Matter CGP Topic 7
What is Hooke’s Law
Key Points
• An object obeys Hooke’s law if the load applied to it is directly
proportional to the extension i.e. if you double the load you
double the extension.
• The constant of proportionality ‘k’ is called the spring constant
and it tells us how much force is required to produce a 1 metre
extension of the object.
• The stiffer an object the more force is required to produce a 1
metre extension i.e. the higher the spring constant.
• The law only applies for the straight line portion of the graph
i.e. up to the limit of proportionality.
• Some books state that the law only applies up to the elastic limit but that is untrue.
F = kx
à where the applied force F equals a constant k times the displacement or change in length x.
Experiment to investigate the elastic potential energy stored in a spring:
Hang a spring off a clamp and measure the original length of the spring , and then the changes in length
when you add more weight to the spring in increasing 100g until you have a complete set of results.
Original length of spring = 2cm
Mass Average length of stretched spring Minus original length
100g 4.9cm 29mm
200g 9 cm 70 mm
300g 12.65 cm 106.5mm
400g 16.9 cm 149 mm
500g 20.1 cm 181 mm
600g 24.6 cm 226 mm
A thinner spring would require a smaller spring constant because it needs less force vice versa a thicker
spring
A graph plotted can be used to calculate the: Chart Title
- Elastic potential energy stored in a spring shown in 250
the area underneath the graph which equals the 200
work done 150
- The spring constant shown by the gradient of the
100
linear part of the graph
50
0
0 100 200 300 400 500 600 700
, Energy in a stretched spring
Work Done
W=F×D
Work done (J) = force (N) × distance in the direction of the force (m)
Work done in a stretched spring = energy stored in a spring
But force changing ∴ average force Nano (n) = x10-9
Micro (μ) = x10-6
Milli (m) = x10-3
Centi (c) = x10-2
Energy in a stretched spring equation: Kilo (k) = x103
Mega (M) = x106
# Giga (G) = x109
E = k × 𝑥$
$
$&
K=
'(
2E
𝑥=*
K
Extension = final length – original length
x = Lf - L o
Plastic deformation is the permanent change in length of an object.
Elastic deformation is when the object return to original length when the load is removed.
Essentially the same experiment with the spring, but with a rubber band:
• Energy beneath a force extension graph represents an energy transferred to the stretched object
• The energy transferred to the rubber band in loading is greater than the energy transferred from
the elastic band in unloading
• The difference in energy transferred is equal to the thermal energy transferred to the elastic band
Sam
ple
Qu
Why is there pressure in fluids? est
io n
Identify and explain where within the container the pressure is the greatest
Apply:
Pressure increases with depth
A 1m B
Mercury is heavier as it has greater density
Pressure increases with density
10cm 10cm
State: Mercury Water
Pressure in a fluid is due to the weight of fluid above a given point
Conclude:
Pressure will be greatest at the bottom of Container A as mercury is more dense and therefore there is
there greatest weight of fluid pressing downwards.
What is Hooke’s Law
Key Points
• An object obeys Hooke’s law if the load applied to it is directly
proportional to the extension i.e. if you double the load you
double the extension.
• The constant of proportionality ‘k’ is called the spring constant
and it tells us how much force is required to produce a 1 metre
extension of the object.
• The stiffer an object the more force is required to produce a 1
metre extension i.e. the higher the spring constant.
• The law only applies for the straight line portion of the graph
i.e. up to the limit of proportionality.
• Some books state that the law only applies up to the elastic limit but that is untrue.
F = kx
à where the applied force F equals a constant k times the displacement or change in length x.
Experiment to investigate the elastic potential energy stored in a spring:
Hang a spring off a clamp and measure the original length of the spring , and then the changes in length
when you add more weight to the spring in increasing 100g until you have a complete set of results.
Original length of spring = 2cm
Mass Average length of stretched spring Minus original length
100g 4.9cm 29mm
200g 9 cm 70 mm
300g 12.65 cm 106.5mm
400g 16.9 cm 149 mm
500g 20.1 cm 181 mm
600g 24.6 cm 226 mm
A thinner spring would require a smaller spring constant because it needs less force vice versa a thicker
spring
A graph plotted can be used to calculate the: Chart Title
- Elastic potential energy stored in a spring shown in 250
the area underneath the graph which equals the 200
work done 150
- The spring constant shown by the gradient of the
100
linear part of the graph
50
0
0 100 200 300 400 500 600 700
, Energy in a stretched spring
Work Done
W=F×D
Work done (J) = force (N) × distance in the direction of the force (m)
Work done in a stretched spring = energy stored in a spring
But force changing ∴ average force Nano (n) = x10-9
Micro (μ) = x10-6
Milli (m) = x10-3
Centi (c) = x10-2
Energy in a stretched spring equation: Kilo (k) = x103
Mega (M) = x106
# Giga (G) = x109
E = k × 𝑥$
$
$&
K=
'(
2E
𝑥=*
K
Extension = final length – original length
x = Lf - L o
Plastic deformation is the permanent change in length of an object.
Elastic deformation is when the object return to original length when the load is removed.
Essentially the same experiment with the spring, but with a rubber band:
• Energy beneath a force extension graph represents an energy transferred to the stretched object
• The energy transferred to the rubber band in loading is greater than the energy transferred from
the elastic band in unloading
• The difference in energy transferred is equal to the thermal energy transferred to the elastic band
Sam
ple
Qu
Why is there pressure in fluids? est
io n
Identify and explain where within the container the pressure is the greatest
Apply:
Pressure increases with depth
A 1m B
Mercury is heavier as it has greater density
Pressure increases with density
10cm 10cm
State: Mercury Water
Pressure in a fluid is due to the weight of fluid above a given point
Conclude:
Pressure will be greatest at the bottom of Container A as mercury is more dense and therefore there is
there greatest weight of fluid pressing downwards.
