A Level Homework and Answers: Springs Questions

(a) One reading from the graph e.g. 1.0 N causes 7 mm C1

Hence 5.0 (N) causes 35 ± 0.5 (mm) A1

(allow one mark for 35 ± 1 (mm)

(b) (i) Force on each spring is 2.5 (N) C1

extension = 17.5 (mm) allow 18 (mm) or reading from graph A1

[allow ecf from (a)]

(ii) strain energy = area under graph / ½ F ´ e C1

= 2 ´ 0.5 ´ 2.5 ´ 17.5 ´ 10–3

= 0.044 (J) A1

[allow ecf from (b)(i)]

(a) (i) F = kx / k is the gradient of the graph C1

k = 2.0 / 250 ´ 10–3 = 8.0 A1

Correct unit for value given in (a)(i)

i.e. 0.008 or 8 ´ 10–3 requires N mm–1.

Allow N m–1 / kg s–2 if no working in (a)(i).

Do not allow unit mark if incorrect physics in part (a)(i) B1

(ii) W = ½ (F ´ extension) / area under the graph C1

= ½ ´ 2.0 ´ 0.250

= 0.25 (J) A1

(b) (i) F = 8 ´ 0.15 = 1.2 (N) A1

(ii) Hooke’s law continues to be obeyed / graph continues as a straight

line / k is constant / elastic limit has not been reached B1

2. tangent in the correct place for downward velocity or implied
by values B1

value between 0.95 to 1.1(m s–1) A1

(ii) 1. X marked in a correct place (maximum or minimum on graph) M1

2. relates the extension / compression to F = kx to explain why the

force is a maximum or maximum extension gives max force or
maximum extension gives max acceleration A1

(a) The extension of a spring is directly proportional to the applied force M1
as long as the elastic limit is not exceeded) A1

(b)   (i)      Correct pair of values read from the graph
force constant = 12/0.080                                                                     C1
force constant = 150 (N m–1)                                                               A1

(ii) extension, x =