Consider the automobile hydraulic system shown in Figure 11.12. A force of 100 N is applied to the brake pedal, which acts on the pedal cylinder through a lever. A force of 500 N is exerted on the pedal cylinder. (The reader can verify that the force is 500 N using techniques of statics from Applications of Statics, Including Problem-Solving Strategies.) Pressure created in the pedal cylinder is transmitted to four wheel cylinders. The pedal cylinder has a diameter of 0.500 cm, and each wheel cylinder has a diameter of 2.50 cm. Calculate the force F₂ created at each of the wheel cylinders.

Strategy

We are given the force F₁that is applied to the pedal cylinder. The cross-sectional areas A₁ and A₂ can be calculated from their given diameters. Then can be used to find the force F₂. Manipulate this algebraically to get F₂on one side and substitute known values:

Transcribed Image Text:

THE F= 100 N FE 0.040 m 0.20 m 0.5 cm 3 Pedal cylinder F₂ F₂ I 2.5 cm Wheel cylinder F₂ F₂