# Archive | M1

## Particles on Wedges Connected By a String

If two particles are in motion on a fixed wedge then we have to resolve for each particle perpendicular to the plane and apply F=ma parallel to the plane. We can use T is the same throughout the string, and the acceleration of both particles is the same to form simultaneous equations and solve them […]

## Projectiles – Starting From Above or Below y=0

If a particle is projected from a point above ground level, we can take this into account by changing the datum, so that it becomes the point of projection. For example, if a particle is projected from a point 2m above the ground then we can take this into account by takingas the point 2m […]

## Basics of Projectiles

Projectile questions involves particles moving through the air subject only to the force of gravity. The path of a projectile is illustrated below. The following points should be noted. The acceleration is alwaysThe negative sign means the acceleration is directed downwards. At the maximum height, the vertically velocityis zero. The particle may still be moving […]

## Finding the Angle a Hanging Lamina Makes With The Vertical

The centre of gravity of a hanging body always hangs vertically below the point of suspension. If we know the distance of the centre of gravity from two axes, we can use the rules of trigonometry to find the angle a line drawn in the lamina makes with the vertical. The lamina is hung from […]

## People in Lifts

When analysing the forces on people in lifts, it is important to remember:Newton’s Third Law – to every action there is an equal and opposite reaction, this means that the reaction of anybody in the lift on the lift is the same as the reaction of the the reaction of the lift on anybody in […]

## Particles on Slopes – Advanced Questions

More advanced particle on slopes questions involve friction or extra external forces. Example: A sledge of mass 78 kg is pulled up a slope by means of a rope. The slope is modelled as a rough plane inclined at an angle α to the horizontal, whereThe rope is modelled as light and inextensible and is […]

## Moving Particles, Position Vectors and Relative Position Vectors

For any particle moving on a flat surface, we can find the position vector relative to a fixed point, by counting to the right x units, up y units and writing downIf instead we move to the left or down thenorare negative. Suppose though that the particle starts from the point with velocityAfterseconds it will […]

## Hanging Particle Connected by a Pulley to a Particle on a Table

I will find the acceleration and tension in terms of Resolving vertically for (1) Apply F=ma to both particles – for (2) Substituting (1) into (2) gives (3) Applyingto (4) (3)+(4) gives Substitute this into (3) to give

## Applications of SUVAT to Two Part Motion

SUVAT may be used whenever motion is broken up into periods of motion where the acceleration is constant. For example, if a heavy ball is dropped from a height and hits soft ground, decelerating rapidly and coming to rest, we can apply SUVAT to the period of motion when the ball is falling before it […]

## Particles on Slopes (2)

There are several things that must be done for every particle that lies on a slope. 1)If you don’t have a diagram, draw one. 2)Do not resolve vertically and horizontally. Resolve perpendicular and parallel to the slope. Remember that the reaction force is always perpendicular to the surface, that gravity always acts downwards, and that […]