Asked by xochitl
How do you calculate the amount of work done when using a lever?
All Answers 1
Answered by
GPT-5 mini
AI
Work done by a force on a lever is the force times the distance the point of application moves (in the force direction). For a lever that rotates about a fulcrum it's convenient to use angular quantities:
- Linear displacement at a distance r from the fulcrum for an angular rotation θ (radians) is s = r·θ.
- Work done by a force F applied at that radius during the rotation is
W = F · s = F · r · θ. (Units: joules)
For an ideal (lossless) lever, input work equals output work:
Win = Wout ⇒ Fin·rin·θ = Fout·rout·θ ⇒ Fin·rin = Fout·rout,
so mechanical advantage MA = Fout/Fin = rin/rout = sout/sin.
Example: a 10 N input at r = 0.5 m rotates the lever by 0.2 rad:
W = 10·0.5·0.2 = 1.0 J.
Notes:
- If the lever doesn’t move, no work is done.
- With friction or deformation, some input work is lost and Wout < Win.
- You can also compute work as the weight lifted times the vertical height gained (mgh) for lifting tasks.
- Linear displacement at a distance r from the fulcrum for an angular rotation θ (radians) is s = r·θ.
- Work done by a force F applied at that radius during the rotation is
W = F · s = F · r · θ. (Units: joules)
For an ideal (lossless) lever, input work equals output work:
Win = Wout ⇒ Fin·rin·θ = Fout·rout·θ ⇒ Fin·rin = Fout·rout,
so mechanical advantage MA = Fout/Fin = rin/rout = sout/sin.
Example: a 10 N input at r = 0.5 m rotates the lever by 0.2 rad:
W = 10·0.5·0.2 = 1.0 J.
Notes:
- If the lever doesn’t move, no work is done.
- With friction or deformation, some input work is lost and Wout < Win.
- You can also compute work as the weight lifted times the vertical height gained (mgh) for lifting tasks.
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