiply it by the distance moved.
The total weight of the anchor and the chain is 220 lb + 70 lb = 290 lb.
The distance moved is 35 ft.
Therefore, the work done to haul the anchor and chain to the surface of the water is 290 lb * 35 ft = 10150 ft-lb (foot-pounds).
To find the work done to haul the anchor and chain to the surface of the water, we can use the following formula:
Work = Force × Distance
First, let's calculate the force required to lift the anchor and the chain to the surface of the water.
The force required to lift the anchor and the chain is equal to their combined weight in water. To calculate this, we need to find the weight of the anchor and the weight of the chain.
Weight in water = Weight in air - Buoyant force
The buoyant force is equal to the weight of the water displaced by the object. For the anchor, the buoyant force is equal to the weight of the water it displaces, which is equal to its weight in air.
Weight in water = Weight in air - Weight of water displaced
Since the weight of the anchor is given as 110 lb in water, we can conclude that:
Weight in water = 110 lb
Therefore, the force required to lift the anchor is 110 lb.
Now let's calculate the force required to lift the chain. The chain weighs 2 lb/ft in water, and we want to lift it from a depth of 35 ft. So, the force required to lift the chain is equal to its weight in water, which is:
Force = Weight per unit length × Length
Force = (2 lb/ft) × 35 ft
Force = 70 lb
Now we can find the total force required to lift the anchor and chain:
Total Force = Anchor Force + Chain Force
Total Force = 110 lb + 70 lb
Total Force = 180 lb
Now that we know the force required, we can calculate the work done. The distance is given as 35 ft.
Work = Total Force × Distance
Work = 180 lb × 35 ft
Work = 6300 ft·lb
Therefore, the work done to haul the anchor and chain to the surface of the water from a depth of 35 ft is 6300 ft·lb.