DESIGNING A BETTER BUMPER: USING IMPULSE TO TURN A LEVEL PHYSICS STUDENTS INTO ENGINEERS

A Level Physics students are often confident with the equation:

Impulse = change in momentum

J = Δp = mv − mu

They may also know that:

Impulse = force × time

J = FΔt

However, knowing an equation is not the same as understanding how it can be used.

A much more interesting question is:

Can students use their knowledge of impulse to design a bumper that reduces the force of a collision?

Using a PASCO trolley, a solid wall and a selection of simple materials, students can move beyond calculations and become experimental engineers. They can design bumpers, test them at different speeds, collect evidence and discover why a bumper that becomes crushed may actually be working perfectly.

FROM EQUATIONS TO ENGINEERING

Imagine a trolley travelling towards a wall.

When it strikes the wall, its velocity rapidly falls to zero. Its momentum therefore changes.

Momentum = mass × velocity

p = mv

The impulse acting on the trolley is equal to this change in momentum.

If the trolley has a mass of 0.5 kg and approaches the wall at 1.2 m/s, its initial momentum is:

p = 0.5 × 1.2

p = 0.6 kg m/s

If it comes to rest, its final momentum is zero. The magnitude of the change in momentum is therefore 0.6 kg m/s.

That change in momentum must happen during the collision. The crucial question is how long the collision lasts.

Average force = change in momentum ÷ collision time

F = Δp ÷ Δt

If the trolley stops in 0.01 seconds, the average force is:

F = 0.6 ÷ 0.01

F = 60 N

If a bumper increases the stopping time to 0.05 seconds, the average force becomes:

F = 0.6 ÷ 0.05

F = 12 N

The momentum change is the same, but the force is much smaller because the collision happens over a longer period.

This is the central principle behind crumple zones, airbags, cycle helmets, protective packaging, crash barriers and many sports safety systems.

THE DESIGN CHALLENGE

Students can be given a simple engineering brief:

Design a bumper that reduces the maximum force experienced by a PASCO trolley when it collides with a wall.

The bumper must:

• fit onto the front of the trolley;

• be made from a limited amount of material;

• allow the trolley to travel normally;

• reduce the peak collision force;

• work at more than one impact velocity;

• be tested using reliable experimental evidence.

Suitable materials might include paper, card, drinking straws, plasticine, masking tape, elastic bands, thin foam and corrugated cardboard.

However, even paper and plasticine alone can produce a surprisingly wide range of designs.

PAPER BUMPERS: SHAPE MATTERS

A flat sheet of paper placed on the front of a trolley is unlikely to provide much protection. It bends easily but may not create enough controlled resistance to slow the trolley gradually.

The same paper becomes much more useful when its shape is changed.

Students could try:

• a concertina or accordion fold;

• a paper cylinder;

• several small paper tubes;

• a triangular prism;

• a folded box structure;

• a honeycomb arrangement;

• layers of curved paper arches.

A concertina bumper may compress progressively as the trolley hits the wall. Instead of stopping almost instantly, the trolley is slowed while the folds collapse.

Paper tubes may work differently. A tube is relatively strong when a force acts along its length, but it can suddenly buckle when the force becomes too great. This buckling absorbs energy and increases the stopping distance.

Students quickly discover that “just using paper” is not a limitation. Engineering often depends less on the material itself and more on how that material is shaped.

PLASTICINE BUMPERS: HARD, SOFT OR STREAMLINED?

Plasticine provides another interesting design problem.

Students might initially assume that adding a large lump of plasticine to the front of the trolley will create the best bumper. It is soft, so it ought to absorb the collision.

But the results may be more complicated.

A thick, compact block of plasticine may deform only slightly. It could add mass to the trolley without increasing the collision time very much. The extra mass may actually increase the trolley’s momentum at a given velocity.

A long plasticine cone may produce a different result. The narrow end can begin deforming first, followed by the wider sections. This can create a more gradual deceleration.

