Download Factors affecting terminal velocity

Factors affecting terminal velocity
Level: Secondary 6
Project aims:
The main purposes of this project are to let students:
1. Apply concepts of Newton’s Laws in scientific explorations.
2.
Investigate the relationships among different factors (e.g. mass, surface area,
object shape etc.) and terminal velocity.
Learning objectives:
1.
2.
Devise appropriate methods and procedures to carry out investigation.
Propose hypotheses for investigation and identify dependent and independent
variables in experiment.
Task:
Students have to find out factors that would affect the magnitude of terminal velocity
and perform experiments to show their relationships. Conclusion should be drawn
based on their results.
Apparatus/Materials:
Any appropriate apparatus and materials proposed by students are welcomed. Typical
examples include stop watch, parachute, video camera, measuring tape and so on.
Pre-knowledge:
There presents frictional force which acts between surfaces, and for an object moving
through a medium such as a gas or a liquid, it is also acted on by a resistive force,
called drag. This resistive force always points in a direction opposite to the direction
of the velocity of the object. Unlike friction, its magnitude depends on the speed of
the object.
Possible investigations:
1.
Relationship between mass and terminal velocity:
Students can carry out investigations on whether object of different masses
would affect the terminal velocity
2.
Study the relationship between surface area and terminal velocity:
Students can carry out investigations on whether object with different surface
areas would affect the terminal velocity
3.
Study the relationship between different object shape and its terminal velocity:
Students can carry out investigations on whether the shape of the falling object
would affect its terminal velocity
Teachers’ note:
For object moving through a liquid or for small objects moving slowly through a gas,
the magnitude of the resistive force, Fd is proportional to the speed, which expressed
as,
Fd  bv
According to Newton’s Second Law,
F net  ma
mg  bv  ma
When the speed of the falling object does not change any longer, it has reached the
terminal speed. So we can find the terminal velocity by simply setting the
acceleration, a  0 , this gives,
vt 
mg
b
For objects moving at high speed through air, the magnitude of the resistive force is
proportional to the square of the speed, which is expressed as,
1
CAv 2
2
where  is the air density (mass per volume), A is the effective cross-sectional area
Fd 
of the object (the area of a cross section taken perpendicular to the velocity), C is the
drag coefficient, which depends on the shape of the object, the inclination and the
flow condition.
For objects reach a terminal velocity, vt , the acceleration again is zero. By setting the
drag equal to mg, the gravitational force on the object, the terminal veloctiy can be
expressed as,
vt 
2mg
C A
Teachers’ guide:
Teachers can encourage the students to predict what factors would affect the terminal
velocity first before they perform any experiments. While at the time that students
obtain preliminary results for analysis, teachers can remind them to control variables.
That is while testing a particular factor, the others should be kept unchanged
throughout the experiments. Students should also ensure their falling object reached
its terminal velocity before reaching the ground. This is one of the challenging tasks
in this project.
Questions:
1.
2.
How do you choose the object that to be tested? What criteria do you think is
important in order to achieve a good result?
Base on your investigation, what conclusion can you draw?
Appendix:
Some Terminal Speeds in Air
Object
Terminal Speed (m/s)
95% Distance* (m)
Shot (from shot put)
145
2500
Sky diver (typical)
60
430
Baseball
42
210
Tennis ball
31
115
Basketball
20
47
Ping-pong ball
9
10
Raindrop (radius = 1.5 mm)
7
6
Parachutist (typical)
5
3
* This is the distance through which the body must fall from rest to reach 95% of its
terminal speed.
Source: Adopted from Peter J. Brancazio, Sport Science, 1984, Simon & Schuster,
New York.