1. Help
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
1

2. Help
Since 10 years I am a co-lecturer for mechanics for our
Industrial Design students and I have lectured dynamics for
our students "Technische Bestuurskunde" for 3 years. I
knew their level, in my view, I was going slow through their
material, and it worked. So compared to those students the
course "Physics" for our math students would be be a piece
cake.
I was so wrong!
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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3. Why is Physics difficult for our math
students?
Because:
1. Their VWO -level for physics is low(er than expected) ?
2. Doing mathematics in a physical environment is something else (it
starts with physical insight, it is calculus, and it is about the basics
of vectors)?
3. It is a long way from Newton to the solution of a medium physics
exercise, because Newton is so general?
4. Interpretations for "common" subjects in physics and mathematics
are sometimes different or vague?
5. If you start with a problem "exactness" can be a handicap in some
sense?
6. It takes (a lot of) time to find a right attitude for understanding the
concepts of physics?
7. The time span of a quarter is too short to acquire insight in physics.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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4. The course CM and SR:
Some characteristics of the course "Mechanics and Special
Relativity" for first year students mathematics in quarter 3 :
◮ Each week 2 x 2-hours (theory-) lecture and 2 x 2 hour "instruction"
for working on exercises,
◮ Teacher for the lectures: Dr. Timon Idema (assistant professor, TU
Delft,nano-physics, and founder of a theoretical biophysics group at
the Department of Bionanoscience at TU Delft (2012),
Instructor: Emiel van Elderen (Diam - Lecturer),
◮ "Mechanics and Special Relativity" is one of the 3 optional subjects
offered to our students during the third quarter of the first year. The
number of participants at the start was ± 28. (The other optional
subjects were Electromagnetism, and some course in the field of
computer science, Algoritm and Data structures )
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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5. Contents and Grading:
The course consists of 2 parts, Classical Mechanics (CM)
and Special Relativity (SR), each 4 weeks.
◮ Book: J.R. Forshaw and A.G. Smith, Dynamics and Relativity.
◮ Topics (CM):
The 3 laws of Newton; some Force laws: Hook, Gravitation,...etc.;
Free Body diagram; composing (differential) equations of motion for
point masses; Rigid (flat) bodies, Conservation Laws for
momentum, mechanical energy and angular momentum and some
examples of collisions.
◮ Topics (SR): Postulates of Einstein, Time dilatation, Galilei- and
Lorentz transformation, four vectors, Minkowski-time space, the
famous formula E = mc2
and some attention for collisions (fission
and fusion).
◮ Grading: 5% for answering (feedback fruit electronic -)questions
during the lectures, 30% midterm exam (only CM), 65% final exam
( CM and SR)
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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6. My first observations 1:
◮ A very good and enthusiastic teacher, some of his quote’s and
lecture style:
◮ Like learning math, or playing the piano, learning
physics takes practice,...
◮ Now if you do not understand, no worries, thats what
we are for...
◮ With feedback fruits the students are very actively
involved during the his lectures...
◮ The main reason for the students choice for "Mechanics and
Special Relativity" is the special relativity part they want to know
finally what it is about!
◮ During the lectures there were experiments (mostly Classical
Mechanical) to illustrate the theory, which the students appreciated
very much.
◮ About the instructions, some of the students could make a start
with the given exercises, most of them couldn’t, not even after
explaining the beginnings.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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7. My first observations 2:
◮ A third of the students lost their motivation during first weeks.
◮ During week 5 (during and because of the midterm exams) the
number of attendants of the lectures and instructions dropped to 5,
while Timon just made a start with special relativity.
◮ At the beginning of the second part of the course the number of
students dropped to 16 to 18 students at most.
◮ Of these students, 14 have got a sufficient grade for the course
(first time).
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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8. Example 1:
Their VWO -level for physics is lower... Doing mathematics in a physics environment is something else...: .
A person throws a ball with a given speed v towards a wall of height h.
Which of the following quantities is the maximum distance the person
can stand from a wall and still able to throw the ball over the wall?
a.
gh2
v2
b.
v2
g
c.
v4
g2h
d.
v2h
g
e.
v2
g
1 −
2gh
v2
f.
v2
g
1 +
2gh
v2
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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9. Example 1:
a.
gh2
v2
b.
v2
g
c.
v4
g2h
d.
v2h
g
e.
v2
g
1 −
2gh
v2
f.
v2
g
1 +
2gh
v2
◮ Starting level: They know the basic physical quantities Length, Time .... and
their unities.
◮ They could answer "what is the dimension of mvt ?" (one of the first
questions of the workshop)
◮ They found that all dimensions of the expressions above are Length so a lot
of them did not know how to go further?
◮ My tip: make a sketch of the situation and try to make qualitative
estimations, it is this crucial aspect of physics which takes a lot of time to
learn.
◮ Another tip: what is the maximum distance in your problem without a wall?
