Lab 4: Gravity and 2-D Ballistic Motion 1 Introduction This lab focuses on ballistic motion, or the path of a body moving only under the

influence of gravity. In particular, we will measure the value of gravitational

acceleration and analyze the trajectories of launched projectiles. Newton?s laws are

important here, since they provide the theoretical foundation for describing such motion

mathematically. This experiment is intended to take two class periods, and you will

write a full laboratory report for it. For guidance, refer to the file on eLearning called

Writing Lab Reports, which has a description of all the information you will need to

include. Remember that this lab report is 25% of your final grade. 2 Key Concepts ?

? Projectile motion ? Newton?s laws ? 3 Gravitational acceleration Full laboratory write-up Theory 31 Newton?s Laws 1. Law of Inertia: Every object in uniform motion?that is, moving with

constant velocity?will stay in uniform motion unless a net external

force acts on it.

~

2. Fnet = m ~a. The net force acting on an object equals the mass of the

object times its acceleration. Remember that force and acceleration are

vector quantities, while mass is a scalar. 3. When one object exerts a force on a second object, the second object

also exerts a force on the first object that is equal in magnitude and

opposite in direction. This is often phrased as ?for every action, there

is an equal and opposite reaction.? The second law is most useful to us in this lab, because we know that the force of

gravity is, to very good approximation, constant and pointing downward near the

surface of the earth. The second law says that a constant force acting on an object

translates into constant acceleration of the object, and under the assumption of constant

acceleration, the following kinematic equations can be derived. See your text or the

appendix of Lab 3 for more details. 1 ~x = ~v0t ~a

+

1t2 , (1) 2

~v = ~v0 + ~a t , (2) ~v2 = ~v02 + 2~a

~x . (3) Time t is the independent variable, ~x is the change in position, ~v 0 is the initial

velocity, ~v is the final velocity (at time t), and ~a is the acceleration. Note that in the

third equation, there is a dot product between ~a and ~x, and the notation ~v 2 means ~v

~v, the square of the magnitude of ~v.

The equations above are vector equations, which we can think of as describing

relationships be-tween geometrical arrows associated with our object moving in threedimensional space. However, it is often more useful to use the equations in component

form relative to a Cartesian coordinate

?? ? system (the usual ?, , and k), although other coordinate systems are possible. This means

that Equations (1) and (2) each really stand for three equations?one for each coordinate

of the motion. For example, from Equation (2), we have v x = v0x +axt, and likewise for y

and z. We can therefore treat the motion along di?erent coordinate directions separately

in our analysis when the motion occurs in more than one dimension. Making a table of

the components of each variable is a helpful tool in keeping track of things. Consider

Figure 1 and Table 1 for a 2-D example of this process. Figure 1: Diagram of general projectile motion. 32 Projectile Motion We will be using the kinematic equations above to analyze the trajectory of a launched

projectile. Projectile motion occurs when an object is subject to an initial force that

propels it into the air, after which it follows an arcing path to the ground. In reality,

projectile motion is complicated by the presence of air resistance and other external

forces besides gravity. However, in this lab, we will neglect these other influences, and

our equations will only reflect the e?ect of gravity on the motion. It is important to

remember that we are applying the kinematic equations to the object only when it is

actually in flight; the launcher just serves to give the projectile an initial velocity, and

what happens inside the launcher is irrelevant to the object?s trajectory. 2 ~x (m) ~v0 (m/s) ~v (m/s) Motion description up v max ? hi v down v x x 0x ~a

(m/s2) t (s) 0x 0 t 0 ?9.80 t fx = v0x 0 t down fy ?9.80 t down v up Motion from hi to hmax

y h x x 0y 0x v up Motion from hmax to hf

y f ? hmax h 0 v Table 1: Table for organizing components of constant acceleration motion problems.

Have a set of x and y rows for each part of the motion, keeping in mind where the

beginning and ending points of the motion are. This table is set up for a projectile where

you want to know the maximum height (hmax) and range (xup + xdown). Calculations in trajectory problems can be lengthy, as there are many quantities of

interest

Experim Extraction of DNA Extraction of DNA Hands-On Labs, Inc. Version 42-0056-00-01 Lab Report Assistant This document is not meant to be a substitute for a formal laboratory report. The Lab Report Assistant is simply a summary of the experiment's questions, diagrams if needed, and data tables that should be addressed in a formal lab report. The intent is to facilitate students' writing of lab reports by providing this information in an editable file which can be sent to an instructor. Questions A. Describe what the DNA from the split peas looked like? B. Were your experimental results what you expected to see? Specifically, was there more or less DNA than you expected? C. What was the purpose of adding the detergent to the experiment? If the detergent was not used, do you think the experiment results would have changed? Explain your answer. D. If you used 5% isopropyl alcohol instead of 91% isopropyl alcohol, do you think the experiment results would have changed? Explain your reasoning. com 1 Hands-On