the small piston of a hydraulic press has an area of 2.0 cm and the large piston has an area of 16 cm if the small piston has a force of 4.0 N applied to it the output force of the large piston is

pressure = 4 N/2 cm^2 = 2 N/cm^2

force = pressure * area = 2 N/cm^2 * 16 cm^2

= 32 N

NOW area is cm^2 , not cm
cm is distance along a line
cm^2 is area of a surface

Well, let's calculate that and see what we get! But first, let me just say, this question really knows how to press my buttons. Alright, let's do some math!

The formula for calculating the force in a hydraulic press is:

Force = Pressure x Area

So, let's start with the small piston. We know that the force applied to it is 4.0 N, and its area is 2.0 cm.

Now, let's find the pressure exerted on the small piston:

Pressure = Force / Area
Pressure = 4.0 N / 2.0 cm

Okay, now let's move on to the large piston. We know its area is 16 cm, and we just calculated the pressure exerted on the small piston. So, we can use the same formula to calculate the output force on the large piston:

Force = Pressure x Area
Force = (Pressure on the small piston) x (Area of the large piston)
Force = (4.0 N / 2.0 cm) x 16 cm

Okay, let's crunch those numbers:

Force = (2.0 N/cm) x 16 cm
Force = 32.0 N

So, the output force on the large piston is 32.0 N. That's quite a powerful press! Now we just need to figure out what to press with it, maybe some grapes for some delicious grape juice?

To find the output force of the large piston, we can use the principle of Pascal's law, which states that the pressure in a fluid is transmitted equally in all directions.

We can calculate the pressure exerted on the small piston using the formula:

Pressure = Force / Area

Given that the small piston has an area of 2.0 cm^2 and a force of 4.0 N applied to it, we can calculate the pressure as follows:

Pressure = 4.0 N / 2.0 cm^2

Converting the area to m^2, we have:

Pressure = 4.0 N / (2.0 cm^2 * 0.0001 m^2/cm^2)

Pressure = 4.0 N / 0.0002 m^2

Pressure = 20000 Pa

Since the pressure is transmitted equally in all directions, the same pressure will be exerted on the large piston.

To find the output force of the large piston, we can multiply the pressure by the area of the large piston:

Force = Pressure * Area

Given that the large piston has an area of 16 cm^2, we can calculate the output force as follows:

Force = 20000 Pa * 16 cm^2

Converting the area to m^2, we have:

Force = 20000 Pa * (16 cm^2 * 0.0001 m^2/cm^2)

Force = 20000 Pa * 0.0016 m^2

Force = 32 N

Therefore, the output force of the large piston is 32 N.

To find the output force of the large piston, we can use the principle of Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted equally in all directions.

1. Identify the given values:
- Area of the small piston (A1) = 2.0 cm^2
- Area of the large piston (A2) = 16 cm^2
- Force applied to the small piston (F1) = 4.0 N

2. Calculate the pressure on the small piston:
Pressure (P1) = Force (F1) / Area (A1)

Since the area is given in cm^2, we need to convert it to m^2:
A1 = 2.0 cm^2 = 2.0 × 10^(-4) m^2

P1 = F1 / A1 = 4.0 N / (2.0 × 10^(-4) m^2)

3. Apply Pascal's law to find the output force on the large piston:
According to Pascal's law, the pressure transmitted by the fluid is the same everywhere in an enclosed system.

Pressure on the large piston (P2) = Pressure on the small piston (P1)

Since P1 = F1 / A1, and P2 = F2 / A2 (where F2 is the output force on the large piston),
we can set up the following equation:

F2 / A2 = F1 / A1

Rearrange the equation to solve for F2:
F2 = (F1 × A2) / A1

Substitute the given values:
F2 = (4.0 N × 16 cm^2) / (2.0 cm^2 × 10^(-4) m^2)

4. Convert the cm^2 units to m^2 units:
1 cm^2 = 10^(-4) m^2

Substitute the value:
F2 = (4.0 N × 16 × 10^(-4) m^2) / (2.0 × 10^(-4) m^2)

Simplify the units:
F2 = (4.0 N × 16) / 2.0

5. Calculate the output force:
F2 = 32 N

Therefore, the output force of the large piston is 32 N.