Results

In this chapter, we’ll use vectors to expand our understanding of forces and motion into two dimensions. Most real-world physics problems (such as with the game of pool pictured here) are, after all, either two- or three-dimensional problems and physics is most useful when applied to real physical scenarios. We start by learning the practical skills of graphically adding and subtracting vectors (by using drawings) and analytically (with math). Once we’re able to work with two-dimensional vectors, we apply these skills to problems of projectile motion, inclined planes, and harmonic motion.

Basic primer on Newton's First Law of motion.

Newton's Laws of Motion

Newton's second law of motion is F = ma, or force is equal to mass times acceleration. Learn how to use the formula to calculate acceleration.

Learn about Newton's third law of motion, which states that for every action there is an equal and opposite reaction. Look at multiple examples that illustrate this law, including pushing a block on ice, pushing against a desk, walking on sand, how rockets work, and how an astronaut could save themselves from drifting in space.

• Predict how current will change when resistance of the circuit is fixed and voltage is varied.
• Predict how current will change when voltage of the circuit is fixed and resistance is varied.

You want a projectile to fly as far as possible, at which angle should you launch it? We'll start with formulas for the initial velocity.

Plotting projectile displacement, acceleration, and velocity as a function of time.

Figuring out the horizontal displacement for a projectile launched at an angle.

• Determine how each parameter (initial height, initial angle, initial speed, mass, diameter, and altitude) affects the trajectory of an object, with and without air resistance.
• Predict how varying the initial conditions will affect a projectile’s path, and provide an explanation for the prediction.
• Estimate where an object will land, given its initial conditions.
• Determine that the x and y motion of a projectile are independent.
• Investigate the variables that affect the drag force.
• Describe the the effect that the drag force has on the velocity and acceleration.
• Discuss projectile motion using common vocabulary (such as: launch angle, initial speed, initial height, range, time).