Physics 271: Advanced Honors Physics I

Recitation #3: Problem Solving Checklist for Newton's Laws Problems

Fall 2017

0. NEVER write only the answer. You need to show where it came from and why it is right.

APPLIES TO ALL PROBLEMS

1. Check that you have drawn at least one diagram and labelled it clearly. This might involve copying the diagram from the problem statement and adding extra labels, or making a diagram from scratch. Make it pretty large to leave room for labels and make it readable. Quantities from the statement of the problem should appear in the diagram.

MOST NEWTON'S LAW PROBLEMS INCLUDE A DIAGRAM SHOWING THE SYSTEM LABELLED WITH GIVEN QUANTITIES (MASSES, FORCES, ACCELERATIONS, VELOCITIES). YOU NEED TO ADD LABELS DEFINING COORDINATES FOR EACH OBJECT IN THE SYSTEM. THEN DRAW FORCE DIAGRAMS FOR EACH OBJECT IN THE SYSTEM.

2. Check that the meanings of any symbols you have introduced yourself are clear. First, if the symbol is a label in the diagram, make sure the diagram makes its meaning clear. If not, or if it is not in the diagram, write a short phrase to explain what the symbol represents.

KK OFTEN DOES NOT GIVE NOTATION FOR THE DESIRED QUANTITY SO YOU HAVE TO CHOOSE IT FOR YOURSELF. TRY TO PICK SOMETHING NATURAL. FOR EXAMPLE, IN PROBLEM 3.1 THEY ASK FOR "THE INITIAL ACCELERATION OF EACH MASS." IF YOU HAVE CHOSEN x AS THE COORDINATE OF THE MASS ON THE FLOOR AND y AS THE COORDINATE OF THE MASS AGAINST THE WALL, THEN ONE NATURAL CHOICE WOULD BE x double dot sub 0 AND y double dot sub 0. IN THE SOLUTION, YOU WOULD WRITE "The initial acceleration of the mass on the floor is x double dot sub 0 and the initial acceleration of the mass against the wall is y double dot sub 0.

IN THIS PROBLEM (KK 3.1) YOU ALSO HAVE TO INTRODUCE NOTATION FOR THE FORCE EXERTED BY THE POLE ON EACH MASS. ONE NATURAL CHOICE WOULD BE vector F sub floor AND vector F sub wall.

3. Check that all vector quantities are written so that their vector character is clear. In typesetting, boldface indicates a vector quantity. In a diagram, if you draw an arrow to indicate the direction and write the magnitude next to the arrow (this is how we draw force diagrams). In handwriting, put an arrow over the quantity to show it is a vector. Velocity is a vector, so write v with an arrow over it. The x component of the velocity is not a vector, so do not put an arrow over it. In a sum, you cannot add a vector to a number. In an equation, you cannot have a vector on one side and a number on the other side.

4. Check that each statement clearly follows from the previous statement. (This is in the same spirit as Checklist item #0 - you can't state things without showing where they came from).

**In a Newton's law problem, this flow is as follows. Draw the diagram of the system and label the coordinates. Write the constraint equations, if any. Draw the force diagram for each object. Apply Newton's 2nd law to each object and write the resulting list of equations. Write any additional equations (for example, the relation of the friction force to the normal force). Go over the system of equations to list out the unknowns you want to solve for and the unknowns you can eliminate. Count the total number of unknowns to check that you have enough equations, then solve for the desired quantities.

5. Check that you have stated the answer at the end of the solution. The answer should be an equation in the form

desired quantity = expression in terms of given quantities

You might want to save writing by just writing the right hand side, but it is best practice to write the whole thing (this acts as a check that your expression is indeed for the quantity the problem asked for).

To make it clear that it is the answer, PUT A BOX AROUND IT.

This page is maintained by Karin Rabe.