To determine which equation shows work being calculated using the correct units, we should look at the formula for work, which is \( W = F \times d \), where:
- \( W \) (work) is measured in Joules (J)
- \( F \) (force) is measured in Newtons (N)
- \( d \) (distance) is measured in meters (m) or feet (ft)
From the options given, we need to check if the units on both sides of the equation match correctly based on the formula.
-
113 N = (17.4 J) × (6.51 m)
- Left side: 113 N
- Right side: Units are Joules × meters. This does not equate since Joules are not a unit of force.
-
113 N = (17.4 J) × (6.51 ft)
- Left side: 113 N
- Right side: Units are Joules × feet. This does not equate for the same reason as above.
-
113 J = (17.4 N) × (6.51 m)
- Left side: 113 J (Correct, as work is measured in Joules)
- Right side: Correct calculation since Newtons × meters will give us Joules. Thus, this is consistent with the formula \( W = F \times d \).
-
113 J = (17.4 N) × (6.51 ft)
- Left side: 113 J (Correct, as work is measured in Joules)
- Right side: Newtons × feet. This would also give a measure of work, but it should be noted that it's using feet instead of meters, which might require conversion.
The equation that shows work being calculated using the correct units is:
113 J = (17.4 N) × (6.51 m).
This is the correct choice since it properly represents the units for work in Joules derived from the units of force in Newtons and distance in meters.