For lot of students this was a "mission impossible", for explaining this I
needed to return to the basics of V.W.O.-physics.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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10. Example 2 statics:
It takes (a lot of) time to find right attitude for understanding the concepts of physics. In general it is a long way
from Newton to the solution of a medium physics exercise:
Keeping a book up and leaning sticks:
Find the extreme values for θ in case of equilibrium!
◮ Starting level: They have seen Newton F = ma and some examples.
◮ Their problem is how to start. "Where" are the forces? (How to Find a Free
Body Diagram?)
◮ Another problem: How to handle a parametric solution. What are your
parameters and what are your variables?
◮ Recognizing a optimization problem.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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11. Example 3 dynamics:
It takes (a lot of) time to find right attitude for understanding the concepts of physics. In general it is a long way
from Newton to the solution of a medium physics exercise
Coupled motion, dragging a board, a collision on ice :
The same holds for
A
B
Find acceleration!
and
How much work?
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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12. Example 4: 2D- collision:
Doing mathematics in a physics environment is something else (At a first year level) it is calculus and basics
of vectors)
A 2D-problem: a moving puck and a stick on an ice-floor
D
v0
massamiddelpunt
stick
b
massamiddelpunt
stick
massamiddelpunt
stick + puck
a) b)
What is happening after the collision?
The last exercise is a 2D-problem . The student has knowledge of linear
algebra and thus about vectors. This was not enough to understand what
is happening here. We need dL
dt
= τ and geometrical interpretations (for
the cross product) in this context of L = r × mv and τ = r × F.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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13. Example 5 oscillations :
Doing mathematics in a physics environment is something else (At a first year level) it is calculus...
If you start with a problem "exactness" can be a handicap in some sense
A small ball with a mass of 50.0 g moves on the end of a
spring with spring constant 25.0 N/m. The ball is released
with an amplitude of 0.300 m. A damping force F = −bv
acts on egg. After it oscillates for 5.00 s, the amplitude of
the motion has decreased to 0.100 m. Calculate the
magnitude of the damping coefficient b.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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14. Example 5 oscillations :
A small ball with a mass of 50.0 g moves on the end of a spring with spring constant 25.0 N/m. The ball is
released with an amplitude of 0.300 m. A damping force F = −bv acts on egg. After it oscillates for 5.00 s,
the amplitude of the motion has decreased to 0.100 m. Calculate the magnitude of the damping coefficient b.
Remarks:
◮ The ambiguity: what is the meaning of the amplitude?
◮ Do we start solving the problem from Newton F = ma to the second order
DE and solving this with calculus which is for the students no routine at this
moment, or do we start with something like ebt cos(at + δ)
◮ Frequently it is in physics common to make reasonable estimations (sloppy)
if the calculations are tedious. Mathematicians don’t like that.
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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15. A slide about vectors :
Interpretations for "common" subjects in physics and mathematics are sometimes different or vague?
• Position 4-vector: x = (ct, x, y, z) = (x0, x1, x2, x3).
• Velocity 4-vector: v = γ(v) dx/dt = γ(v) (c, v1, v2, v3).
• Momentum 4-vector: p = mv = m γ(v) dx/dt = (p0, p1, p2, p3).
• Expand: γ(v) = 1/(1 − v2 / c2)½ = 1 + ½(v/c)2 + ⅜(v/c)4 + …
• p1 = mv1, p2 = mv2, p3 = mv3 + correction terms.
• cp0 = mc γ(v) dx0/dt = mc2 γ(v) = mc2 + ½mv2 + …
MOMENTUM
kinetic
energy
rest
energy
= Etot
owever, the combination
(∆s)2 = (c∆t)2 − (∆x)2 − (∆y)2 − (∆z)2
invariant. After showing this slide, what do students think that a vector is? What is the connection to L.A.?
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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16. Something about The Axioms of Newton :
If you start with a problem "exactness" can be a handicap in some sense?
The first and the second Law of Newton:
◮ In an inertial reference frame, an object either remains at rest or
continues to move at a constant velocity, unless acted upon by a
force.
◮ In an inertial reference frame, the vector sum of the forces F on an
object is equal to the mass m of that object multiplied by the
acceleration a of the object: F = ma. (It is assumed here that the
mass m is constant.)
Remark: One of the questions of the exam was: What are the 3 laws of
Newton?
In the view of a Mathematician there are lot of things to do: What is a
inertial frame? and is the first one not a consequence of the second?
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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17. Save me:
1. It takes (a lot) of time for finding a right attitude for
understanding the concepts of physics?
The time slot of one quarter of a year is too short, a half
year with a midterm exam will be better.
2. Doing mathematics in a physics environment is
something else (it is calculus and the basics of
vectors)?
More experience with calculus and its interpretations is
needed.
3. 14 students had passed the exam. Within Diam we
also have a Double Bachelor program (a mathematics -
physics combination), are they in the nearby future the
only ones who can deal with physics (and modelling?).
4. Give me a helping hand...
Why is Physics difficult for our math students? Emiel van Elderen TUDelft June 22, 2017
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