Dimas reads that it takes 270 N to lift a firefighter's equipment. If a firefighter does 5400 J of work carrying the equipment up a staircase, how high does the firefighter climb? (Work: W = Fd)
A. 20 m
B. 200 m
C. 5130 m
D. $1,458,000 m$
Answer (2)
We know the force required to lift the equipment is F = 270 N and the work done is W = 5400 J.
Apply the formula W = F × d to find the distance d .
Rearrange the formula to solve for d : d = F W .
Calculate the height: d = 270 5400 = 20 m. The firefighter climbs 20 m .
Explanation
Understanding the Problem We are given that the force required to lift the firefighter's equipment is 270 N, and the work done by the firefighter is 5400 J. We need to find the height the firefighter climbs. We know that Work (W) = Force (F) × Distance (d). In this case, the distance is the height the firefighter climbs.
Identify Given Values We are given: Force, F = 270 N Work, W = 5400 J We need to find the distance, d , which represents the height the firefighter climbs.
Apply the Work Formula Using the formula for work, W = F × d , we can rearrange to solve for d :
d = F W Substitute the given values: d = 270 N 5400 J
Calculate the Height Now, we perform the calculation: d = 270 5400 = 20 So, the height the firefighter climbs is 20 meters.
State the Final Answer The firefighter climbs 20 meters.
Examples
Imagine you're lifting a heavy box straight up. The amount of energy you use (work) depends on how heavy the box is (force) and how high you lift it (distance). Similarly, firefighters use energy to carry their equipment up stairs. Knowing the force needed to lift the equipment and the total work done, we can calculate the height they climbed. This concept applies to many real-world scenarios, such as calculating the work done by elevators, cranes, or even your own muscles when lifting objects.
The firefighter climbs a height of 20 meters after doing 5400 J of work while lifting equipment that requires 270 N of force. This is calculated using the formula for work: W = F × d. By rearranging the formula to solve for distance and substituting the values, we find d = 20 m.
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