force and pressure

Pressure is the force on an object that is spread over a surface area. The equation for pressure is the force divided by the area where the force is applied. Although this measurement is straightforward when a solid is pushing on a solid, the case of a solid pushing on a liquid or gas requires that the fluid be confined in a container. The force can also be created by the weight of an object.

When you apply a force to a solid object, the pressure is defined as the force applied divided by the area of application. The equation for pressure is:

P = F/A

where

• P is the pressure
• F is the applied force
• A is the surface area where the force is applied
• F/A is F divided by A

For example, if you push on an object with your hand with a force of 20 pounds, and the area of your hand is 10 square inches, then the pressure you are exerting is 20 / 10 = 2 pounds per square inch.

Pressure equals Force divided by Area

You can see that for a given force, if the surface area is smaller, the pressure will be greater. If you use a larger area, you are spreading out the force, and the pressure (or force per unit area) becomes smaller.

Solid pressing on confined fluid

When a liquid or gas is confined in a container or cylinder, you can create a pressure by applying a force with a solid piston. The pressure created in the cylinder equals the force applied divided by the area of the piston: P = F/A.

In a confined fluid—neglecting the effect of gravity on the fluid—the pressure is the same throughout the container, pressing equally on all the walls. In the case of a bicycle pump, the pressure created inside the pump will be transmitted through the hose into the bicycle tire. But the air is still all confined.

Pressure is in all directions in a fluid

Increasing the force will increase the pressure inside the cylinder.

Caused by gravity

Since the weight of an object is a force caused by gravity, we can substitute weight in the pressure equation. Thus the pressure (P) caused by the weight (W) of an object is that weight divided by the area (A) where the weight is applied.

P = W/A

If you place a solid object on the floor, the pressure on the floor over the area of contact is the weight of the object divided by the area on the floor.

Pressure equals Weight divided by Area

Example with shoes

A good example of how a force on small area can result in a very high pressure is seen in women's shoes with high spiked heels. These types of shoes can cause damage to some floors due to the very high pressure on the floor at the heel.

An average shoe distributes the weight of the person over 20 square inches. Thus, a 100-pound person applies 100/20 = 5 pounds per square inch on the floor.

Since a spike-heel is only 0.25 square inches, the 100-pound person would be applying 100/0.25 = 400 pounds per square inch on the floor at the heel! In some cases, that is sufficient to damage the floor.

) A needle will exert enormous pressure because the surface area (A) of the point where the force (F) is being applied is very small. That's why it penetrates skin and other materials.

2) If your mass is 50 kg , what is the pressure you exert on the ground when you are standing up, assuming that the surface area of your shoes is 0.05 m².

Answer:

(remember that mass is not the same as weight)

Assuming that g =10 m/s² , F = 50kg x 10 m/s² = 500 N (weight)

A = 0.05 m²

P = F/A = 500 N / 0.05 m² = 10000 N / m²

3) A jack is projected to lift a bus which has a mass of 4 000 kg. If the large piston (the one that moves up in the animation) has an area of 1 m² , and the small piston on the other end of the circuit has an area of 0.05 m² , what is the minimum force that must be applied (to the little piston) in order to lift the bus?

Answer: We want find out a force, which is given by : F = P x A . P is the same in the whole circuit , and to do this exercise we don't need to know its value so that we will simply call it P.

Lets call the force on the small piston Fs and the force on the large piston Fl. Likewise, the area of the small piston will be called As and the area of the large piston Al. Because the pressure (P)is the same in both pistons we can write:

Fs = As x P and

Fl= Al x P

We know the areas (As = 0.05 m²and Al = 1 m²), so that we can substitute them in the equations:

Fs = 0.05 m² x P

Fl = 1 m² x P

We have 2 equations and 2 unknowns.It is a system.From now on you will have to use your maths skills. You could even pretend that you have x's and y's instead of F's , A's and P's , if it makes things easier to you.

There are many ways to solve this system . We will do it by dividing the top equation by the bottom one:

Fs / Fl = 0.05 / 1

That is all (Remember that P / P = 1) .

So,

Fs / Fl = 0.05

Rearranging:

Fs = 0.05 Fl

In order to lift the bus , the force on the large piston (Fl) must be al least 40 000 N (because the mass of the bus is

4 000 kg). So,

Fs = 0.05 x 40 000

Fs = 2 000 N (Final answer)

This example illustrates how a small force can be multiplied many times by using a hydraulic jack. This is the type of calculation that mechanical engineers do.

Fluid weight

If you put a liquid in a container, the weight of that liquid would be pressing on the bottom of the container similar to that of the weight of a solid object. The pressure on the bottom of the container would be the same as if the weight was from a solid: P = W/A.

The only difference is that pressure in a fluid goes in all directions. So the pressure on the sides at the bottom would be the same.

Gases and liquids exhibit pressure due to their weight at every point in the fluid.

Summary

To end it off, Pressure is the force on an object that is spread over a surface area. The equation for pressure is P = F/A. Pressure can be measured for a solid is pushing on a solid, but the case of a solid pushing on a liquid or gas requires that the fluid be confined in a container. The force can also be created by the weight of an object.

done by : qi hui

http://www.school-for-champions.com/science/pressure.htm

http://sci-culture.com/advancedpoll/GCSE/hyd.htm