Use the data below to rank machines A,
B, and C from:
(a) highest to lowest mechanical advantage
(b) highest to lowest efficiency
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5.2 CHECK and REFLECT
S T B33 Thinking about Science, Technology, and Society S E
Machine
Input
Force (N)
Input
Distance
(m)
Output
Force (N)
Output
Distance
(m)
A 5.0 10 20 2.0
B 10 25 50 3.5
C 20 6.0 27 4.0
To rank the machines from highest to lowest mechanical advantage, we need to calculate the mechanical advantage for each machine. The mechanical advantage is calculated by dividing the output force by the input force. The higher the mechanical advantage, the more the machine amplifies the input force.
(a) Ranking from highest to lowest mechanical advantage:
Machine A: Mechanical Advantage = Output Force/Input Force = 20N/5N = 4
Machine B: Mechanical Advantage = Output Force/Input Force = 50N/10N = 5
Machine C: Mechanical Advantage = Output Force/Input Force = 27N/20N = 1.35
Therefore, the ranking from highest to lowest mechanical advantage is B > A > C.
To rank the machines from highest to lowest efficiency, we need to calculate the efficiency for each machine. Efficiency is calculated by dividing the output work by the input work, and multiplying it by 100 to express it as a percentage. The higher the efficiency, the more effective the machine is at converting input work into useful output work.
(b) Ranking from highest to lowest efficiency:
Machine A: Efficiency = (Output Work/Input Work) x 100 = (Output Force x Output Distance)/(Input Force x Input Distance) x 100 = (20N x 2m)/(5N x 10m) x 100 = 80%
Machine B: Efficiency = (Output Work/Input Work) x 100 = (Output Force x Output Distance)/(Input Force x Input Distance) x 100 = (50N x 3.5m)/(10N x 25m) x 100 = 70%
Machine C: Efficiency = (Output Work/Input Work) x 100 = (Output Force x Output Distance)/(Input Force x Input Distance) x 100 = (27N x 4m)/(20N x 6m) x 100 = 90%
Therefore, the ranking from highest to lowest efficiency is C > A > B.