Students could compare:

• a flat plasticine slab;

• a rounded dome;

• a long cone;

• several small plasticine columns;

• a hollow plasticine shell;

• a layered design combining plasticine and folded paper.

The best design may not be the softest or the largest. It may be the structure that deforms in the most controlled way.

SETTING UP A FAIR TEST

For the investigation to be meaningful, students must control the important variables.

The mass of the trolley should remain constant unless mass is the variable being investigated. If one bumper uses much more material than another, the extra mass should be measured and considered.

The wall and track should remain in the same position.

The trolley should strike the wall straight on. An angled impact could cause rotation and make the results difficult to compare.

Each bumper should be tested at the same set of initial velocities.

For example:

0.4 m/s

0.6 m/s

0.8 m/s

1.0 m/s

The trolley’s velocity should be measured immediately before impact rather than assumed from how strongly it was pushed.

Each test should also be repeated. A single result is not enough, especially when paper folds and plasticine shapes may change after each collision.

MEASURING WHETHER THE BUMPER WORKS

There are several possible measurements students can use.

The most direct measurement is the peak force during the collision. A force sensor or instrumented PASCO trolley can produce a force-time graph.

Students can compare:

• maximum force;

• average force;

• duration of the collision;

• area under the force-time graph;

• amount of rebound;

• permanent deformation of the bumper.

The area under a force-time graph represents the impulse.

This gives students an important opportunity to connect graphical analysis with the equation:

Impulse = FΔt

For a changing force, the force is not constant throughout the collision. The area beneath the graph gives the total impulse more accurately than simply multiplying the maximum force by the collision time.

THE PEAK FORCE IS NOT THE WHOLE STORY

Students may focus immediately on finding the design with the smallest maximum force.

That is important, but a good investigation should consider more than one measurement.

A bumper that produces a very low peak force may allow the trolley to travel a long distance before stopping. In a real vehicle, there is only a limited amount of space available for a crumple zone.

Another bumper may reduce the peak force but cause the trolley to bounce backwards.

This introduces a deeper point about momentum.

If the trolley simply stops, its momentum changes from mv to zero.

If it rebounds, its velocity changes direction. Its final momentum is now in the opposite direction.

For example, a 0.5 kg trolley travelling at +1.0 m/s has an initial momentum of:

p = 0.5 kg m/s

If it rebounds at −0.4 m/s, its final momentum is:

p = −0.2 kg m/s

The change in momentum is:

Δp = −0.2 − 0.5

Δp = −0.7 kg m/s

The magnitude of the momentum change is 0.7 kg m/s, which is greater than if the trolley had simply stopped.

A successful bumper may therefore need to increase the collision time while also reducing rebound.

WHEN A CRUSHED BUMPER IS A SUCCESS

One of the most valuable lessons in this investigation is that visible damage does not necessarily mean the design has failed.

Students often judge a bumper by how well it survives.

If a paper bumper remains perfectly shaped after a collision, they may regard it as successful. If another bumper is crushed, folded or torn, they may call it a failure.

In engineering, the opposite may be true.

A bumper is supposed to deform if that deformation absorbs energy and protects the object behind it.

The front of a car is designed to crumple during a serious collision. A cycle helmet may crack. Protective packaging may become permanently compressed. These components sacrifice themselves to reduce the forces acting on people or valuable equipment.

The important question is not:

“Did the bumper survive?”

It is:

“What happened to the trolley during the collision?”

USING DIFFERENT IMPACT VELOCITIES

Testing at different velocities makes the investigation much more revealing.

Momentum is proportional to velocity:

p = mv

Kinetic energy, however, is proportional to the square of velocity:

Ek = ½mv²

This means that doubling the velocity doubles the momentum but increases the kinetic energy by a factor of four.

A bumper that performs well at 0.4 m/s may collapse completely at 0.8 m/s. Another design may be too rigid at low speed but become effective during a faster impact.

Students can plot graphs such as:

Peak force against impact velocity

Collision time against impact velocity

Impulse against impact velocity

Stopping distance against impact velocity

They could also investigate whether the peak force is directly proportional to velocity or whether the relationship changes as the bumper begins to buckle or collapse.

