In a hydraulic lift, if the radius of the smaller piston is 2 cm and the radius of the larger piston is 20 cm, what weight can the larger piston support when a force of 250 N is applied to the smaller piston?
d = diameter of smaller piston
D = diameter of larger piston
I just have to use the formula
[(250 N)(pi*d^2/4)] / (pi*D^2/4)
is this correct??
the pressure in each side is the same.
F1/Area1=Force2/area2
Flarger=arealarger*250N/PI*.02^2 in N
= .1^2/.02^2 *250N = 25*250N
check my thinking.
Yes, your formula is correct for calculating the weight that the larger piston can support in a hydraulic lift. However, there seems to be a small error in the formula you wrote.
The formula to calculate the weight that can be supported by the larger piston is:
Weight = (Force x Area of smaller piston) / Area of larger piston
Using the given information:
Force = 250 N
Radius of smaller piston (r) = 2 cm = 0.02 m (convert to meters)
Radius of larger piston (R) = 20 cm = 0.20 m (convert to meters)
Area of smaller piston = π * r^2
Area of smaller piston = π * (0.02 m)^2
Area of larger piston = π * R^2
Area of larger piston = π * (0.20 m)^2
Plug in the values into the formula:
Weight = (Force x π * (0.02 m)^2) / (π * (0.20 m)^2)
Weight = (250 N x π * 0.0004 m^2) / (π * 0.04 m^2)
Weight = (250 N x 0.0004 m^2) / 0.04 m^2
Weight = (250 N x 0.0004) / 0.04
Weight = 1 N
Therefore, the weight that the larger piston can support when a force of 250 N is applied to the smaller piston is 1 N.
Yes, you are on the right track. To find the weight that the larger piston can support, you can use the principle of Pascal's law in hydraulics.
Pascal's law states that when there is an equilibrium of pressure in a fluid, the pressure is transmitted equally in all directions. In the case of a hydraulic lift, the pressure exerted on the smaller piston is transmitted to the larger piston.
To calculate the weight that the larger piston can support, you can use the formula you mentioned:
Weight on larger piston = (Force on smaller piston * Area of larger piston) / Area of smaller piston
Using the given information:
Force on smaller piston = 250 N
Radius of smaller piston = 2 cm = 0.02 m
Radius of larger piston = 20 cm = 0.2 m
To find the area of a circle, you need the radius (r) or diameter (d). Here, we have the radius, so we can use the formula:
Area of a circle = π * (radius)^2
Now, substitute the values into the formula:
Area of smaller piston = π * (0.02)^2
Area of larger piston = π * (0.2)^2
Weight on larger piston = (250 N * π * (0.2)^2) / (π * (0.02)^2)
Simplify:
Weight on larger piston = (250 N * 0.04 m^2) / (0.0004 m^2)
Cancel out the units:
Weight on larger piston = 250 N * 0.04 / 0.0004
Calculate:
Weight on larger piston = 25,000 N
Therefore, the larger piston can support a weight of 25,000 N when a force of 250 N is applied to the smaller piston in the hydraulic lift.