a metal cutting machine has a stroke of 0.7 m. the resistance to cutting varies uniformly from 850N at the beginning of the stroke to 1600N when the cutter has moved 0.5 m. for the last 0.2 m of the stroke the resistance is constant at 1600N. Calculate the work done during the stroke.
To calculate the work done during the stroke, we need to find the total force applied and the distance over which the force acts. We can break down the stroke into three parts:
1. Part 1: From the beginning of the stroke to when the cutter has moved 0.5 m.
2. Part 2: From when the cutter has moved 0.5 m to when the cutter has moved 0.7 m.
3. Part 3: The last 0.2 m of the stroke.
Let's calculate the work done for each part separately:
1. Part 1: The resistance to cutting varies uniformly from 850 N to 1600 N over a distance of 0.5 m. Since the resistance varies uniformly, we can find the average value of the resistance by taking the average of the initial and final values:
Average resistance = (850 N + 1600 N) / 2 = 1225 N
The work done in Part 1 is given by the formula:
Work = Force (average) * Distance
Work = 1225 N * 0.5 m
2. Part 2: In this part, the resistance is constant at 1600 N. The force remains constant, so the work done is given by:
Work = Force (constant) * Distance
Work = 1600 N * (0.7 m - 0.5 m)
3. Part 3: The resistance is also constant at 1600 N. The distance is 0.2 m. So, the work done in Part 3 is:
Work = Force (constant) * Distance
Work = 1600 N * 0.2 m
To find the total work done during the stroke, we add the work done for each part:
Total Work = Work Part 1 + Work Part 2 + Work Part 3
Now you can substitute the values and calculate the total work done during the stroke.