Physics MIDTERM Original Elaboration 2021
ASSESSING PHYSICAL PHENOMENA BY USING MATHEMATICAL METHODS
Learning Objective: Model natural processes through basic Laws-of-Motion
Translating between the (concrete) physical principles and (abstract) mathematical representations.
Lesson Goal: Create and interpret instances of “real-life” MECHANICS that demonstrates or reveals understanding.
Make predictions using uniform forces, correctly RESOLVED as vectors, and inertia.
Directions You will invent scenarios for the three situations shown (idealized) here:
1. ACCELERATION & PROJECTILES §§ 2.1, 3.2 & 5.3 A freely falling mass m is initially at height yi, moving horizontally at vx [There is only one GRAVITY FORCE, ‒ mg: Its path is a parabola]
2. FORCS & LAWS-OF-MOTION §§ 4.2 &4.3 A mass m is being PUSHED along a flat (level) surface, with kinetic coefficient-of-friction μK [There are two opposing forces: constant PUSHING FORCE and FRICTION = ‒ μFN, with NORMAL FORCE = mg]
Let the mass start initially at rest and then (suddenly) be released when it reaches velocity vxi.
Criteria
A Make the story about events “realistically” encountered: What is hurling? Who is pushing what? [Try imagining interesting “characters and situations”!]
Choose definite mass, horizontal velocity and (if needed) height or friction-coefficient values, which may be different for the problems!
B List the meanings of all symbols, both chosen and calculated; fully write the scenario and solutions using this appropriate vocabulary. Also , usage should show understanding of “real-life” context!
C Using Dynamics=> Make a Free-Body Diagram labeling all forces involved and write the ∑F = ma equations. Calculate all named (or symbolized) forces in the Diagram.
D Using Kinematics=> Solve both situations for acceleration.
[NOTES: For Problem #1, there is no air-resistance. Problem #2 has two stages]
Case #1 Find how much time elapses and the horizontal displacement until the mass lands, yf = 0.
Case #2 Find how much time elapses and the horizontal displacement until the mass gets released at vxi .
Find how much time elapses and the horizontal displacement until the mass (released at vxi) stops.
E Inquiry Use kinematics, dynamics or “common sense” but very clearly state your reasoning:
(a) All falling objects, through an empty vacuum, will fall at the same acceleration g. However, why might it make sense that any object subject FRICTION will also have the same acceleration, regardless of mass?
(b) When GRAVITY stops objects, this is a turning-point; when FRICTION stops objects, they just remain at rest.
How does the way GRAVITY and FRICTION affect motion when objects reverse direction explain this?
