Answers · Stretching springs

Stretching springs — final check key

Check meaning, not exact wording. These are teaching points, not official Cambridge marks.

1. SK1 · Final check

Model answer. (a) Take the zero reading, 15.0 cm, off each reading: the extensions are 2.8, 5.6, 8.4 and 11.2 cm. (b) Yes. Each 100 g adds the same 2.8 cm, so double the load gives double the extension, and no load gives no extension. (c) A straight line through the origin, with the load up the side and the extension along the bottom. (d) The key ring’s extension is 18.5 cm − 15.0 cm = 3.5 cm. That is 3.5 ÷ 2.8 = 1.25 times the extension for 100 g, so the key ring weighs as much as 125 g: 0.125 kg × 9.8 N/kg ≈ 1.2 N. (e) The loads stretch the spring: it gets longer, a change of size, and its coils move further apart, a change of shape.

A full answer includes

(a) I took 15.0 cm off every reading.
(a) I wrote 2.8, 5.6, 8.4 and 11.2 cm.
(b) I wrote yes.
(b) I gave the reason: each 100 g adds the same 2.8 cm.
(b) I gave the reason: no load gives no extension.
(c) I wrote a straight line.
(c) I wrote that it goes through the origin.
(d) Method: extension = 18.5 cm − 15.0 cm = 3.5 cm.
(d) Method: 3.5 cm ÷ 2.8 cm = 1.25, so the key ring weighs as much as 125 g.
(d) Method: weight = 0.125 kg × 9.8 N/kg.
(d) Answer: about 1.2 N.
(e) I wrote that the spring gets longer: its size changes.
(e) I wrote that its coils move further apart: its shape changes.
I did not use 18.5 cm as the extension in (d).

Also accept

(a) 2.8, 5.6, 8.4 and 11.2 cm; (b) yes, each 100 g adds 2.8 cm and no load gives no extension; (c) a straight line through the origin; (d) about 1.2 N; (e) longer, with its coils further apart.

Watch for

“(a) The extensions are the readings, 17.8, 20.6, 23.4 and 26.2 cm.” — Those are the readings. The extension is the reading minus the zero reading, 15.0 cm.
“(d) 18.5 cm gives 18.5 ÷ 2.8 × 0.98 N ≈ 6.5 N.” — 18.5 cm is the reading. Take away the zero reading first: the extension is 3.5 cm, which gives about 1.2 N.
“(b) No: the readings are not proportional to the load.” — The question is about the extensions. Take off the 15.0 cm zero reading: each 100 g adds the same 2.8 cm.

2. SK2 · Final check

Model answer. (a) Yes. For the first four rows each 1.2 N adds 2.0 cm, so double the load gives double the extension, and zero load gives zero extension. (b) On the straight part, 1.2 N gives 2.0 cm = 0.020 m, so k = 1.2 N ÷ 0.020 m = 60 N/m. (c) From 3.6 N to 4.8 N the extension rises by 2.7 cm, and from 4.8 N to 6.0 N by 3.7 cm. The extension stops being proportional after 3.6 N, so the limit of proportionality is about 3.6 N: it lies between 3.6 N, the last row on the line, and 4.8 N, the first row off it. (d) 5.0 cm is less than 6.0 cm, so it is on the straight part. F = k × x = 60 N/m × 0.050 m = 3.0 N. (e) The 6.0 N row is beyond the limit of proportionality, where the extension is bigger than proportion gives, so it makes k too small. The spring constant comes from the straight part only: k = 60 N/m.

A full answer includes

(a) I wrote yes.
(a) I gave the reason: each 1.2 N adds the same 2.0 cm.
(a) I gave the reason: zero load gives zero extension.
(b) Method: on the straight part, 1.2 N gives 2.0 cm = 0.020 m.
(b) Method: k = 1.2 N ÷ 0.020 m.
(b) Answer: 60 N/m.
(c) I wrote about 3.6 N, or between 3.6 N and 4.8 N.
(c) I gave the reason: beyond 3.6 N, each 1.2 N adds more than 2.0 cm.
(d) I checked that 5.0 cm is on the straight part.
(d) Method: F = k × x = 60 N/m × 0.050 m.
(d) Answer: 3.0 N.
(e) I wrote that 6.0 N is beyond the limit of proportionality.
(e) I wrote that k must come from the straight part only: 60 N/m.
I did not use the 6.0 N row for k.

Also accept

(a) yes, each 1.2 N adds 2.0 cm; (b) 60 N/m; (c) about 3.6 N (between 3.6 N and 4.8 N); (d) 3.0 N; (e) 6.0 N is beyond the limit, so k = 60 N/m from the straight part.

Watch for

“(b) k = 1.2 ÷ 2.0 = 0.6 N/m.” — 0.6 is in N/cm, because the extension was in centimetres. With the extension in metres, 1.2 N ÷ 0.020 m = 60 N/m.
“(c) The limit is 6.0 N, the biggest load.” — The limit is where the extension stops being proportional to the load, after 3.6 N.
“(d) F = 60 × 5.0 = 300 N.” — The spring constant is in N/m, so the extension must be in metres: 5.0 cm = 0.050 m.