To determine which equation shows work being calculated using the correct units, we need to recall the formula for work:
\[ W = F \times d \]
Where:
- \( W \) is the work in joules (J)
- \( F \) is the force in newtons (N)
- \( d \) is the distance in meters (m)
From the formula, we can deduce that the units for work (Joules) is equivalent to the units of force (Newtons) multiplied by the units of distance (meters):
\[ 1 , J = 1 , N \times 1 , m \]
Now let's analyze the responses provided:
-
113 N = (17.4 J) × (6.51 m)
- Incorrect because the left side has units of force (N), but the right side calculates to units of work (J).
-
113 J = (17.4 N) × (6.51 ft)
- Incorrect because the right side has units of force (N) multiplied by distance in feet, which will not result in joules.
-
113 N = (17.4 J) × (6.51 ft)
- Incorrect because the left side is in newtons (N) and the right side has units of work (J) multiplied by distance in feet, which is incorrect.
-
113 J = (17.4 N) × (6.51 m)
- Correct because the left side is in joules (J), and the right side correctly calculates work as a force (N) multiplied by distance (m).
Thus, the correct response is:
113 J = (17.4 N) × (6.51 m)