MEI Conference 2015
Revisiting Mechanics
in Action
http://stem.org.uk/cxbc
Tom Button
tom.button@mei.org.uk
Mechanics in Action
Worksheet 7
Three masses
Vary B whilst keeping the A = C. You may need to change A and C but you should
ensure they are equal.
Take measurements of the angle for different masses on B, recording the mass of A,
B and C.
You may find it easier to split angle D either side of the vertical:
θ
A
B
φ
C
θ
φ
Validate your readings using the theory.
Now try situations where A and C have different masses.
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Mechanics in Action
Worksheet 9
Balancing a ruler
By varying the mass on the end of the ruler, find the distance d from the end where
the pivot should be place to balance the ruler.
Record the mass M, and the distance d.
Mass M
distance d
predicted d
Are you able to predict the value of d for other masses?
By applying moments find the mass of the ruler.
Use your data to draw a graph of d against M and find a function for the distance d
in terms of the mass M.
Extension
Repeat the experiment for two or three rulers combined.
Use moments to verify your formulae are correct.
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Mechanics in Action
Worksheet 17
The ‘law’ of Friction
By varying the mass M on the block, find the smallest mass m required to make the
block slide.
Record the mass M, and the mass m.
Mass M
Mass m
Estimated µ
Use the values of M and m to estimate the value of the coefficient of friction, µ.
Verification
You can check the value of the coefficient of friction, µ, by tilting the table and
measuring the minimum angle at which the block slides. This should be independent
of the mass M.
µ = tan θ
Can you explain why this works?
Why should be independent of the mass?
Extension
Repeat the experiment with a different surface between the block and the table (e.g.
sandpaper).
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Mechanics in Action
Worksheet 25
Connected masses problem
Put the masses on the pulley so that they are level but there is sufficient space and
string for the heavier mass to reach the ground. Measure the distance to the ground,
h, from the point where they are level to the ground.
Set the mass m to 50g. Vary the mass M so that it is heavier than m. Record the
time taken for the heavier mass to reach the ground. You should use the median of
three readings.
m = 50g
h = ____
Mass M
Time 1
Time 2
Time 3
Median
time
Predicted
time
Set up a mathematical model that will allow you to use the values of M and m to
estimate predicted times.
How well does this match you readings?
Extension
Devise an experiment that you could use to estimate the acceleration due to gravity.
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Mechanics in Action
Worksheet 28
A projectile problem (1)
Once you have the equipment set up so that the ball is following a consistent path,
dampen the ball and then trace over the path with a marker pen.
P (x,y)
x
(0,0)
Let the start of the path be the origin, (0,0).
Mark on the paper vertically lines at regular intervals and record the horizontal and
vertical displacements (x,y) of points on the path.
Roll the ball along the path recording the time to reach the points. This should be
repeated to ensure reliability and consistency.
X
y
t
Using the data, plot graphs of x against y, x against t and y against t.
Interpret your graphs
Find suitable functions, y=f(x), x=f(t) and y=f(t) which fit your data.
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Mechanics in Action
Worksheet 40
Cake Tin
Measure the height of the tin.
Measure the height at which the marble leaves the tin, a, and the distance from the
vertical diameter of the tin to the point where the marble lands on the table, d.
Calculate the angle that the marble has turned through before it leaves the tin.
Repeat the experiment a few times recording a and d each time. Use your value of a
to predict the value of d and compare this to the measured value.
a
d
Predicted d
Hints for a model
Where does the marble leave contact with the tin?
What is the condition for loss of contact?
Can you calculate the potential energy of the marble at the top of a tin of radius r
and the velocity of the marble as it leaves the tin by using conservation of energy?
Using Newton’s second law radially gives mg cos   N 
Conservation of energy gives
1 2
mv  mgr (1  cos  )
2
Further questions


Is the radius of the cake tin relevant?
Is the mass of the marble relevant?
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mv 2
r
Mechanics in Action
Worksheet 49
Bouncing ball (1)
Drop the ball from height h and record the rebound height H.
Record the rebound height for different values of h. You should take three readings
and find the median.
v2  u 2  2as so you can calculate the velocity before (u) and after (v) the bounce
using: u  19.6h and v  19.6H .
Verify the ‘law of restitution’ by calculating the coefficient of restitution using v  eu .
h
H1
H2
H3
Median
H
Try finding the value of e for different balls.
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u
Predicted
v
e
Mechanics in Action
Worksheet 52
Rebound
Roll the ball toward the wall at an angle θ and record the angle of rebound φ
Record the rebound angle for different values of θ.
The component of velocity parallel to the wall should remain unchanged; the
component perpendicular to the wall will be affected by the coefficient of restitution.
Verify the ‘law of restitution’ by calculating the coefficient of restitution using v  eu .
θ
φ
Predicted e
Try finding the value of e for different balls.
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