Question

1. What mass can be lifted by the hydraulic press if it is known that the are:

of the small piston is 48cm and that of the large piston is 1440cm, and
the force acting on the small piston can be as large as 1000N. (use g =
10m/s)
C. 3000kg
B. 30kg
D. 30,000kg
A. 300kg
​

Answer 1

Answer: C. 3000kg

Step-by-step explanation:

Hydraulic Jack

It's a device that is used to lift heavy loads by applying force via a hydraulic cylinder.

Since the internal pressure on the liquid of the jack is constant, the following relation applies:

`\displaystyle (F_1)/(A_1)=(F_2)/(A_2)`

Where

F1 = Force applied in one end of the jack

A1 = Area of the cylinder of the same end

F2 = Force applied in the other end of the jack

A2 = Area of the cylinder of the other end

If we assume the force is being applied on side 1, then the force on side 2 is calculated by solving for F2:

`\displaystyle F_2=(F_1.A_2)/(A_1)`

We have F1=1000N, A1= 48~cm^2, A2= 1440~cm^2, thus:

`\displaystyle F_2=(1000.1440)/(48)`

`F_2 = 30000 ~N`

Since we need to know the mass that can be lifted by that force, we use the formula:

W = m.g

Where W is the weight of the mass and g= 10~m/s^2. Since the weight is equal to the force exerted by the jack:

`\displaystyle m=(W)/(g)=(30000)/(10)`

m = 3000 Kg

Answer: C. 3000kg