A single force applied to an object will result in movement in the direction of that force.
When forces are applied inwards from opposite sides, the spring will compress.
If one end of a spring is fixed and a force is applied to the other end, a reaction force from the fixed point means that more than one force is acting on the spring.
Deformation
Definition of Deformation:
Deformation refers to the change in shape of an object when a force is applied.
Types of Deformation:
Elastic Deformation:
The object returns to its original shape once the load is removed.
Example: An elastic band exhibits elastic deformation.
Plastic Deformation:
The object does not return to its original shape after the load is removed.
Example: A spring that has been stretched beyond its limit.
Linear Elastic Distortion & Hooke’s Law
Hooke’s Law:
States that the extension of a spring is directly proportional to the force applied.
Mathematical representation:
F=kx
Where:
F = force applied to the spring (in Newtons, N)
k = spring constant (in Newtons per meter, Nm⁻¹)
x = extension of the spring (in meters, m)
Force/Extension Graph:
The linear section of the graph indicates that it follows Hooke's Law, characterized by a constant gradient, k, which represents the spring constant.
Elastic Limit:
The point at which the graph stops being linear, marking the end of elastic behavior and the onset of plastic deformation.
Non-Linear Section:
Indicates that the material is not behaving elastically and does not conform to Hooke’s Law anymore.
Plastic Deformation Characteristics:
If shallow, implies significant extension with minimal force.
A purely linear graph suggests the material is brittle, causing it to snap instead of stretch after reaching the elastic limit.
Work Done:
The area under the force/extension graph, calculated as:
ext{Work Done} = rac{1}{2} kx^2
Atmosphere and Pressure
Atmospheric Pressure:
Defined as the total weight of the air above a unit area at a specific altitude.
As altitude increases, atmospheric pressure decreases due to fewer air molecules above the unit area, resulting in diminished weight and thus, reduced pressure.
Fluid Pressure:
A fluid is any liquid or gas.
Pressure in a gas depends on atmospheric pressure.
Example: A balloon's gas exerts an outward force while the air exerts an inward force.
If the inward force is greater, the balloon collapses.
In the vacuum of space, the balloon can expand as the outward gas pressure exceeds the lower atmospheric pressure outside.
Increasing gas particles in the balloon creates more collisions with the balloon surface, increasing pressure and enabling expansion.
Fundamental Pressure Calculation:
Pressure is expressed as:
ext{Pressure} = rac{ ext{Force}}{ ext{Area}}
Pressure in Liquids
Pressure Variation with Depth:
In fluids, the pressure experienced increases with depth.
Greater depth means more fluid above the object, resulting in greater weight hence, increased pressure.
Density and Pressure:
The greater the density of a fluid, the higher the pressure it exerts:
extmass=extdensityimesextvolume
A denser fluid has more weight, resulting in increased force on submerged objects, causing higher pressure.
Floating and Sinking
Principle of Floating:
An object will float if its weight is less than the weight of the water it displaces.
Example: A 1000 kg boat sinks until it displaces an equivalent weight of water (1000 kg) but maintains buoyancy as long as it does not submerge completely.
Buoyancy Force:
The buoyancy force is the upward force that counteracts the weight of the floating object.
This force equals the weight of the fluid displaced by the object.
Example of Floating:
A ping pong ball floats in water because its density is less than that of the water.
Thus, for the volume displaced by the ping pong ball, the weight of the displaced water is greater than that of the ball, resulting in a buoyant force that allows it to float.
Depth and Pressure:
As depth increases, the weight of the water above increases, leading to an increase in pressure.