Final answer:
To calculate the force needed at piston A to support the 850 kg car at piston B in a hydraulic system, apply Pascal's principle and use the cross-sectional areas of the pistons, along with the car's weight.
Step-by-step explanation:
The question revolves around the concept of hydraulics and uses Pascal's principle to determine the force required to lift an object using a hydraulic system. A hydraulic lift uses this principle to enable a small force applied at one point to be magnified at another point, allowing heavy objects to be lifted with relatively small input forces.
In this case, to support an 850 kg car using a hydraulic lift, where piston A has a diameter of 17 mm and piston B has a diameter of 300 mm, we will use the formula derived from Pascal's principle: F1 = (A1/A2) * F2, where F1 is the force applied at piston A, A1 is the cross-sectional area of piston A, A2 is the cross-sectional area of piston B, and F2 is the force due to the weight of the car (weight = mass x gravitational acceleration). The cross-sectional areas can be calculated using the formula for the area of a circle, πr², where r is the radius of the piston.
Since the force due to weight (F2) is the product of the car's mass and gravitational acceleration (850 kg x 9.81 m/s²), and the radii can be derived from the given diameters, the force at piston A can be calculated accordingly. Given that the hydraulics are in equilibrium (the car is held steady with no acceleration), the force at piston A must be equal to the force at piston B when adjusted for the difference in piston areas.