SUVAT equations

v = u +at

s = ut + 1/2 at^2

v^2 = u^2 + 2as

s = 1/2 (u + v) t

What is the value of g in maths?!!!!

10 Nkg^-1 !!!

Pulleys:

1) Tension when mass is accelerating in the direction of the tension

2) Tension when mass is accelerating in the opposite direction to the direction of the tension

1) T = mg + ma

2) T = mg - ma

These equations can also be used for lifts

Normal contact force in a lift

When the lift is accelerating upwards: R = mg + ma

When the lift is accelerating downwards: R = mg - ma

Equations for vehicles in motion:

For a car towing a trailer

Forces on the car only: D - T - X = ma

Forces on the trailer only: T - y = ma

Forces on the whole system: D - X - y = (m1 + m2)a

Where D is driving force

T is tension in the towbar

X is resistive forces on the car and y is resistive forces on the trailer

For slope angled at theta degrees

The angle between the slope and the horizontal id the same as the angle between the weight and the normal reaction force (line drawn perpendicular to the slope)

Principle of the conservation of linear momentum

If no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and isn’t effected by their mutual interactions

Coalesced

When objects travel together with the same velocity after impact

Newton’s law of restitution

When two bodies collide, the speed with which they move after the collision depends on the method from which they are made

Coefficient of restitution

e = speed of seperation (relative speed after the collision)/ speed of approach (relative speed before collision)

e = (v2 - v1)/(u1/u2)

e has a value between zero and one

0 = perfect inelastic (no rebound/ coalesce on impact)

1 = perfect elastic collision

Resultant force on pulley due to the tensions

equal to 2 x tension or 2 x components of tension in the relevant direction

if one of the masses hits the floor and the tension becomes zero then the resultant force on the pulley is zero

Limitations/assumptions for projectile motion

the real objects are considered to be particles

there is no air resistance

nothing impedes the motion of the particle (no other forces, no rotation)

the motion is in one vertical plane 2D

acceleration is due to gravity

there is no acceleration in the horizontal plane so horizontal component of velocity is constant