In a car lift, compressed air exerts a force on a piston with a radius of 5.00 cm.
This pressure is transmitted to a second piston with a radius of 15.0 cm.
a. How large a force must the compressed air exert to lift a 1.33 × 104 N car?
b. What pressure produces this force? Neglect the weight of the pistons.
Answers
Answer:
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Answer: In a car lift, compressed air exerts a force F1 on a small piston having a radius of 5cm. This pressure is transmitted to the second piston of a radius of 15cm. If the mass of the car to be lifted is 1350 kg. What is F1?
From pascal’s law P1 = P2 F1A1 = F2A2 F1pir1^2 = F2pir2^2 F1 = F2r1^2r2^2 F1 = 1350 × 9.8 × (5 × 10^-2)^2(15 × 10^-2)^2 F1 = 1470 N F1 = 1.47 × 10^3
According to Pascal's law, Pressure is transmitted equally and undiminished throughout the fluid.P1=P2F1/A1=F2/A2F1= (A1/A2 ) F2=[π(5 x10⁻²m)²/π(15x10⁻²m)² ](1350Nx9.8m/s2)=1470N=1.5 x 10³ NThe air pressure that will produce this forceP=F1/A1=1.5x10³N/π(5x10⁻²)² m=1.9 x 10⁵ PaThis is almost the double of atmospheric pressure.
Explanation:
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