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Springs, stretching and Hooke's law
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Forces can stretch, squash or bend objects. Springs obey a simple rule up to a point.
Elastic and inelastic
More than one force is needed to change the shape of an object.
Elastic distortion: the object returns to its original shape when the forces are removed.
Inelastic (plastic) distortion: it stays permanently changed.
Elastic distortion: the object returns to its original shape when the forces are removed.
Inelastic (plastic) distortion: it stays permanently changed.
Hooke's law
F = k × x: force (N) = spring constant (N/m) × extension (m).
Extension is directly proportional to force up to the limit of proportionality. Beyond this the force-extension graph curves.
Extension is directly proportional to force up to the limit of proportionality. Beyond this the force-extension graph curves.
Energy stored
A stretched spring stores energy in its elastic potential energy store.
E = ½ × k × x2 (as long as the limit of proportionality is not passed).
The energy is also the area under the force-extension graph.
E = ½ × k × x2 (as long as the limit of proportionality is not passed).
The energy is also the area under the force-extension graph.
A spring with k = 40 N/m is stretched by 0.15 m. Find the force.
- F = k × x
- F = 40 × 0.15
Answer: 6 N
F = kx up to the limit of proportionality. E = ½kx2. Elastic objects return to shape; inelastic ones do not.
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