Can you save a falling object?

by David Price

Life in the land of cartoons

 

Donald Duck

Donald Duck Image (Public Domain)

If you’ve ever seen a cartoon you’ll know this law of cartoon science:

The time required for an object to fall twenty stories is greater than or equal to the time it takes for whoever knocked it off the ledge to spiral down twenty flights to attempt to capture it unbroken

Or more simply:

Fragile (or expensive) things fall slow enough for you to run downstairs to catch them…just in time

Acceleration

To find out whether this could happen in real life, we need to think about a bit of science called acceleration.  To most people this word means speeding up, with its opposite, deceleration, meaning slowing down.  However scientists think of acceleration as the rate of change of speed over time. So, how quickly is something getting faster or slower.

Speeding cars

If two cars set off from standing, and accelerate to reach a speed of 60mph, the one that reaches 60mph in 3 seconds is accelerating at a greater rate than the one that takes 6 seconds.

There are cars, though, that can go a lot faster than 60mph.  ‘Bloodhound SuperSonic Car‘ is being designed and built in the UK and is aiming to be the faster car in the world- reaching over 1000mph in an amazing 42 seconds!

 

Catching the vase

Let’s say the four-storey block of flats where my mum lives is 80m high, and I accidentally knock her prize flower vase off her balcony, oops!  Can I run down the stairs and catch it in the nick of time?

Gravity is going to exert a force on the vase and pull it down, so it starts to accelerate until it reaches a speed of falling of 10 meters per second for every second it falls.  This rate of acceleration doesn’t continue indefinitely though.  When the vase reaches what’s known as terminal velocity (an apt name in these circumstances!) it can accelerate no faster, as other forces (such as air resistance) will prevent this.

To work out how long it takes the vase to hit the ground you need to know speed of the vase against time.  The gradient of the plot will be the acceleration due to gravity (about 10m/s2).  The area under the graph is the distance travelled.  Measure the area under the graph until you get up to 80m.  This should happen when the vase has been falling for 4 seconds.

 

Speed-time graph of vase falling under gravity.  After 4 seconds it has travelled 80m and will hit the ground

Speed-time graph of vase falling under gravity. After 4 seconds it has travelled 80m and will hit the ground. Image: science made simple (CC-BY-NC)

I would need to run down about 125 meters of stairs to catch the vase at the bottom, and I’d need to run faster than the vase was falling.  To catch my mum’s vase I’d need to run at around 40 meters per second or 94 miles an hour!  No way is this going to happen, except in cartoon-land!

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Curriculum Links

Key Stage 3:

Physics (Motion and Forces)

Describing motion

  • speed and the quantitative relationship between average speed, distance and time (speed = distance ÷ time)

Forces and motion

  • forces being needed to cause objects to stop or start moving, or to change their speed or direction of motion (qualitative only)

 

Mathematics

Ratio, proportion and rates of change

  • solve problems involving direct and inverse proportion, including graphical and algebraic representations

Statistics

  • describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

 

 

Key Stage 4:

This science made simple blogpost aims to enrich and give context to:

AQA GCSE PHYSICS Unit 2
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Posted in Physics