Question

if ( w = f\times d ), which of the following equations shows work being calculated using the correct units? (1 point)
( 113n=(17.4j)\times(6.51ft) )
( 113j=(17.4n)\times(6.51m) )
( 113j=(17.4n)\times(6.51ft) )
( 113n=(17.4j)\times(6.51m) )

Explanation:

Step1: Recall the formula for work

Work \( W = F\times d\), where \(F\) is force (in Newtons, \(N\)) and \(d\) is displacement (in meters, \(m\)). The unit of work is Joule (\(J\)), and \(1J=1N\times1m\).

Step2: Analyze each option

• Option 1: \(113N=(17.4J)\times(6.51ft)\). Units on the right - hand side: \(J\times ft\) (incorrect, since \(W = F\times d\) should have \(N\times m\) for correct work units).
• Option 2: \(113J=(17.4N)\times(6.51m)\). Units on the right - hand side: \(N\times m\) (correct, because \(1N\times1m = 1J\)).
• Option 3: \(113J=(17.4N)\times(6.51ft)\). Units on the right - hand side: \(N\times ft\) (incorrect, since the displacement unit should be \(m\) for the work unit \(J\)).
• Option 4: \(113N=(17.4J)\times(6.51m)\). Units on the right - hand side: \(J\times m\) (incorrect, since \(W = F\times d\) should have \(N\times m\) for correct work units).

Answer:

\(113J=(17.4N)\times(6.51m)\) (the second option in the original multiple - choice list)