Physics: Mechanics 2

Physics 2

Speed and velocity

• Displacement is a distance in a given direction
• Velocity is a speed in a given direction
• Speed can be calculated from the gradient of a distance time graph

• speed of a non-linear distance time graph can be found from the gradient of the tangent at the point of interest
• for an object moving at a constant speed in a circle;

        speed = (2 x pi x radius) / period of rotation

Acceleration

• acceleration is defined as rate of change of velocity

        acceleration = difference in velocity / difference in time#

• for all falling objects which experience negligible air resistance;

        a = g

• an object instantaneously at rest can be accelerating

Acceleration along straight lines

Equations of constant acceleration:

• v = u + at
• s = (v + u)t / 2
• v^2 = u^2 + 2as
• s = ut + 0.5at^2,

when s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time

• acceleration is equal to the gradient of velocity time graph

• the area under a speed time graph is equal to the distance travelled

Freefall

• when the only force acting on a mass is its weight, it is said to be in freefall
• different masses fall with the same acceleration when in freefall
• all objects fall out g when in free fall

Projectile motion

• a projectile is any object acted upon by the force of gravity
• horizontal and vertical motion is independent because they are perpendicular vectors
• acceleration is always g and only affects the vertical component of its motion

Forces and acceleration

Newtons laws:

1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
2. the relationship between an object's mass m, its acceleration a, and the applied force F is F = ma. Acceleration and force are vectors (as indicated by their symbols being displayed in slant bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector
3. for every action there is an equal and opposite reaction.

• Gravitational field strength / g = gravitational force / W  ÷ unit mass / m
• Force = mass x acceleration
• gravitational field strength near the surface of the earth is uniform
• the tension in an inextensible string running over frictionless pulleys has the same magnitude at any point along its length.

Terminal speed

• for an object falling in a fluid, the resultant force ma = mg - D (m = mass, D = drag force)
• drag force increases as speed increases ( D α v^2)
• when drag forces are significant, a falling object will release its terminal velocity when weight is balanced by drag forces.
• at this point, resultant force and acceleration = zero

Work, kinetic energy and potential energy

• Energy cannot be created or destroyed
• for an object in freefall,
• mgΔh = 0.5mv^2
• kinetic energy is the energy of an object due to its motion
• Ek = 0.5mv^2
• gravitational potential energy is the work done to raise an object through a height
• Ep = mgΔh
• if the force is at an angle of the direction of motion,
• W = FsCosθ
• work is done on an object when a force acting on it makes it move
• work done = force x distance moved in direction of the force

Power and energy efficiency

• power is the rate of doing work
• P = W / Δt
• work done per second - force x distance moved
• efficiency = energy output / energy input