Suppose the input piston of a hydraulic jack has a diameter of 3 cm and the load piston a diameter of 24 cm. The jack is being used to lift a car with a mass of 1700 kg.
- a. What are the areas of the input and load pistons in square centimeters? (A = πr2)
- b. What is the ratio of the area of the load piston to the area of the input piston?
- c. What is the weight of the car in newtons? (W = mg)
- d. What force must be applied to the input piston to support the car?
(a)
The area of input and load piston.
Answer to Problem 1SP
The area of input piston is
Explanation of Solution
Given info: Diameter of input piston is
Write the equation to find the area of input piston.
Here,
Substitute
Write the equation to find the area of load piston.
Here,
Substitute
Conclusion:
The area of input piston is
(b)
Ratio of area of load piston to area of input piston.
Answer to Problem 1SP
The ratio is
Explanation of Solution
Write the equation to find the ratio of area of load piston and input piston.
Substitute
Conclusion:
The ratio is
(c)
The weight of car.
Answer to Problem 1SP
The weight of car is
Explanation of Solution
Write the equation to find the weight.
Here,
Substitute
Conclusion:
The weight of car is
(d)
The force applied to piston to balance the car.
Answer to Problem 1SP
The force applied is
Explanation of Solution
Write the equation to find the pressure.
Here,
Substitute
Conclusion:
The force applied is
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