Dynamics

In this lesson, we explore the concept of pressure. Pressure, a fundamental concept in physics, quantifies the force exerted per unit area on a surface (P = F/A).

Understanding pressure is essential for comprehending the behaviour of fluids, solids, and gases and their interaction with the environment. This knowledge is crucial for designing efficient systems in engineering, such as hydraulic systems, which rely on pressure to transmit force effectively. Moreover, an understanding of pressure informs various scientific and industrial applications, contributing to advancements in technology and everyday practices.

Pressure is defined as a force acting on a body per unit area of contact perpendicular to the force.

Pressure is mathematically expressed as:

Pressure = Force Applied_______________________ Perpendicular to Area of Contact Where P = pressure, F = force acting on body and A = area where pressure acted.

F is measured in newtons (N), A in metre square (m²). P = F/A = Nm⁻²Hence the unit of pressure is Nm⁻²or Pascal (Pa).

Activity 2.14 Calculating for pressure on the ground Materials needed:

• Graph paper

• Pencils

• Rulers

• Weighing scales What to do:

1. Pick a piece of graph paper and trace the outline of one of your feet.

2. Count the number of squares enclosed within the foot outline to estimate the area of your foot.

3. Record the foot area measurements in various units, such as centimetres (cm²), metre square (m²). Note: often one small square of graph paper is equal to 1cm², but you should confirm this by measuring 1cm x 1cm!

4. Stand on weighing scales to obtain your body weight in kilograms (kg)

5. Using your foot area and body weight, calculate the pressure on the ground using the formula: Pressure = Weight / Area

6. Share your results with your peers and collect their data too. Tabulate the results.

Mass(kg) Weight (N) Area on 1

foot (A₁) Area of 2ⁿᵈfoot(A₂) P = F / (A₁ + A₂) Trial Questions 8

1. Find the pressure when a bag of gari of weight 50N is exerted on a 50m²surface.

2. Find the force produced when 10Nm⁻²pressure is exerted on 50m²surface.

3. A dog of weight 20 N stands on the foot of a cross-sectional area of 1000cm².

What pressure is exerted on the ground.

4. What is the pressure exerted by a cow of weight 500N who stands on an area of 1.0 cm²?

Hydrostatic Pressure

Hydrostatic pressure specifically refers to the pressure exerted by a fluid at rest due to the force of gravity. It increases with depth in a fluid due to the increasing weight of the fluid above. The hydrostatic pressure at a certain depth h can be derived from the pressure at the surface using the equation for hydrostatic pressure:

Hydrostatic pressure equation P = pgh Where P is the hydrostatic pressure caused by a certain depth (in Pascals, Pa), ρ (rho) is the density of the fluid (in kilograms per cubic metre, kg m-³), g is the acceleration due to gravity (in meters per second squared, m s⁻²) h is the depth of the point within the fluid (in metres, m).

This equation helps to understand how pressure increases with depth in a fluid due to the weight of the fluid above it. For example, in a water tank, the hydrostatic pressure at the bottom is higher than at the top due to the weight of the water above pressing down on it.

Trial Questions 9

1. A vessel has a base area of 0.15m². Water is poured into a depth of 3cm.

What is the pressure on the base? Calculate the force exerted on the base.

(Density of water = 1000kgm⁻³, g=10ms⁻²)

2. A poly tank which is 20m deep is full of water. Calculate the pressure at the bottom of the tank due to the liquid.

[Density of water =1000 kgm⁻³and g = 10 ms⁻²]

Activity 2.15 Exploring water pressure and flow Materials needed:

• Large plastic bottles with holes made at various heights

• Water What to do:

1. Individually or in a small group, take a plastic bottle with holes made at different heights.

2. Fill the bottle with water and observe what happens when the lid is removed.

3. Examine the path of the water flowing out of the holes at different heights.

4. Explain your observations using the key words; radius, depth, force, pressure and particles.

5. Share your observations and explanations.

Pascal’s Principle

Pascal’s principle states that, in a confined fluid, an externally applied pressure is transmitted equally in all directions. Both hydraulic systems and brake systems work on the principle of Pascal’s law, which is based on the transmission of fluid pressure. Pascal’s principle plays a fundamental role in various aspects of our lives, ranging from mechanical systems to biological processes, contributing to the functioning of many everyday objects and systems.

Trial Questions 10

1. The area of the smaller piston in a hydraulic press is 5m². If an effort of 80 N is applied on the plunger of the effort cylinder, calculate the force produced by the piston cylinder of a cross-sectional area of 600m².

2. A hydraulic press consists of two cylinders with a cross-sectional area of 0.15 m². The piston in the smaller cylinder is pushed down with a force of 15 N through a distance of 0.04m. Calculate

a. the pressure transmitted by the fluid.

b. the force exerted by the piston experiences a friction of 80 N.

