Presentation on theme: "Acceleration And related topics: average velocity, instantaneous velocity, acceleration due to gravity."— Presentation transcript:
1AccelerationAnd related topics: average velocity, instantaneous velocity, acceleration due to gravity
2Acceleration (a) Your concept of acceleration is probably lacking. When the velocity of an object is changing it is accelerating.acceleration = rate of ∆ in velocityAcceleration is the derivative of velocity as a function of time.a = ∆v/∆tUsing physics variables, how would you write that formula in calculus?
32 ways a body can accel. ∆ in mag. (speed up or slow down) ∆ in direction (traveling in a curved path)
4Annotation of velocity Initial velocity = vo or viFinal velocity = v or vfOther velocities = v1,v2,v3 ……
5Average velocityWhen an object is accelerating we can not speak of velocity as we do when an object has constant velocity. We must speak in terms of average velocity during a time interval.Acceleration is always implied.
7Acceleration formulas - table 3-3 p.68 v = vo + atd = vot + 1/2at2v2 = vo2 + 2adDerivationsThese are the forms of the equations I want you to use. These are slightly different than those given in your text. Write these formulas on your formula note card.
8Dimensions of acceleration MKS?CGS?Discuss what the dimensions mean.
9Uniform accelerationConstantly changing velocity - magnitude or direction.
10Instantaneous velocity one instant in time.Define instantVelocity for which the displacement is measured over shorter & shorter time intervals.Vins = vave over a short time intervalAcceleration is always implied.
11Vins cannot be measured w/ 100% accuracy Since vins is only used with accel. Motion, velocity is changing within an instant.No matter how short the time interval is a shorter time interval will yield a ∆ value of vins.
12100% accuracy cont.Vins would be absolutely correct if it were so instantaneous that the displacement were meas. over the exact path. This would be impossible.Either constant ∆ of direction or∆t = 0, then d/0 = undefined or ∆d = 0 the 0/0 = 0 and the object is obviously moving.Therefore, vins cannot be meas. W/ 100% accuracy.
13More vins vave = vins only in the special case of constant v. Vins can change in 2 ways:- ∆ speed- ∆ direction
14Consider vins & 100% accuracy when direction not speed is changing
16vins & 100% accuracy cont.Therefore it is impossible to measure vins w/ 100% accuracy due to changes in either speed or direction.When direction is involved vins > vave
17Instantaneous acceleration Also existInvolves velocity & time instead of displacement & time.
18Acceleration due to gravity (g) g = the accel. due to gravity.g is a function of the mass of the body causing the accel.. Therefore since the mass of the earth is constant, g is also constant.g ≠ gravity. Gravity is the force that causes g and F ≠ a, although F a a.
19g g = - 9.8 m/sec2 = - 980 cm/sec2 = -32 ft/sec2 Notice g is only in 2 sign. dig.
20g formulas v = vo + at ---> v = vo + gt d = vot + 1/2at > d = vot + 1/2gt2v2 = vo2 + 2ad > v2 = vo2 + 2gd
21g exercise 1. Present the data from the handout in a data table. 2. What general conclusion do youdraw from your data?3. From your data, hypothesize aboutthe value of g at sea level on the equator.4. What does the value of g at the N polecompared to other locations tell you?5. Name a U.S. city with a N latitude of 45°.6. What is our approx. latitude?
22Data table Location Value of g (m/s2) Location & the value of g. N pole-9.832Sea 45o N latitude-9.806Denver-9.796