Dynamics
Dynamics is the study of things that move, and why they move.
Basic equation
The motorcycle was traveling at 250 km/h. Convert this to ms-1 “See- think- react” usually takes 1 second. How far does the rider travel before braking?
the bike rider was found INSIDE the car. The Volkswagen actually flipped over from the force of impact and landed 3 m from where the collision took place.
Acceleration equation
Kinematic Equations
A cliff on the Milford Track is called “10 second cliff” Why? How high is it?
Displacement/time Graphs (not assessed) stationary
d t Moving forward constant velocity
Displacement Time Graph STOP d constant Velocity (L) stopped STOP constant Velocity (R) constant Velocity (L) constant Velocity (R)
For a displacement/time graph Positive slope means moving to the right Negative slope means moving to the left
d t Δ d Δ t Gradient = Rise = Δ d = velocity Δ t Run
Constant gradient Constant velocity Increasing gradient acceleration Decreasing gradient decceleration d t
d t acceleration
d t decceleration
V t Velocity/time Graphs (not assessed) constant V Increasing V decreasing V decreasing V Increasing V V t
Positive velocity : Moving to the right accelerating deccelerating constant velocity v t Negative velocity : Moving to the left accelerating deccelerating
Positive area, moving to the right Negative area, moving to the left
v t Δ v Δ t Gradient = Rise = Δ v = acceleration Δ t Run
Scalars Vectors Scalars and Vectors have only size Distance Speed Vectors have size and direction Displacement m Velocity ms-1 Acceleration ms-2 Force N
Vectors Adding Vectors. When is 3 + 3 not equal to 6? Courtney rides 3 km north then 3 km south. What is her displacement? In this case 3 + 3 = 0 if you take into account direction.
Displacement is Direction is 0450 Sarah rides 3 km north then 3 km east. What is her displacement? Displacement is Direction is 0450
So you can see that to ADD vectors, you put them tail to head. The total is from tail to head B A To find A + B A + B
The order doesn’t matter B A + B A To find A + B
Adding Forces What size is the total (net) force? 300 N
What size is the total (net) force?
Find the Net Force 300 000N 900 300 000N
TAIL to HEAD 900 TAIL to HEAD
A Skier on the Slope why does her acceleration depend on the angle of the slope?
consider the forces on her
consider the forces on her
consider the forces on her θ θ
changing the angle
Adding Velocities Jess is walking at 3.0 ms-1 in the bus. The bus is moving at 4.0 ms-1 What is her velocity if…..
Adding Velocities Jess is walking at 3.0 ms-1 in the bus. The bus is moving at 4.0 ms-1 What is her velocity if…..
Adding Velocities Jess is walking at 3.0 ms-1 in the bus. The bus is moving at 4.0 ms-1 What is her velocity if…..
River and Boat
A plane is pointing north with an airspeed of 400 kmh-1. The wind is from the west at 300 kmh-1. What is the plane’s ground velocity?
Plane in still air Plane pushed by wind.
Wind/ground Plane/air plane/ground Speed = θ
What direction must the plane point so it flies north? Plane in still air Plane pushed by wind.
Wind/ground plane/ground Plane/air
φ What is the ground speed? Wind/ground plane/ground What direction does the pilot point? Plane/air φ
Change in Velocity The change in anything is what it is minus what it was. Confused???????? What is the change in your height in the last 5 years? Height change= height now – height then
You had $5 yesterday now you have $10 What is the change in your wealth? You had $10 yesterday now you have $5 What is the change? You had $5 yesterday now you owe $10
Vi = 5 ms-1 Vf = 0 ms-1 What is the ball’s change in velocity?
What is the ball’s change in velocity? 5 ms-1 3 ms-1
Δv vi -vi vf vf
What direction is the force of the floor on the ball? Velocity change and force are in the same direction Velocity change force
What is the velocity change if the ball hits on an angle? vi vf Δv -vi -vi vf vf
Components We have seen that you add vectors tail to head.
You can also separate a vector into two parts at right angles. The parts are called components. OR
The force from the rope can be split into two components The horizontal component pulls her forward The vertical component tries to lift her.