Forces

Exemplar Project: The Physics of Hockey website

Detailed Objectives:

PSc.1.2.1

• Recognize that the weight of an object is a measure of the force of gravity and is the product of its mass and the acceleration due to gravity: Fg = mg

• With negligible air resistance, explain acceleration due to gravity as an example of uniformly changing velocity: g = 9.8 m/s^2

• Relate the presence of air resistance to the concept of terminal velocity of an object in free fall.

PSc.1.2.2

• Identify friction as a force that opposes motion of an object. (Review from middle school.)

• Classify the frictional forces present in a situation such as a book resting on a table (static), a box pushed across the floor (sliding), a ball rolling across the floor (rolling), a boat moving through a river (fluid), or an object in free-fall (fluid).

PSc.1.2.3

• Explain the property of inertia as related to mass - the motion of an object will remain the same (either at rest or moving at a constant speed in a straight line) in the absence of unbalanced forces; if a change in motion of an object is observed, there must have been a net force on the object.

• Explain balanced and unbalanced forces mathematically and graphically with respect to acceleration to establish the relationship between net force, acceleration, and mass: a ∝ F and a ∝m

(no trigonometry).

• Explain qualitatively and quantitatively the relationship between force, mass and acceleration– the greater the force on an object, the greater its change in motion; however, the same amount of force applied to an object with less mass results in a greater acceleration.

• While the second law describes a single object, forces always come in equal and opposite pairs due to interaction between objects. Give examples of interaction between objects describing Newton’s third law – whenever one object exerts a force on another, an equal and opposite force is exerted by the second on the first. The third law can be written mathematically as FA→ B = − FB→ A . Students should explain why these forces do not “cancel each other out”.

Vector and Matrix Quantities

Represent and model with vector quantities.

1. (+) Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes

2. (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

3. (+) Solve problems involving velocity and other quantities that can be represented by vectors.

Perform operations on vectors.

4. (+) Add and subtract vectors.

a. Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.

b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction component-wise.