Additional Physics Topic 5 - Forces and Elasticity

Forces can change the shape of objects.  If we squash an object, we call it a compressive force.  If we stretch the object, we call it a tensile force.

 

Elastic objects bounce back to their original shape when the force is removed.  This is essential for the suspension of a car.  When the car goes over a bump in the road, the springs get squashed, then bounce back to their original shape.

You can see the spring (painted blue) behind the brake discs in the picture above.

 

Some people like to do bungee-jumping.  It's a adrenalin thrill that results from hurling oneself from a high bridge or a basket that is eighty or more metres above the ground.

 

Photo http://uneidee.asso.fr/, Wikimedia Commons

 

Question 1

What is the acceleration of the bungee-jumper as it leaves the platform?

Answer

 

The speed reached by the person jumping 80 metres is going to be about 40 m s-1, by the time the bungee cord is uncoiled.

 

Question 2

The Milau Bridge in France takes a motorway 300 metres above a valley.  If you were to do a bungee-jump from that bridge, what is the maximum speed you will reach, before the bungee cord uncoils?  Explain why you don't need to do a calculation.

Answer

 

When the bungee cord has uncoiled, it stretches, slowing the bungee-jumper.

 

Question 3

Use the ideas of forces you have learned in previous topic to explain what happens next to the bungee-jumper.

Answer

 

The bungee-jumper will continue to bounce up and down for several minutes.  Eventually the movement will stop, and, if nothing is done, the bungee-jumper will be left dangling in the air.  However the jumper is lowered gently to the ground.

 

An even bigger thrill is experienced when there are crocodiles in the river below...

 

Some fair-ground rides give the same kind of thrill, but on a lesser scale.  A baby-bouncer obeys exactly the same laws of physics.

 

 

And you paid 5 to go on an adult baby-bouncer?  At my age, I am not into adrenalin rushes...  Nor, I guess, the young woman who was doing a bungee-jump, and the cord broke, landing her in the river, in which there were crocodiles.  Fortunately she was not badly hurt, nor did she end up as dinner for the crocs.

 

 

When the bungee cord stretches, kinetic energy from the jumper is converted to elastic strain energy in the cord.  The cord stretches as it gains elastic strain energy. 

 

Question 4

The formula for kinetic energy is:

 

Kinetic energy (J) = 1/2 mass (kg) (speed (m/s))2

 

What is the kinetic energy of a 60 kg jumper who has reached a speed of 40 m s-1.

 

What happens to the energy?

Answer

 

 

Elastic Energy in a Spring

Before batteries were common, people used clockwork motors to:

These days clockwork motors are still used:

Picture by J D Pfaff, Wikimedia Commons

Clockwork motors are sometimes called spring-motor mechanisms.

 

Source not known

 

A spiral (helical) spring is coiled up tighter using a key or a handle.  When the key is released, the elastic energy is released to turn a number of cogs that spin.  In the wind-up radio above, the motor drives a small generator that charges up rechargeable batteries, which in turn are connected to the electronics in the radio.  This simple device allows the radio to be used anywhere where there is no mains electricity, and batteries are not easy to get hold of.

 

Question 5

Identify the energy chain from winding up the radio to the sound coming out of the radio.

Answer

 

The recoil starter mechanism for a lawnmower engine has a spiral spring that tightens up when you pull the cord.  The coiled up spring pulls the cord back.  If it breaks, the cord dangles uselessly out of the starter.  Or the cord breaks and the remaining cord disappears into the mechanism.  Either way, you have problems...

 

Don't be tempted to take a clockwork motor apart. The spring jumps out and completely uncoils.  It is a swine to get back.  I know; I have done it.

 

 

Hooke's Law

A rule that tells us about the behaviour of springs was first outlined by Robert Hooke (1635 - 1703) in the Seventeenth Century.  He was the same man who used primitive microscopes to study human fleas.  He was not a pleasant man - "spiteful", "vengeful", "jealous", "selfish", "anti-social", were a few of the adjectives used to describe him.

 

Hooke's Law for a spring states:

the extension of a spring is directly proportional to the force applied to it.

 

In Physics code:

F e

 

The equation is:

Force (N) = spring constant (N m-1) extension (m)

In Physics code:

F = ke

 

In triangle form:

 

 

If we plot a graph of force against extension, we get a straight line going through the origin.

 

Question 6

Explain why this graph shows that Force is directly proportional to the Extension.

Answer

 

The spring constant is the amount of force that will stretch a spring by an extension of 1 m.  It is the gradient of the graph above.  The area under the graph is the energy, but this is not on the syllabus for GCSE.  You will do this at AS level.

 

At AS level, you would normally be expected to use SI units, i.e. Newtons, metres, and Newtons per metre.  Although it is possible to use non-SI units, it is worth getting into the habit now.

 

Question 7

When a 500 g mass is placed on a spring, it stretches by 12 cm. 

 

What is its spring constant in N m-1

 

Answer

The force on the spring is always in Newtons.  You must convert using W = mg.