PHYSICS 197 Section 1 Chapter N2 Forces from Motion October 9, 2017

Exam Information Exam 1 on Thursday, October 12 from 6.30-11 pm. Room Assignment: Last name A-G: Rebstock 215 Last name H-Z: Hillman 070 Bring pencils, erasers, ruler, and calculator (shouldn’t store any text). May also bring a 8.5”x11” (A4) sheet (two-sided) containing hand-written formulas, problem-solving tips and any other info you might think useful. But NO worked-out or example problems allowed in the sheet. It will be inspected at the door and must be turned in with your exam. No need to include numerical constants (will be given in question paper). Last 3 years’ exams with solutions available on Blackboard (Main Course Homepage  Exam Information) Next class (Wednesday, 10/11) is review for Exam. Email me (by tomorrow 9pm) any particular problem you would like me to go over in Wednesday’s review session. Other resources: Cornerstone, Tu & Th help sessions in Phys. Dept.

Other Important Information Weekly HW 6 (due Wed 10/11) will not be turned in or graded. But please do it anyway for your own benefit. Daily Reading Assignment for Chapter N3 will be due Saturday, 10/14 11.59pm (instead of Thursday). More info: Blackboard Main Course Homepage  Course Info  Basic Course Info  Detailed Course Policies and Procedures

Review of Chapter N1 Newton’s Laws Implications of the Conservation of Momentum Important Concepts to Remember: Force = Mass x Acceleration Velocity = Rate of change of Displacement Acceleration = Rate of change of Velocity Instantaneous vs. average velocity (and acceleration) Centripetal acceleration (for uniform circular motion):

Outline of Chapter N2 Kinematic Chain Classification of Forces Force Laws Free-body Diagrams Motion Diagrams Graphs of One-Dimensional Motion

The Kinematic Chain Forces from motion (this chapter): Motion from forces (next chapter):

Classification of Forces

Force Laws Laws of physics are independent of one’s orientation in space. Forces exerted by long-range interactions between two objects must be directed along the line between them. Must point either directly toward or directly away. Described by potential energy functions. Example:

Important Force Laws Newton’s law of gravitation: Coulomb’s law: If Qq < 0, then toward the other object. Hooke’s law: If r < r0, then away from the other object. No potential energy functions for contact interactions. So can’t write such nice force laws for them.

Free-body Diagram Graphical tool to display external forces acting on a single object. Very useful 1st step in most of the problems involving Newton’s 2nd law of motion (acceleration is determined by external forces). How to draw a free-body diagram: Imagine the object in its context (especially its boundary). Draw a sketch of the object alone (as if it were floating in space). Draw a dot representing its center-of-mass and an arrow for each external interaction showing its magnitude and direction (starting from the dot). Label each arrow appropriately.

Useful Tips Do not draw any arrows depicting quantities that are NOT forces (e.g. velocity, acceleration). Draw arrows for ONLY those forces that act directly on the object in question. Make sure that every force arrow you draw reflects an interaction with some other object.

Clicker Question N2T.5 A box sits at rest on an inclined plank. How do the magnitudes of the normal force and the gravitational force exerted on the box compare? (Hint: Draw a free-body diagram!)

Answer N2T.5 A box sits at rest on an inclined plank. How do the magnitudes of the normal force and the gravitational force exerted on the box compare? (Hint: Draw a free-body diagram!)

Demo: Roller Coaster What is the maximum initial height from which the car should be released so that it does not lose contact with the track?

Motion Diagrams A graphical tool to determine both the magnitude and direction of an object’s acceleration from its motion. Consists of the following elements: A single image of the object in question A set of dots representing the position of the object’s center of mass at successive, equally spaced instants of time. Average velocity arrows drawn between adjacent dots. Acceleration arrows attached to each dot (except the first and last). Imagine a multi-flash (stroboscopic) photograph!

Clicker Question N2T.8 A bike (shown in a top view in the diagram) travels around a curve with its brakes on, so that it is constantly slowing down. Which of the arrows shown most closely approximates the direction of the bike’s acceleration at the instant it is at the position shown? (Hint: Draw a motion diagram)

Answer N2T.8 A bike (shown in a top view in the diagram) travels around a curve with its brakes on, so that it is constantly slowing down. Which of the arrows shown most closely approximates the direction of the bike’s acceleration at the instant it is at the position shown? (Hint: Draw a motion diagram)

One-Dimensional Motion Only the x-component of the position, velocity and acceleration vector relevant, which are simple signed numbers. Sign of the number gives the direction and the absolute value gives the magnitude. Given a graph of x(t), we can derive v(t) [by taking slope of x(t)] and a(t) [by taking the slope of v(t)] Gives qualitatively accurate information (not necessarily quantitatively).

Clicker Question N2T.13 An object’s x-position is shown in the boxed graph below. Which of the other graphs most correctly describes its x-velocity?

Answer N2T.13 An object’s x-position is shown in the boxed graph below. Which of the other graphs most correctly describes its x-velocity? B. The slope of the x(t) graph is negative at first, then goes to zero.

Clicker Question N2T.14 Which graph most correctly describes its x- acceleration?

Answer N2T.14 Which graph most correctly describes its x- acceleration? D. The slope of v(t) graph is initially zero, then becomes large and positive for a brief time and then goes back to zero.

Practice Problem N2R.1 The top of a small hill in a certain highway has a circular (vertical) cross section with an approximate radius of 57 m. A car going over this hill too fast might leave the ground and thus lose control. What speed limit should be posted?

Solution