Forces acting on solids
Like we have learnt before, forces can change the size and shape of an object by:
- Stretching it.
- Twisting it.
- Squashing it.
- Bending it.
To investigate the effect of forces on objects, we can use foam rubber because it springs back to its original shape when it is deformed.
However, there are some objects which become deformed for life when a force is applied on them. Some of these are soft metals like silver and gold.
The simplest way to investigate how things deform is by using a spring.
The spring needs to be hung from a rigid clamp in order to get its top in a fixed position.
Weights known as load is hung to the end of the spring; as the load is increased, the spring’s length increases as well.
In general, as the load of the spring is increased uniformly, its length increases uniformly as well.
However, if the load is increased too far, the spring becomes permanently stretched and will not return to its original length. The spring is said to be in-elastically deformed.
Extension of a spring
An extension is the increase in length of a spring. It is important to note the extension of the spring in order to find the point at which the spring gets in-elastically deformed.
Extension = length of stretched spring – original length of the spring.
English scientist Robert Hooke was the first person to describe the mathematical pattern for the stretching of spring.
Hooke realised that the extension of the spring was proportional to its load until a point where the spring got in-elastically deformed. This point is called the limit of proportionality (and is also known as the elastic limit).
In general, Hooke’s law states that:
The extension of a spring is proportional to the load applied to it, provided that the limit of proportionality is not exceeded.
Hooke’s law can also be represented as an equation:
F = kx
‘F’ is the load (force).
‘k’ is the stiffness of the spring.
‘x’ is the extension of the spring.
Rubber and Hooke’s law
When a piece of rubber is stretched in a similar way as a spring is stretched, the following is observed:
- The graph obtained when a rubber is stretched with uniform amounts of load, is not straight like that of a spring! It is rather ‘S’ shaped. This shows that the extension is not exactly proportional to the load and hence rubber does NOT obey Hooke’s law.
- Rubber doesn’t produce an extension after a certain point; it feels rather stiff and the graph doesn’t come to zero when the load is withdrawn.
The force acting per unit area at right angles to a surface is known as an object’s pressure.
High pressure and low pressure
Pressure tells us how concentrated a force is.
If a force is concentrated over a wide area, the pressure is low.
When the force is concentrated over a small area, it is said to pose a higher pressure onto it.
Pressure can be calculated using a simple formula:
Pressure = force / area
P = f /a
The SI unit for pressure is pascal (Pa)
Pressure in fluids
The deeper you travel through a fluid, the greater the pressure around it will act on you. Deep sea divers have to be careful especially due to this, as the pressure is extremely enormous undersea, than on surface. This is because the deeper you go, the greater the amount of water pressing on you from above.
Though the atmosphere is at such a high altitude, we don’t get to experience the pressure crushing upon us as compared to when a diver jumps into the sea. This is because of the fact that the atmosphere is not as dense as water is. Hence when calculating pressure in fluids, its density must be also taken in account.
Pressure, depth and density
As we have seen before, the deeper a person dives into a fluid, the greater will the pressure be. Thus, it means that other than the area, pressure also has a significant relationship with depth h.
Pressure ‘p’ is proportional to depth‘d’
Along with the depth, the pressure of a fluid also depends upon its density (in this case, density is represented by the Greek letter, pronounced as ‘rho’)
We can write an equation for the pressure at a depth h in a fluid of density:
Pressure = depth x density x acceleration due to gravity
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