Calculating Spring Constant

When an athlete pulls a resistance band to position A, the band is stretched by 0.12 m.

The elastic potential energy stored in the band is 3.6 J.

When the athlete pulls the band further to position B, its elastic potential energy increases to 6.4 J.

Calculate the extension of the resistance band when it is at position B.

Assume the resistance band obeys Hooke’s law.

[5 marks]

• What stays the same for the elastic band?

  Spring constant (k) is how stretchy/ stiff an elastic object is.

  If it’s the same band, the k value will be the same in Positon A and Position B.

• Key values?

  • Spring constant = ?

  • Extension at A = 0.12m

  • Extension at B = ?

  • Elastic Energy at A = 3.6 J

  • Elastic Energy at B = 6.4 J

• Which formula?

  Elastic potential energy (E) = ½ x spring constant (k) x extension² (e²)

  E = ½ k e²

  Units:

  • E in J

  • k in N/m

  • e in m

Position A

• How do we find spring constant at A?

  k = E / 0.5e²

  k = 3.6 / (0.5 x 0.12²)

  k = 500 N/m

Position B

• New key values?

  • Spring constant = 500 N/m².

  • Extension at B = ?

  • Elastic Energy at B = 6.4 J

• How do we find extension at B?

  e² = E / 0.5k

  e = √ (E / 0.5k)

  e = √ (6.4 / 0.5 × 500)

  k = 0.16 m

Continue Revising Paper 2

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