Mechanical Rate (a.k.a. Motion)

Mechanical Rate(a.k.a. Motion) http://www.uhigh.ilstu.edu/tech/PT/

TEKS • TLW knows the laws governing motion (TEKS 7) • TEKS 7.A - Generate and interpret relevant equations using graphs and charts for one- and two-dimensional motion • i. One dimensional equations for: displacement, distance, speed, velocity, average velocity, acceleration, and average acceleration • ii. Two-dimensional equations for projectile and circular motion • iii. Using and describing vector forces and resolution

TEKS • TLW knows the laws governing motion (TEKS 7) • TEKS 7.B – Describe and calculate the effects of forces on motion of objects including law of inertia, impulse, and conservation of momentum • TEKS 7.C – Develop and interpret a free-body diagram • TEKS 7.D – Identify and describe motion relative to different frames of reference

Lesson Plan Objectives • Identify and describe motion relative to different frames of reference – such as heights and orbits • Use real-time technology (photo-gates, ramps, stop watchers, etc.) in hands-on labs • Prepare and interpret graphs from data collected on linear, projectile, and circular motion • Define Speed, velocity, and acceleration. • Explain the difference between speed and velocity. • Explain the difference between velocity and acceleration. • Use speed, velocity, and acceleration to solve problems involving linear (one-dimensional) motion.

Lesson Plan Objectives • Use speed, velocity, and acceleration to solve problems involving projectile motion • Define angular speed and angular acceleration. • Use angular speed and angular acceleration to solve problems involving rotational motion. • Create and use free-body diagrams to analyze force scenarios

Speed • Speed is the ratio between the distance traveled and the elapsed time. (scalar quantity) Distance traveled (d) Speed = Time interval (t) Examples of units to use: m/sec, km/hr, ft/sec, or miles/hr

Average Speed • When speed varies between point A and B Average Speed Distance traveled (d) = Time interval (t) savg d d2 – d1 = = t t2 –t1 d2 = final distance (df) d1 = initial starting point (di) t2 = final time (tf) t1 = initial time (ti)

Velocity • A vector quantity giving the speed (magnitude) and direction of travel. distance Velocity = time d vavg = t

Acceleration Average Acceleration • Describes the rate of change of an object’s velocity Velocity change (v) = Time interval (t) v v2 – v1 aavg = = t t2 –t1 v2 = final velocity (vf) v1 = initial velocity (vi) t2 = final time (tf) t1 = initial time (ti) Negative acceleration is called deceleration

Free Fall • Definition – the movement of an object in response to gravitation attraction • As an object falls towards Earth it will accelerate at a constant rate of 9.8 m/s2 – regardless of mass ( g = 9.8 m/s2) • It is common to neglect air resistance in high school curriculum… but it does play a part in real life • Downward acceleration will be positive, upward will be represented by a negative. …. Likewise, upward velocity will be negative and upward direction will be negative.

Free Fall • Displacement of falling object = Δd = vinitialΔt + (1/2)g Δt2 • Final velocity of falling object = vfinal2= vinitial2 + 2g Δd • OR Final velocity of falling object = vfinal = vinitial + g Δt

Free Fall • Time for object to reach Earth = Δt = vfinal - vinitial g • OR Time for object to reach Earth = Δt = 2 Δd g

Projectile Motion • A projectile is any object upon which the only force is gravity • Projectiles travel with a parabolic trajectory due to the influence of gravity • There are no horizontal forces acting upon projectiles, and thus no horizontal acceleration

Projectile Motion • Projectiles always maintain a constant horizontal velocity (neglecting air resistance) • Projectiles always experience a constant vertical acceleration of 9.8 m/s2 downward (neglecting air resistance). • Horizontal and vertical motion are completely independent of each other. (i. e. – there are horizontal and vertical components to velocity)

Projectile Motion • For an object beginning and ending at the same height it takes the same amount of time to reach highest point as it does to return to original position • Objects dropped from a moving vehicle have the same velocity as that vehicle

Projectile Motion • horizontal distance (dx) in meters = vxt • vertical distance (dy) in meters = vy∆t + 1/2g∆t2 • vertical distance (dy) at an angle in meters = vy(sin θ) ∆t + 1/2g∆t2

Projectile Motion • angular range (R) in meters = vi2sin 2 θ g • hang time (t) in seconds = 2vy(sin θ) g

Angular Speed radians or revolutions • Rate of rotational motion. angular displacement () Angular Speed () = time interval (t) omega 1 revolution = 360º = 2 radians

Angular Acceleration • Ration of the change in angular speed to the time interval. Angular speed change () Angular Acceleration = Time interval (t)  2 – 1 a = = t t2 –t1

Summary • Speed is a measure of the rate of motion of an object. It is the ratio of distance traveled to the time interval. Speed is a scalar quantity. • Velocity is the ratio of displacement to the time interval. Velocity and displacement are vector quantities. Speed is the magnitude of velocity. • Acceleration is a measure of the rate of change of an object’s velocity. It is the ratio of change in velocity to the time interval. • Angular speed is a measure of the rate of rotational motion of an object. It is the ratio of angular displacement to time interval. • Angular acceleration is a measure of the rate of change of an object’s angular speed. It is the ratio of change in angular speed to the time interval.

Mechanical Rate (a.k.a. Motion)