To determine the force exerted on the brake system, we need to clarify a few points from your question, as it seems there may be some confusion with the units or terminology used.
You have mentioned:
- A driver applies a force of 50 N on the brake pedal.
- The area of the brake pedal is 0.2 m².
- You mentioned "the brake pass has an area of 1m/s²," which seems to be a mix-up; we typically refer to force and pressure per unit area.
If you meant to refer to the brake mechanism, let's proceed by applying the principle of pressure transmission in hydraulic systems, which states that pressure is constant in a closed system:
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Calculate the pressure applied on the brake pedal: \[ \text{Pressure} (P) = \frac{\text{Force (F)}}{\text{Area (A)}} = \frac{50 , \text{N}}{0.2 , \text{m}^2} = 250 , \text{Pa} \]
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Assuming a system with a larger area (like a brake mechanism): If the brake pad area is larger, say 1 m², we then can calculate the force exerted on the brakes by using the same pressure:
\[ \text{Force on brake} (F) = P \times A = 250 , \text{Pa} \times 1 , \text{m}^2 = 250 , \text{N} \]
Thus, if our assumption about the areas is correct, the force exerted on the brake mechanism would be 250 N.
Let me know if there are any corrections or if you want to clarify any terms!