IMPROVING THE FIRST DESIGN

The first bumper is unlikely to be the best one.

That is part of the value of the activity.

Students should be encouraged to follow a design cycle:

Plan

Predict

Build

Test

Analyse

Modify

Retest

A paper concertina might initially fold sideways rather than compressing evenly. Students could add guides or change the width of the folds.

A plasticine cone might bend rather than compress. Its base could be widened, or it could be supported by a paper tube.

A paper cylinder might be too strong to deform at low velocity. Students could cut small slots into it to encourage controlled buckling.

This is how genuine engineering develops. Designs are not simply declared good or bad. Evidence is used to identify weaknesses and guide improvements.

PRACTICAL QUESTIONS FOR STUDENTS

Students might investigate questions such as:

Which paper shape produces the longest collision time?

Does a longer bumper always reduce the peak force?

How does bumper mass affect the result?

Does the best design change as impact velocity increases?

Is a plasticine cone more effective than a flat slab?

Can paper and plasticine be combined to create a better bumper?

Does a reusable elastic bumper work better than a single-use crumple bumper?

How much does each design reduce rebound?

Which design gives the best balance between force reduction, size, mass and durability?

These questions allow the activity to develop into a full practical investigation rather than a simple demonstration.

PERSONAL REFLECTION: THE MOMENT THE EQUATION BECOMES REAL

I often find that students can quote the definition of impulse long before they have developed a real feeling for what it means.

They know that increasing the time reduces the force, but the statement can remain rather abstract.

The trolley experiment changes that.

Students can see a narrow, high force peak when the trolley strikes a hard wall. They can then add a folded paper structure and watch the peak become lower and wider.

The equation is no longer just something written on a formula sheet. It has become a visible event.

One of the most productive moments comes when a carefully made bumper is crushed during the test. The student may initially be disappointed, but the force graph shows that the design has significantly reduced the peak force.

The apparently damaged bumper has done exactly what it was designed to do.

That creates a much deeper understanding than completing another page of calculations.

WHAT THIS TEACHES BEYOND IMPULSE

Although the investigation begins with impulse, it develops many wider scientific skills.

Students must decide what they mean by “best”.

They must identify independent, dependent and control variables.

They must distinguish between accuracy, precision, reliability and validity.

They must repeat readings and deal with anomalous results.

They must use graphs to identify patterns.

They must recognise that engineering involves compromises.

A very effective bumper might be too large. A reusable bumper might not reduce the force as much as a disposable crumple zone. A very soft bumper might work at low speeds but fail at higher speeds.

There may be no single perfect answer.

That is not a weakness in the experiment. It is what makes it realistic.

FROM THE PHYSICS LABORATORY TO THE REAL WORLD

The same principles can be seen in many familiar situations.

Airbags increase the time over which a passenger’s momentum changes.

Crumple zones deform and absorb energy.

Crash barriers bend rather than bringing vehicles to an immediate stop.

Gymnasium mats increase stopping time when someone falls.

Catching a ball by moving the hands backwards reduces the force on the hands.

A tennis player follows through with the racket, changing the momentum of the ball over a longer contact time.

Protective packaging uses paper, cardboard, foam or air pockets to extend the duration of an impact.

The trolley experiment provides a small-scale model of these much larger engineering systems.

CONCLUSION: PHYSICS IS SOMETHING STUDENTS CAN USE

Impulse is sometimes taught as little more than two equations:

J = Δp

J = FΔt

But these equations describe decisions that can prevent injuries, protect equipment and save lives.

When A Level Physics students design bumpers for a PASCO trolley, they are doing more than verifying a formula. They are applying physics to a problem, collecting evidence, improving a design and learning that failure can be useful.

A folded piece of paper or a carefully shaped piece of plasticine may look simple, but it can reveal some sophisticated physics.

The real achievement is not producing a bumper that looks impressive.

It is producing a design that can be shown, through reliable evidence, to control a collision more effectively.

That is when students stop merely learning physics and begin using it.