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Further Mathematics Support Programme
the Further Mathematics Support Programme
www.furthermaths.org.uk
Mechanics Misconceptions
Sue de Pomerai
the Further Mathematics Support Programme
June 2010
Miconceptions
http://nagty.lboro.ac.uk/pages/resources.html
When I got to the top of the building I rigged up a beam and a
pulley and hoisted up a couple of barrels of bricks. When I had
finished there were a lot of bricks left over so I hoisted the barrel
to the top again and secured the line at the bottom. I filled the
barrel with bricks and
climbed down. I cast off the line but
unfortunately the barrel of bricks
was heavier than I was and before
I knew what was happening the barrel
started down jerking me off my feet.
I hung on.
Halfway up I met barrel coming down …….
the Further Mathematics Support Programme
www.furthermaths.org.uk
Practical approaches to
mechanics
June 2010
Why do practicals?

Mechanics is all about modelling the real world, so some
insight (‘feel’) about how the real world behaves is vital.

Every Mechanics lessons should have a practical
element to this – this can be a full-scale experiment, a
short practical or a thought-experiment. This ensures
that the theory is linked with experiences of interacting
with the physical world.

Practicals are fun!
Why short easy practicals?

We don’t have much time!

We teach maths, not science - we are more
interested in the modelling than the experiments
themselves.

Accurate experiments and measurements are
not necessary to get a ‘feel’ for a mechanical
situation, sufficient to justify the modelling.
The experiments

The experiments require little specialised apparatus.

They are quick and easy to carry out.

The questions accompanying the experiments are key to
their use.
Newton’s laws rephrased

N1: No change in momentum No net force

N2: A net resultant force in a direction  change of
momentum in a direction

N3: Forces are subjective (I push down with 3N on you
means you push up with 3N on me)
N1 covers two situations: a stationary object and one with a
constant velocity.
Short easy practicals



Forces on stationary objects (N1 stationary, N3)
 Stand up and feel the forces on your feet. What forces
are on you?
 Lift one foot off the floor. What happens to the forces?
 Push down on a table whilst stood up. What happens
to the forces?
 Stand with one foot in contact with the floor and one on
scales or both feet on the scales and pushing down on
a table. What is your maximum/minimum “weight” on
the scales?
How can you make a set of scales show more than your
weight?
(Push up on the ceiling standing or jump to give an
acceleration).
Short easy practicals

Net resultant force (N2)
 Two people push against each other. Who moves?
 As above but one on wheels/ice/socks on lino.
 Drop an object. Drop an object whilst walking fast and
observe its vertical motion.
Short easy practicals

Looking at the force due to the same object in different
places (N3)
 Two people pull either side of a bungee cord. Compare
the extension to 2 people pulling on one side with it
fixed to a door/wall. How can we get the same
extension? (4 people – 2 each end).
 Attach 2 tables with a bungee cord. Pull the first table
using another bungee cord. Which one will stretch
more?
Short easy practicals

Forces on objects with constant velocity (N1 not
stationary)
 Drop a ball whilst walking fast and observe its horizontal
motion.
 Stand up and imagine you are on a train. What would
happen when it accelerates/decelerates/turns?
Compare this to when it is not turning/accelerating.
Dropping a heavy and a light ball
simultaneously

Before you do the experiment, try to predict which ball
will hit the ground first and why.

What forces are acting on the balls when they are
falling?

Can you explain what actually happens?
Sliding a graphical calculator on a
desk

Try to slide it button
side up

And button side
down

What do you
notice?

Can you explain?

How could this be
modelled
mathematically?
Sliding fingers together under a ruler
Rest a ruler on two fingers, then
slide your fingers together

What do you think will
happen?

Try it out – were you
right?

Try starting your fingers
at different positions on
the ruler

Can you explain?

Can you suggest how to
model this
Playing catch

When the ball is in the air, what path does it follow?

What forces are acting on the ball when it is in the air?

How can you throw the ball so that it goes further?


angle projectiles
projectiles component
Hanging a mass between two masses
suspended over pulleys

Set up the apparatus as shown
Vary the masses
to see what
happens. Can
you predict the
angles from the
masses, or vice
versa? (as shown
in the photo,
where the masses
are hidden)
Stretching a rubber band between
masses suspended from pulleys
?

Measure the length of the unstretched rubber band

Set up the apparatus as shown in (1), with equal
weights suspended from strings attached to each
end of the band and then passed over pulleys

Measure the length of the stretched rubber band

Now change the set up by tying the strong off at
one end and transferring all of the weight to hang
from the pulley at the other end, as in (2)

Measure the length of the stretched rubber band
again
(1)
?
(2)
What do you notice? Can you explain?
Closing a door by pushing at
different distances from the hinge

What do you think will happen?

Try it out – were you right?

Can you explain?

Can you suggest how to model this mathematically?