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Hooke's Law (AQA GCSE Physics: Combined Science)
Revision Note
Hooke's Law
What is Hookes' Law?
- The relationship between the extension of an elastic object and the applied force is defined by Hooke's Law
- Hooke's Law states that:
The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality
- Directly proportional means that as the force is increased, the extension increases
- If the force is doubled, then the extension will double
- If the force is halved, then the extension will also halve
- The limit of proportionality is the point beyond which the relationship between force and extension is no longer directly proportional
- This limit varies according to the material
Hooke's Law states that a force applied to a spring will cause it to extend by an amount proportional to the force, this can be tested by this Hooke's Law experiment
Using Hooke's Law
Hooke's Law Equation
- Hooke's Law is defined by the equation:
F = k × e
- Where:
- F = force in newtons (N)
- k = spring constant in newtons per metres (N/m)
- e = extension in metres (m)
- The symbol e can represent either the extension or compression of an elastic object
- The spring constant represents how stiff a spring is
- The higher the spring constant, the higher the stiffness
- The extension of an object can be calculated by:
final length – original length
- The extension of the spring can be measured by marking the position of bottom of the unstretched spring
- When the spring is stretched the final length must be measured from the bottom of the spring
Force, extension and spring constant are used to define Hooke's Law
- The Hooke's Law equation can be rearranged with the help of the following equation triangle:
Worked example
The figure below shows the forces acting on a child who is balancing on a pogo stick.The child and pogo stick are not moving.The spring constant of the spring on the pogo stick is 4900 N/m. The weight of the child causes the spring to compress elastically from a length of 40 cm to a new length of 33 cm.Calculate the weight of the child.
Step 1: List the known quantities
- Spring constant, k = 4900 N/m
- Original length = 40 cm
- Final length = 33 cm
Step 2: Write the relevant equation
F = ke
Step 3: Calculate the extension, e
e = final length – original length = 40 – 33 = 7 cm
Step 4: Convert any units
- Since the spring constant is given in N/m, e must be in metres (m)
7 cm = 0.07 m
Step 5: Substitute the values into the Hooke's Law equation
F = 4900 × 0.07 = 343 N
Examiner Tip
Look out for unit conversions! Unless the spring constant is given in N/cm, make sure the extension is converted into metres (÷ 100) before substituting values into the Hooke's Law equation
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