Speed and Velocity
Distance time graphs
- Speed = gradient of graph = vertical / horizontal
- If object is accelerating or decelerating, find the gradient of the tangent of the curve
- Flat = object is stationary
- Straight uphill or downhill = steady speed
- Downhill = Moving back to starting point
- Curves = acceleration or deceleration
- Finding the gradient of a tangent drawn just touching an acceleration or deceleration curve will give the speed.
Velcotity time graphs
- Acceleration = Change in velocity / time taken
- A = (v-u) / t
- Gradient = acceleration
- Uphill = acceleration
- Downhill = deceleration
- Gravity or Weight acts DOWNWARDS
- Reaction Force from a surfance acts UPWARDS
- Thrust, Push or Pull speed something up
- Drag, Air Resitance or Friction slow something down
- Lift holds something up
- Tension is held in a rope or cable
Forces are measured in Newtons (N)
Add forces in one direction and subtract forces acting against to give the resultant force.
Resultant force = Change in Velocity.
- An object will remain stationary if the resultant force is zero.
- An object will accelerate in the direction of a non-zero resultant force.
- An object will continue to move at the same velocity if there is no resultant force.
Forces and Acceleration
A non-zero resultant force = acceleration
a = F/m
Acceleration (m/s^2) = resultant force (N) / mass (kgs)
Reaction forces are equal and opposite.
Momentum and Collision
p = m x v
Momentum (kg m/s) = Mass (kgs) x Velocity (m/s)
- The greater the mass of an object the greater its velocity and the more momentum it has.
Conservation of Momentum = The total momentum before a collision is the same after the event, in a closed system [no external forces]
/\ p = F x t
Change in momentum (kg m/s) = Force acting (N) x Time taken (s)
- Seat beltsincrease time taken for the passenger to stop, decreasing the rate of change of momentum, therefore, reducing force on body.
- Cycle helmets, cushioned playground surfaces, airbags and crash mats also reducetime takenfor impact to take place, reducing force acting on you and decreasing rate of change of momentum.
Friction and Terminal Velocity
Friction slows you down, acting in the opposite direction to movement.
Most resistive forces are caused by air resistance (drag). Making an object streamlined reduces drag.
Drag increases with speed.
Falling objects reach a terminal velocity when they have reached their maximum speed. At first gravity is larger than the frictional force so they accelerate. Friction increases with speed so acceleration reduces.
Terminal velocity is the speed at which the object has reached maximum, falling from then on at a steady speed.
Terminal velocity of a falling object depends on its shape and area.
Stopping distance = thinking distance + braking distance
This depends on:
- Speed before braking
- Tiredness of driver
- Drugs and alcohol
- Condition of car - maintenance of brakes etc
- Road surface and weather conditions
Weight, Mass and Gravity
Weight (N) = mass (kgs) x gravity (N/kg)
W = m x g
Gravity on Earth is 10 N/kg
On the Moon it is 1.6 N/kg
- Work done (J) = Force (N) x Distance (m)
- W = f x d
- Work done/Energy transfer is when a force moves an object across a distance.
Gravitational Potential Energy
- Gravitational Potential Energy (J) = mass (kg) x gravity (N/kg) x height (m)
- Ep = mxgxh
- Kinetic Energy (J) = 0.5 x mass (kg) x speed^2
- Ek = 0.5 x m x v^2
- Kinetic energy gained = Potential energy lost
An object that returns to its original shape after being stretched is called elastic. Energy is stored by the object as Elastic potential energy.
Extension (m) = Force (N) / Spring constant (N/m)
E = f / k
Extension of an object is directly proportional to the force applied until it reaches its limit of proportionality when it can no longer extend. It has taken the maximum force that it can.
Power determines the rate of energy transfer. It is not the same thing as force or energy.
A powerful machine is one that transfers a lot of energy in a short space of time.
Power (W) = Work done (or energy transferred) (J) / Time Taken (s)
One watt = One Joule/second
Moment (Nm) = Force (N) X perpendicular distance from the line of action of the force to the pivot (m)
M = F x d
Moment = 20 x 0.2 = 4Nm
If Total anticlockwise moment = Total clockwise moment, the object will not turn
A: 1x1000 = 1000
B: 500x2m = 1000
Levers use the idea of balanced moments. The force that is needed to produce a moment depends on the distance from the pivot.
Increasing the distance from the pivot where the force is applied means less force is needed.
If the total anticlockwise moment does not equal the total clockwise moment there will be a resultant moment.
The most stable objects have a wide base and low centre of mass. If the object's centre of mass moves beyond the edge of the base, it will tip over.
This is because of the resultant moment.
Suspending a weight from a piece of string creates a pendulum. It will swing back and forth when pulled and let go. Time taken for the pendulum to swing from one side to the other is called the time period. The longer the pendulum, the greater the time period.
Time period (s) = 1 / F (Hz)
- If an object is travelling in a circle, it is constantly changing direction. It's velocity is changing (not speed) so the object is accelerating.
- A resultant force must be acting on the object to cause acceleration. It is called the centripetal (sen-tree-peet-al) force and it acts towards the centre of the circle.
- The centripetal force could be: Tension, gravity or friction.
- More speed, More mass and asmaller circle radius require a larger centripetal force.
Pressure in liquid is transmitted equally in all directions. It has the same volume and density when compressed.
Pressure (Pa) = Force (N) / Cross sectional area (m^2)
P = F/A
Hydraulic systems use liquid to increase an applied force. One piston will have a smaller cross sectional area. Force is applied to the smaller piston, increasing pressure which is then transmitted to the larger piston. Larger area = larger force.
Hydraulic systems can be used in:
- Car breaking systems
- Hydraulic car jacks
- Manufacturing and deployment of aircraft landing gear