* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download V - USU Physics
Rindler coordinates wikipedia , lookup
Laplace–Runge–Lenz vector wikipedia , lookup
Hunting oscillation wikipedia , lookup
Frame of reference wikipedia , lookup
Classical mechanics wikipedia , lookup
Coriolis force wikipedia , lookup
Specific impulse wikipedia , lookup
Matter wave wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Faster-than-light wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Derivations of the Lorentz transformations wikipedia , lookup
Fictitious force wikipedia , lookup
Variable speed of light wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Equations of motion wikipedia , lookup
Velocity-addition formula wikipedia , lookup
Sudden unintended acceleration wikipedia , lookup
Classical central-force problem wikipedia , lookup
Jerk (physics) wikipedia , lookup
Proper acceleration wikipedia , lookup
Recap. • Velocity is a vector and represents a bodies speed and direction. • A force must act on a body to change its velocity (i.e. its speed, direction or both). • The force causes the body to accelerate resulting in a change in its velocity. • Acceleration is a vector and represents the rate of change of velocity with time. Change in velocity V2 - V1 = Average acceleration = t Time interval r r a = DV m s 2 t Instantaneous Acceleration: • Rate of change of velocity at a given instant. • ie. The average acceleration measured over a very short time interval. • If acceleration changing fast we need to sample it very frequently. Acceleration: Vector Direction The direction of acceleration vector is given by the direction of the change in the velocity vector, DV . V2 V1 car accelerating - Acceleration increasing. V1 + DV V2 = a vector in same direction as velocity when velocity is V1 car decelerating V1 V2 + DV a = V2 - When the velocity is decreasing the change in DV is in the opposite direction to motion (ie. to slow car down) - Acceleration vector is opposite direction when velocity is decreasing. - Deceleration is negative acceleration. Example: Negative Acceleration -Jet preparing to land Initial velocity V1=200 km/hr (=55.6 m/s) Final velocity V2=120 km/hr (=33.3 m/s) Time interval t=5 sec Acceleration: DV V2 - V1 a = t = t 33 . 3 - 55 . 6 2 m / s = a 5 a = - 4 . 46 m /s 2 toward runway In general: - Whenever the velocity is changing we say the object is accelerating (positive or negative). Return to car on a bend • Car moved at a constant speed but its direction continuously changed – thus its velocity was changing. • But we now know that velocity changes are produced by an acceleration. • Thus when the car rounds the bend at a constant speed it is accelerating!! • Direction of acceleration is given by DV direction. V1 Acceleration Direction Question: what is DV ? V1 + DV = V2 V1 V2 DV V2 Result: the vector DVacts towards the center of curvature of the bend! Thus the acceleration is also directed towards the center of curvature. • This is why the car does NOT change speed but you still feel a force on your body as you round the bend… (change in direction). • Force is due to friction of tires on road enabling the car to change direction. Example: For a given speed the acceleration experienced (force) depends on the curvature of the bend. shallow sharp V1 V2 DV V1 V1 V2 V1 V2 DV a= DV t V2 = Large a= DV t = Small Skiing - sudden turns create large accelerations & large associated forces! Summary: Acceleration involves changes! • Acceleration is the rate of change of velocity with time. • Acceleration occurs whenever there is a velocity changes (ie. a change in its magnitude or direction). • Acceleration vector has a direction corresponding to the change in the velocity vector (i.e., not necessarily in the direction of the instantaneous velocity vector). • For circular motion the acceleration is always directed towards the center of curvature (i.e. perpendicular to velocity vector). (Chapter 5) Graphs can help understand motion: Distance vs. Time V=0 V=const D D t t - Stationary object -Constant velocity: Slope gives value of speed toward Higher speed d2 (d2 > d1) D d1 Lower speed t t away D Variable speed t Key: slope tells you about the instantaneous speed. Velocity vs. Time Plots V= constant V V a = constant t t Constant velocity (no change with time) Constant acceleration ( V increases uniformly with time) Slope gives value of acceleration. away High constant acceleration Low const. acceleration V t toward V Variable acceleration t Key: - Slope of velocity-time plots gives information on the instantaneous acceleration. - Area under curve gives distance traveled. Example: Car at rest accelerates uniformly up to a constant speed of 50 m/sec 60 in 10 sec. V (m/s) 50 40 Constant speed (zero acceleration) 30 20 Constant acceleration (speed increasing uniformly) 10 0 0 2 4 6 8 10 12 14 t (sec) - Constant acceleration produces a linear increase (decrease) in velocity with time. a= constant a Acceleration does NOT change with time. 10 s t This is the simplest form of acceleration and occurs in nature whenever a CONSTANT FORCE is applied e.g. gravity! Equations of Motion for Uniform (Constant) Acceleration (aa = constant constant) D V t Produces a linear increase in velocity with time. V=at Or if initial velocity (V0) NOT zero: V = V0 + a t t Distance covered grows very rapidly with time. (as velocity is increasing with time). D = 1/2 a t 2 Or if initial velocity NOT zero: D = V0 t +1/2 a t 2 • Important formulas for calculating velocity and distance under constant (uniform) acceleration (i.e., constant force) • Laws developed by Galileo (1638)! Summary: D Stationary object t Distance increase uniformly with time V Constant velocity D t a Constant acceleration t t V D t Velocity increases uniformly with time t Distance increases rapidly with time. (t2) Constant acceleration “a” occurs in nature whenever the force is constant e.g. gravity.