Motion without friction is in most practical situations an unachievable ideal. There is always some friction and some work must always be done to overcome it. If the friction forceis constant for a distance movedthen the work done to overcome that force is We can obtain another very useful equation from this by differentiation. is […]

# Archive | M3

## The Work Energy Principle for a Particle Attached to an Elastic String on a Rough Slope

The Work Energy Principle states that for an isolated system, as the system proceeds to evolve, the difference between the initial energy and the energy at any instant has been used to overcome air resistance or friction of some sort. Consider a particle of masson a rough slope. The coefficient of friction between the particle […]

## When Acceleration is Given in Terms of x

If acceleration is a function ofsowe can find the velocity by integration: and then find the displacement by integrating again If the acceleration is a function ofwe cannot do this becauseis an unknown function ofWe would have We can however use the chain rule to express the acceleration as a function of Now the equationbecomesWe […]

## Centres of Mass, Integral Method

We apply the formulae, To find the distances of the centre of gravity about certain axes. Suppose we want to find the distance of the centre of gravity of a uniform circular cone from it’s base. By symmetry, and will be on a vertical line through the centre of the cone. We must apply the […]

## Simple Harmonic Motion for a Horizontally Stretched String

The tension in a stretched string is usually expressed in terms of it’s modulus of elasticity4b42b39e.gif” name=”Object1″ align=”ABSMIDDLE” width=”80″ height=”40″ hspace=”8″>This is in fact an expression of Hooke’s Law – Force is proportional to extension. Suppose that a string of length l is stretched between two points A and B. A particle P is attached […]

## Motion of Particle on Inner Surface of Smooth Sphere

A particle travelling on the inside surface of a smooth sphere will just leave the surface when the reaction between the particle and the inner surface is zero. Suppose a particle of massat the bottom A of a sphere of radius r is given a horizontal speedIt will move along the internal surface of the […]

## Ring Threaded on Elasic String Suspended From the Ceiling

When a ring is threaded on an elastic string which is attached to the ceiling at two points, then ignoring friction, the particle will come to equilibrium at the midpoint of the string and the tension will be the same throughout the string. Suppose the modulus of elasticity of the string isand the natural length […]

## Multi Stage Rockets

It is very expensive to get a mass into orbit. A lot of the mass of a rocket is useless in space. For this reason rockets are not usually sent into space as complete units, but are divided into stages, with each stage acting as a store of fuel and a means of propulsion, which […]

## Maximum Extension of Elastic String Attached to Particle on Rough Plane

When a particle is attached to a an elastic string on a rough plane, it will come to rest at a point on the slope where whatever gravitational potential energy the particle started with has been turned into elastic potential energy in the string of been used to overcome friction. The particle below is attached […]

## Lamina Suspended at Angle to Horizontal

In general for a system to be in equilibrium, the forces must balance in each direction, and the moments about any point must sum to zero. When a lamina is suspended by two inelastic strings, we can find the tensions in the strings by resolving vertically and taking moments about a point where one of […]