When cutting sheet metal, scissors with long handles and short blades are used. Determine the cutting force if the force applied to the handles is 40N, and the length of the arms is 20 and 5 cm.
F1 = 40 N.
L1 = 20 cm = 0.2 m.
L2 = 5 cm = 0.05 m.
The metal scissors are a lever. On the long shoulders, which are subjected to the force of the arms, the smaller shoulders, which are the cutting surface, act on the metal with force.
Let us write down the condition for the balance of the lever: M1 = M2, where M1, M2 are the moments of forces that act from opposite sides of the lever.
The moment of force M is called the product of the applied force F to the smallest distance from the application of force in the axis of rotation of the lever L: M = F * L.
F1 * L1 = F2 * L2.
F2 = F1 * L1 / L2.
F2 = 40 N * 0.2 m / 0.05 m = 160 N.
Answer: the force with which the scissors act on the metal is F2 = 160 N.
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