Activity 2.16A Creating a Cartesian Divers

Materials needed:

• Water bottle (full)

• Small test tube (or similar object open at one end) What to do:

Explore:

1. Place a small amount of water into the bottom of the small test tube and then quickly put inside the full water bottle so that the closed end of the test tube is at the top.

2. Put the cap onto the water bottle.

3. Squeeze the water bottle hard and observe the motion of the test tube.

4. Discuss your observations with a peer. Try to explain what has happened, using the key words: pressure, Pascal, force and density.

Activity 2.16B

1. Take a large-gauge syringe and place your finger over the end so that the air inside it is trapped. Push the plunger and observe how far you are able to move it.

2. Repeat the experiment above, but this time with the syringe full of water.

How far are you able to push the plunger? How does this compare to when air is inside the syringe, and can you explain why?

3. Discuss your ideas with a peer or with your teacher.

Activity 2.17

1. Take a plastic bottle and pierce 4 to 8 holes around the bottom, in a circle at a constant depth. Cover the holes, and then fill the bottle with water.

2. Remove the coverings. What do you observe about the radius of the water jets which escape the bottle? How does this help to demonstrate Pascal’s principle?

3. Discuss your ideas with a peer or with your teacher.

Activity 2.18

1. Research a use of hydraulic systems which has not been covered in these learning materials.

2. Create a presentation to report your findings and deliver this to a small group of peers or your whole class.

Pressure in Fluids

Pascal’s law is a principle in fluid mechanics given by Blaise Pascal that states that;

a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere.

This principle is demonstrated by means of a glass barrel fitted with piston and a bulb with pierced holes of uniform diameter. The barrel is filled with water when the bulb is dipped in water and then removed.

When the piston is pushed in, water spurts equally from all the holes. This shows that the pressure applied to the plunger has been transmitted uniformly throughout the liquid.

Brake Systems and Hydraulic Press

1. The Hydraulic Press

It consists of a force pump of smaller diameter, piston of larger diameter, an oil supply tank and connecting pipes. The force pump of smaller diameter is connected to the piston or ram of larger diameter by a pipe. Oil is pumped into the cylinder from a supply tank.

The moment the effort handle of a force pump is lifted up, the valve of the force pump opens by atmospheric pressure. Oil from the supply tank is pumped into the effort cylinder of smaller diameter. However, when the effort is pressed or exerted downward, the same valve closes, high pressure is exerted on the oil due to decrease in volume; the pressure is transmitted equally in all direction in accordance with Pascal’s principle. The pressure on the liquid pushes the valve of the ram, large force is then produced on the ram because of its larger area and this force exerts on the load to lift, compress or to crush it. The release valve is provided to release the pressure and also allow the oil to return to the tank after the press has done its work.

Fig. 2.4: Hydraulic lift Suppose the effort cylinder has an area of 2m²and an effort of 1000 N is applied to its plunger.

The pressure produced by the effort is:

P = F/A = 1000/2 = 500Nm⁻²This pressure is transmitted equally throughout the whole of the liquid in accordance with Pascal’s principle. Therefore, the pressure exerted on the piston is also 500Nm⁻². Since the area of the piston is equal to 800m², the force generated to lift the load.

F = P × A = 500 × 800 = 400000 N Thus, a force of 40000N is simply produced by exerting an effort of 1000 N.

Uses of the Press

1. It is used for the compression of soft materials such as wastepaper and cotton into compact bales.

2. It is used for the shaping of motor cars.

3. It is used for lifting heavy objects.

2. Hydraulic Brakes

Brake systems in vehicles are crucial for safe and controlled stopping. They work through a combination of mechanical and hydraulic components such as brake pedal, master cylinder, brake fluid, brake pad, shoes etc. The brake system’s operation relies on the driver’s input, which is converted into hydraulic pressure to apply friction on the wheels, allowing the vehicle to slow down or stop safely.

It works based on the principle that pressure in fluid is transmitted equally in all directions.

Fig. 2.5: Hydraulic brake The moment the brake (foot) pedal is pressed, the volume of the master cylinder decreases which exerts greater pressure on the fluid in the master cylinder. The pressure set in the master cylinder is equally transmitted through the fluid to the wheel piston on the brake shoes, which are hinged on the wheel cylinder. The brake shoes are then pushed against the brake drums, which are fixed to the wheels.

Friction then sets in between the tyres and the ground and therefore decelerates the car to a stop. When the pressure on the pedal is released, the brake shoes pull the springs and force the wheel’s piston back into the cylinder. The liquid then returns to the master cylinder. The braking effects on all wheels are equal, since the pressure set up in the master cylinder is transmitted equally throughout.