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Zorluk: KolayLevers and Fulcrums

A construction worker uses a rigid pry bar to lift a concrete slab that weighs 400 lbs400\text{ lbs}. The fulcrum is placed exactly 1 foot1\text{ foot} away from the point where the pry bar contacts the slab. If the worker applies a downward force exactly 5 feet5\text{ feet} away from the fulcrum, how many pounds of effort force must be applied to just balance the slab?

Cevap: 80 lbs

Cevap

80 lbs
To balance the lever, the torque on both sides of the fulcrum must be equal. The load torque is generated by the slab: 400 lbs×1 ft=400 ft-lbs400\text{ lbs} \times 1\text{ ft} = 400\text{ ft-lbs}. To create an equal effort torque on the other side at a distance of 5 feet5\text{ feet}, an effort force of 80 lbs80\text{ lbs} is required because 80 lbs×5 ft=400 ft-lbs80\text{ lbs} \times 5\text{ ft} = 400\text{ ft-lbs}.

Adım Adım Çözüm

1
Identify the known variables given in the problem statement.
Load Force (FLF_L) = 400 lbs400\text{ lbs}, Load Distance (dLd_L) = 1 ft1\text{ ft}, Effort Distance (dEd_E) = 5 ft5\text{ ft}.
These values are required to calculate the unknown effort force using the law of the lever.
2
Apply the law of the lever (torque balance equation).
FE×dE=FL×dLF_E \times d_E = F_L \times d_L
A lever is in static equilibrium when the input torque exactly equals the output torque.
3
Substitute the known values and solve for the effort force (FEF_E).
FE×5=400×1→5FE=400→FE=80F_E \times 5 = 400 \times 1 \rightarrow 5F_E = 400 \rightarrow F_E = 80
Isolating FEF_E provides the exact pounds of force needed to balance the concrete slab.

Anahtar Kavram

Torque Balance and the Law of the Lever
Tahmini Süre:45s
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Konular

Levers and Fulcrums

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