What force must be exerted on the master cylinder of a...

What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2500-kg car (a large car) resting on the slave cylinder? The master cylinder has a 3.00-cm diameter and the slave has a 24.0-cm diameter. A) 136 N B) 383 N C) 245 N D) 178 N

Transcript

00:01 All everyone in this question we're given that there is a hydraulic lift which is used to support a mass m equal to 2500 kgg 500 kg is the mass of the car and the car rests on the slave cylinder we're given the diameter of the slave cylinder which you take is d1 and it is equal to 24 centimeter if we convert this to s i unit we'll get diameter d1 is equal to 0 .24 meter then we're given the diameter of the master cylinder which you take is d2 and it is equal to 3 centimeter again converting into s i unit d2 it equal to 0 .03 meter we have to find out the force that must be exerted on the master cylinder which you take is f2 so that the hydraulic lift is able to support the car which has a mass of 2500 gg so first of all let us find out the area of the slave cylinder we take this area to be a 1 and it is given by pi by 4 multiplied by square of its diameter which is t1 square so area a 1 will be equal to pi divided by 4 multiplied by 0 .24 square and the area of the master cylinder which you take as a 2 is given by pi by 4 multiplied by square of the diameter of the master cylinder so we have a 2 is equal to pi by 4 multiplied by the diameter of the master cylinder is 0 .03 so 0 .0 3 square how to further solve this question we'll first find out the force on the slave cylinder that means the cylinder on which the car is lying we take this force to be f1 it will be equal to the gravitational force on the car that is m g so the force f will be equal to the mass is 2 ,500 kg multiplied by the acceleration due to gravity is 9 .8 meter per second square this comes out to be equal to 24 ,500 newton.

02:23 Now we'll apply pascal's law according to which f1 by a1 will be equal to f2 by a2.

02:36 From this equation we will get the force f2 is equal to 2 divided by a 1 multiplied by f1 so this is equal to a 2 is 5 by 4 multiplied by 0 .03 square so a 2 divided by a 1 which is pi by 4 multiplied by 0 .24 square multiplied by f1 which came out as 24 ,500 newton so if we calculate this we'll get the value of force which is f2 and it comes out to be equal to 382 .81 newton...

Question

What force must be exerted on the master cylinder of a hydraulic lift to support the weight of a 2500-kg car (a large car) resting on the slave cylinder? The master cylinder has a 3.00-cm diameter and the slave has a 24.0-cm diameter. A) 136 N B) 383 N C) 245 N D) 178 N

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