Calculating Forces & Heights in a Hydraulic Lift

In summary, a hydraulic lift is a machine that uses fluid mechanics to move objects by applying force through a confined fluid. The force in a hydraulic lift can be calculated using the formula F = P x A, where F is the force, P is the pressure, and A is the surface area of the piston. The relationship between force and pressure in a hydraulic lift is that the force applied to the piston is multiplied by the surface area to create a higher pressure that is transmitted to lift larger or heavier objects. To calculate the height or distance a hydraulic lift can lift an object, the weight of the object, surface area of the piston, and pressure of the fluid are needed, and the formula is h = W x A / P. Real
  • #1
Mowgli
31
0

Homework Statement



In a hydraulic lift the radii of the pistons are 1.75cm and 10.5cm. A car weighing 18.5kN is to be lifted by the force of the large piston.

a.) what force must be applied to the small piston?

b.) when the small piston is pushed 1.00cm, how far is the car lifted?

c.) find the mechanical advantage of the lift (this is the ratio of the large force to the small force)

The Attempt at a Solution



a.) F= (r/R)^2 (F)
= (1.75 cm/10.5 cm)^2 (18.5 kN)
= .514 or 514 N

b.) Win(f)= Wout(F)= fh=FH=H= (f/F)h= (pi)r^2/(piR^2=(r/R)^2
= (1m/R)^2 = (100cm/10.5cm)^2
= 90.7cm

c.) MA= F/f= 18.5kN/1.75cm
= 10.57I have no clue if I am doing this right.. can anyone help?
 
Last edited:
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  • #2
Mowgli said:
a.) F= (r/R)^2 (F)
= (1.25 cm/15.0 cm)^2 (14.5 kN)
= .1007 or .101 N
Good, but careful with units. (Those are kN, not N.)

b.) Win(f)= Wout(F)= fh=FH=H= (f/F)h= (pi)r^2/(piR^2=(r/R)^2
= (1m/R)^2 = (100cm/10.5cm)^2
= 90.7cm
FH = fh is correct. What's the ratio of the forces?

c.) MA= F/f= 18.5kN/1.75cm
= 10.57
What's the ratio of the forces?
 
  • #3
I'm not sure how to find that?
 
  • #4
Mowgli said:
I'm not sure how to find that?
Use what you found in part a.
 
  • #5
is it 1/10?
 
  • #6
Mowgli said:
is it 1/10?
Nope. You were given one force and for part a you found the other force. What's their ratio?
 
  • #7
14.5/101
 
  • #8
I just realized my problem had the wrong numbers- so I edited the problem...

For part b.) is my ratio now 18.5/514?
 
  • #9
Mowgli said:
For part b.) is my ratio now 18.5/514?
(18.5/514)^2 ??

and then I think c.) is MA=F/f = 18.5/.514
= 35.9

Can anyone help?
 
  • #10
Trying to figure this out:

b.) (r/R)^2
so, therefore it should be (1.75/10.5)^2
which = .0278

c.) MA= F/f = 18.5/.514 = 35.9

?
 
  • #11
Mowgli said:
Trying to figure this out:

b.) (r/R)^2
so, therefore it should be (1.75/10.5)^2
which = .0278

c.) MA= F/f = 18.5/.514 = 35.9

?
That's fine. The ratio of forces is given by (R/r)^2 = (10.5/1.75)^2 = 6^2 = 36.

So for b, the large piston will raise by 1/36 of the distance the small piston is lowered.

And for c, the mechanical advantage is just that ratio of forces.
 

FAQ: Calculating Forces & Heights in a Hydraulic Lift

What is a hydraulic lift?

A hydraulic lift is a type of machine that uses the principles of fluid mechanics to move objects by applying force through a confined fluid. It consists of a cylinder filled with fluid, a piston that moves up and down, and a platform or arm that is attached to the piston to lift or move objects.

How do you calculate the force in a hydraulic lift?

To calculate the force in a hydraulic lift, you need to know the surface area of the piston, the pressure of the fluid, and the height or distance the piston moves. The formula for calculating force is F = P x A, where F is the force, P is the pressure, and A is the surface area of the piston.

What is the relationship between force and pressure in a hydraulic lift?

In a hydraulic lift, the force applied to the piston is multiplied by the surface area of the piston to create a higher pressure in the fluid. This pressure is then transmitted through the fluid to the other end of the lift, where it is used to lift objects that are larger or heavier than the initial force applied.

How do you calculate the height or distance a hydraulic lift can lift an object?

To calculate the height or distance a hydraulic lift can lift an object, you need to know the weight of the object, the surface area of the piston, and the pressure of the fluid. The formula for calculating height is h = W x A / P, where h is the height, W is the weight of the object, A is the surface area of the piston, and P is the pressure of the fluid.

What are some real-life applications of hydraulic lifts?

Hydraulic lifts are commonly used in car repair shops, construction sites, and warehouses to lift heavy objects. They are also used in elevators, cranes, and forklifts. In addition, hydraulic lifts are used in medical equipment, such as patient lifts and dental chairs, and in aircraft to operate landing gears and control systems.

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