Presentation on theme: "Acceleration And related topics: average velocity, instantaneous velocity, acceleration due to gravity."— Presentation transcript:
1 AccelerationAnd related topics: average velocity, instantaneous velocity, acceleration due to gravity
2 Acceleration (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?
3 2 ways a body can accel. ∆ in mag. (speed up or slow down) ∆ in direction (traveling in a curved path)
4 Annotation of velocity Initial velocity = vo or viFinal velocity = v or vfOther velocities = v1,v2,v3 ……
5 Average 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.
7 Acceleration 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.
8 Dimensions of acceleration MKS?CGS?Discuss what the dimensions mean.
9 Uniform accelerationConstantly changing velocity - magnitude or direction.
10 Instantaneous 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.
11 Vins 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.
12 100% 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.
13 More vins vave = vins only in the special case of constant v. Vins can change in 2 ways:- ∆ speed- ∆ direction
14 Consider vins & 100% accuracy when direction not speed is changing
15 With circular motion speed is the limit of vins
16 vins & 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
17 Instantaneous acceleration Also existInvolves velocity & time instead of displacement & time.
18 Acceleration 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.
19 g g = - 9.8 m/sec2 = - 980 cm/sec2 = -32 ft/sec2 Notice g is only in 2 sign. dig.
20 g formulas v = vo + at ---> v = vo + gt d = vot + 1/2at > d = vot + 1/2gt2v2 = vo2 + 2ad > v2 = vo2 + 2gd
21 g 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?
22 Data table Location Value of g (m/s2) Location & the value of g. N pole-9.832Sea 45o N latitude-9.806Denver-9.796