Vertical motion: the stationary tennis ball
Hold a tennis ball, stationary, in the flat of your hand. Describe its motion
using the terms displacement, velocity and acceleration. Describe the forces
acting on the ball in the vertical.
To check your answer, try another question: name the forces acting on the
ball in the vertical.
You should have observed that while the ball has zero velocity, zero
acceleration and zero displacement, it is experiencing the force due to
gravity. The only way this would not be the case would be if the gravitational
field had been switched off! With your understanding of forces and Newton’s
laws you should be able to explain why the ball does not fall.
Vertical motion: the tennis ball travelling vertically upwards
Imagine a tennis ball thrown vertically upwards (don’t worry about
the coming back down section yet).
Describe its motion. You can use a digital camera to record the motion and a
free software package such as tracker.jar to analyse its motion. This should
allow you to describe the ball’s motion in detail using the words
displacement, velocity and acceleration. You should also consider the forces
acting on the ball in the vertical as it travels upwards.
Graph the motion (displacement–time, velocity–time and acceleration–time)
and explain your interpretation of the graphs.
Vertical motion: the tennis ball dropped vertically
Consider the motion of the tennis ball dropped vertically. Again,
describe its motion, graph its motion and consider the forces acting
on the ball in the vertical as it falls.
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Vertical motion: prediction
Consider two tennis balls, one filled with a fluid such as water, but otherwise
identical. Both are dropped from the same height. Which one hits the ground
first? Explain your answer in terms of forces and acceleration.
Vertical motion: freefall (or which falls faster, the hammer or the
feather?)
Consider the image opposite. What
does the spacing between the
feathers tell you about its motion?
Under what circumstances could
this photograph have been taken?
The Apollo 15 hammer–feather
drop
At the end of the last Apollo 15
moon walk, Commander David
Scott…performed a live
demonstration for the television
cameras. He held out a geologic
hammer and a feather and dropped
them at the same time. Because
they were essentially in a vacuum,
there was no air resistance and the
feather fell at the same rate as the
hammer, as Galileo had concluded
hundreds of years before – all
objects released together fall at the
same rate regardless of mass. Mission controller Joe Allen described the
demonstration in the Apollo 15 Preliminary Science Report:
‘During the final minutes of the third extravehicular activity, a short
demonstration experiment was conducted. A heavy object (a 1.32 -kg
aluminum geological hammer) and a light object (a 0.03 -kg falcon feather)
were released simultaneously from approximately the same height
(approximately 1.6 m) and were allowed to fall to the surface. Within the
accuracy of the simultaneous release, the objects were obser ved to undergo
the same acceleration and strike the lunar surface simultaneously, which was
a result predicted by well-established theory, but a result nonetheless
reassuring considering both the number of viewers that witnessed the
experiment and the fact that the homeward journey was based critically on the
validity of the particular theory being tested.’
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Joe Allen, NASA SP-289, Apollo 15 Preliminary Science Report, Summary
of Scientific Results, p. 2–11.
The video of this experiment can be seen at
http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html.
The phrase ‘all objects released together fall at the same rate, regardless of
mass’ is a very important one. Of course, this applies only in the absence of
air resistance, which is why the moon is a good place to choose! Galileo
(1564–1642) (see
http://www.bbc.co.uk/history/historic_figures/galilei_galileo.shtml) had theorised
about this. Whether or not he actually carried out experiments involving
cannonballs being dropped from the Leaning Tower of Pisa, however, is
unknown. Galileo’s approach to science was significant in that he used
mathematics to analyse the results of his experiments. Like Newton (1642 –
1727) and Einstein (1879–1955), Galileo used ‘thought’ experiments:
experiments carried out entirely in the mind using reasoning and logic to help
explain complex ideas.
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Calculating Weight
A planet’s gravitational field strength equals the force of gravity per unit
mass.
The equation linking weight, mass and gravity is:
W = mg
w = weight in newtons (N)
m = mass in kilograms (kg)
g = gravitational field strength in newtons
per kilogram (N kg –1 )
Near the surface of a planet, all objects experience the same acceleration a
due to the force of gravity.
On Earth:
g = 9.8 N kg –1
a = 9.8 m s –2
Consider:
 Is the gravitational field strength the same on each planet?
 How does distance affect gravitational field strength?
 How will an object’s weight vary as distance from a planet’s surface
increases?
Gravitational field strength and the force due to gravity will be examined
more closely later on within this unit.
Vertical motion: the tennis ball
1. Dropped vertically and allowed to bounce.
2. Thrown vertically upwards and allowed to fall back to its
starting position.
Using your understanding of vertical motion, you should now be able to
describe, explain and sketch graphs of motion for a tennis ball dropped
vertically and allowed to bounce until it comes to rest, and for a ball thrown
vertically upwards and allowed to fall back to its starting position.
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Using the equations of motion for vertical motion
Estimate the initial acceleration of a jumping popper. Calculate the initial
acceleration of the jumping popper. What assumptions are you making? How
could your calculation be improved?
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