PHY131H1S Class 13. Today: Nonuniform Circular Motion. Review of Chapters 1-8 Review of Error Analysis

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1 PHYHS lass Today: onuniform ircular Motion Review of hapters -8 Review of Error nalysis 80 minute test tomorrow evening at 6:00pm in H40 see you there!. n = w. n > w. n < w onuniform ircular Motion onuniform ircular Motion The inward radial force component (F net ) r creates a centripetal acceleration and causes the particle to change directions. The tangential force component (F net ) t creates a tangential acceleration and causes the particle to change speed. Force and acceleration are related to each other through ewton s second law. verage Speed, verage Velocity To quantify an object s fastness or slowness, we define a ratio as follows: verage speed does not include information about direction of motion. verage velocity does include direction. The average velocity of an object during a time interval Δt, in which the object undergoes a displacement Δr, is the vector cceleration The average acceleration of a moving object is defined as the vector Motion with onstant cceleration s an object moves, its velocity vector can change in two possible ways:. The magnitude of the velocity can change, indicating a change in speed, or. The direction of the velocity can change, indicating that the object has changed direction.

2 Projectile Motion Projectile motion is made up of two independent motions: uniform motion at constant velocity in the horizontal direction and free-fall motion in the vertical direction. The kinematic equations that describe these two motions are car travels at constant speed along the curved. Which vector best represents the car s velocity at position? car travels at constant speed along the curved. Which vector best represents the car s acceleration at point? car travels at constant speed along the curved. Which vector best represents the car s velocity at position? car travels at constant speed along the curved 4. Which vector best represents the car s acceleration at point?

3 car travels at constant speed along the curved 5. Which vector best represents the car s velocity at position? car travels at constant speed along the curved 6. Which vector best represents the car s acceleration at point? Mass Mass is a scalar quantity that describes an object s inertia. Loosely speaking, it also describes the amount of matter in an object. Mass is an intrinsic property of an object. It tells us something about the object, regardless of where the object is, what it s doing, or whatever forces may be acting on it. Gravity It was ewton who first recognized that gravity is an attractive, long-range force between any two objects. Somewhat more loosely, gravity is a force that acts on mass. When two objects with masses m and m are separated by distance r, each object pulls on the other with a force given by ewton s law of gravity, as follows: Static Friction The box is in static equilibrium, so the static friction must exactly balance the pushing force: The force of gravity is also often called the weight : w = mg.

4 Static Friction There s clearly a limit to how big f s can get. If you push hard enough, the object slips and starts to move. In other words, the static friction force has a maximum possible size f smax. the two surfaces don t slip as long as f s < f smax. The surfaces begin to slip when f s = f smax. static friction force f s > f smax is not physically possible. where the proportionality constant μ s is called the coefficient of static friction. Kinetic Friction The kinetic friction force is proportional to the magnitude of the normal force. where the proportionality constant μ k is called the coefficient of kinetic friction. Interacting Objects If object exerts a force on object, then object exerts a force on object. The pair of forces, as shown, is called an action/reaction pair. Significant Figures When multiplying or dividing several numbers, taking roots, etc, the number of significant figures in the answer should match the number of significant figures of the least precisely known number used in the calculation. You should keep at least one or two extra digits during intermediate steps of a calculation so you don t propagate round-off errors in the calculation. Just be sure to display the final answer to the proper number of significant figures. 4

5 Error nalysis Every measurement has two parts: the value and the error. For example, I have measured my height to be 80 cm +/- cm. 80 cm is the value, and cm is the error. Saying my height is 80 cm +/- cm means that I am about 68% certain that my true height falls within the range 79 to 8 cm (one sigma). It also means I am 95% certain that my true height falls within the range 78 to 8 cm (two sigma). ll of this error analysis assumes the data are normally distributed; ie that a histogram of results can be fit with a Gaussian function. Error nalysis There are many ways of estimating the error in a value. Here are two examples:. Half the last digit ie, 8.6 volts on a digital multimeter would be reported as 8.60 V +/ V.. Standard eviation In most situations, repeated measurements of the exact same quantity give different values. x = x i i= σ = i= ( x i x) Propagation of Errors Error in the Mean Repeat a measurement n times and find the mean to report as your final answer. Each individual measurement has the same error of precision Δx The error in the mean is: z = x Δz = Δx See you tomorrow! Good luck! 6:00pm in H40 Haultain is 70 ollege Test is 80 minutes; you should be done by 7:0. ring a calculator and an aid sheet with equations and helpful info on it. id sheet may be double-sided. I prefer hand-written but typed is also okay just please no incredibly tiny fonts or shrunken photocopies, etc, and of course you must prepare your own aid sheet! On Wednesday we begin hapter 9 Momentum! 5