Lecture 4: Physics of Energy & the Environment- PHYS 161

Let the Force be with You... the Sequel, where Luke Skywalker and Rebels get their Comeuppance.

In the last lecture we tried the experiment shown below with a fan exerting a constant net force pointing away from the motion detector (positive direction by our convention) on a cart. Under the influence of the fan, the cart accelerated away from the detector.

We undertook this experiment to explore the relationship between the cart's acceleration and mass, and the net (total) force exerted on the cart. Our schema, which is based on the scientific process discussed in Lecture 1, lead us to ask the following questions, form the following hypotheses, test them through experimentation, and refine them if necessary:

Question: What are the important and unimportant variables? (We know in advance that net force, mass and acceleration are. We are pretty certain that they form a complete list of important variables. For other experiments, we may not know all important variables in advance of experimentation.)
Assumption: The net force acting on the cart is equal to the force of the fan on the fan cart. We are neglecting any frictional forces (and air resistance) for now.
Hypothesis I: acceleration is proportional to total force (for constant mass).
Experiment I: We tested this hypothesis by varying the net force on the cart (more or less batteries powering the fan) and observing its acceleration while keeping the mass constant. We observed the following plot (made from our observations during Lecture 3).
Hypothesis II: acceleration is inversely proportion to mass (when force is held constant).
Experiment II: To understand mass's relationship with acceleration, hold force constant and vary the mass of the cart. See what happens to the acceleration. An example graph from this experiment is given below:
Result: Hypotheses I and II are correct. They can be summarized as Newton's Second Law:
The acceleration of an object is proportional to the net force acting on it, and the constant of proportionality is the object's mass.

When net force is zero, a special case:

What happens when the net force on the cart is zero, but the cart is already moving? According to our result, above, the acceleration of the cart would be zero. Hence its speed would not change. If it is stationary to begin with, then it would remain stationary. If it is moving at a constant velocity, it would keep moving at that constant velocity.... until an non-zero net force acted on it!

Let's revisit our experiment involving the cart; level, low-friction track and motion detector to verify that this is true.

Definitions for speed, velocity, acceleration, force and mass in words.

What is "gravity?"

Let's observe the effect of "gravity" on a softball with the following experimental setup:

Question: What happens when the board is pulled out from under the softball?

Answer: Duh, let me guess.....

Question: So, HOW is the ball moving towards the ground?

Answer: The ball is accelerating towards the ground, as we observe its velocity to be changing at a constant rate over time.

Question: If the ball is accelerating, what is causing the acceleration?

Answer: The "force of gravity," the attraction between the Earth and the softball, is causing the ball to accelerate downwards.

Question: Is the "force of gravity" the same for lighter or heavier (less or more massive) objects of a similar shape?

Try this experiment:

Answer: OK, so they both hit at the same time (after suitable modification). That means that they both accelerated in an identical manner, speeding up towards the table at the same rate. By Newton's II Law, the force of gravity acting on them is NOT the same. It varies in just the right way, according to their mass, so that they accelerate the same way.

Introduction to Work and Energy

One definition used by physicists to describe the energy of simple objects is expressed in terms of work:

Energy is the ability to do work.

The more work a simple object can do, the more energy it has. But what, specifically, is work? Scientists have a very particular definition for work-- a term that can mean many different things in every day language (e.g., I worked out, I got worked up or, we can work it out.). For simple objects, work is defined as the net force exerted on the object times the distance it is moved:

Work = Force x Displacement

In this case, the only important part of a force doing work is that part which points in or away from the direction of of displacement (remember, "displacement" is a distance and a direction).