A 30 m long chain weighing 120N/m hangs from the drum of a winch. calculate the work done to wind up the first 9 m of the chain
To calculate the work done to wind up the first 9 m of the chain, we need to use the formula for work:
Work = Force x Distance
In this case, the force is the weight of the chain and the distance is the length of the chain being wound up. Here's how we can calculate it step by step:
Step 1: Determine the weight of the entire chain.
Since the weight is given as 120N/m, we have to multiply it by the length of the chain to find the total weight:
Weight = 120N/m x 30m
Weight = 3600 N
So, the weight of the entire chain is 3600 N.
Step 2: Determine the weight of the first 9m of the chain.
To find the weight of the first 9m, we can use the proportion:
Weight of the first 9m = (Weight of the entire chain / Total length of the chain) x Length of the first 9m
Weight of the first 9m = (3600N / 30m) x 9m
Weight of the first 9m = 120N/m x 9m
Weight of the first 9m = 1080N
So, the weight of the first 9m of the chain is 1080 N.
Step 3: Calculate the work done.
Now that we know the weight of the first 9m of the chain is 1080 N, we can use the work formula:
Work = Force x Distance
Work = 1080N x 9m
Work = 9720 N·m (or Joules)
Therefore, the work done to wind up the first 9m of the chain is 9720 N·m (or Joules).