A machine has an IMA of 6.0 and an AMA of 5.0. What is the work input needed by the machine to raise a 40 kg load by 3.0 m?
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To find the work input needed by the machine, we need to use the formula for mechanical advantage (MA):
MA = AMA / IMA
Given that the IMA is 6.0 and the AMA is 5.0, we can substitute these values into the formula:
5.0 = 6.0 / IMA
Rearranging the formula to solve for IMA:
IMA = 6.0 / 5.0
IMA = 1.2
Now, let's calculate the work output of the machine lifted a 40 kg load by 3.0 m. The formula for work is:
Work = force * distance
The force required to lift the load can be calculated by multiplying the mass (40 kg) by the acceleration due to gravity (9.8 m/s^2):
Force = mass * acceleration
Force = 40 kg * 9.8 m/s^2
Force = 392 N
Now, we can calculate the work output:
Work output = force * distance
Work output = 392 N * 3.0 m
Work output = 1176 J (joules)
The work input is the work output divided by the IMA:
Work input = Work output / IMA
Work input = 1176 J / 1.2
Work input = 980 J (joules)
Therefore, the work input needed by the machine to raise a 40 kg load by 3.0 m is 980 joules.