Answers · Stretching springs

Stretching springs — return questions key

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

1. SR1 · Return

Model answer. (a) A force can change the size and the shape of an object: it can stretch it, squash it, bend it or twist it. (b) Each 0.5 N adds 1.7 cm: 1.7, 3.4, 6.8 and 8.5 cm are 1, 2, 4 and 5 steps of 1.7 cm. The 1.5 N reading, 5.9 cm, does not fit. 1.5 N is 3 steps of 0.5 N, so its extension should have been 3 × 1.7 cm = 5.1 cm: it was probably misread. (c) Draw one ruled straight best-fit line through the origin and the points that fit. Leave the anomalous point off the line, and do not join the points dot to dot. (d) If your eye is above or below the pointer, the pointer seems to sit against a different mark on the rule. This parallax error is avoided by looking straight across, with your eye level with the pointer.

A full answer includes

(a) I wrote its size.
(a) I wrote its shape.
(b) I found that the other readings go up by 1.7 cm for each 0.5 N.
(b) I identified the 1.5 N reading, 5.9 cm, as anomalous.
(b) Method: 1.5 N is 3 steps of 0.5 N, so 3 × 1.7 cm.
(b) Answer: 5.1 cm.
(c) I wrote a ruled straight line.
(c) I wrote that it goes through the origin.
(c) I wrote that the line leaves out the anomalous point.
(c) I did not join the points dot to dot.
(d) I wrote that from above or below, the pointer seems to sit against a different mark.
(d) I named this parallax.
I did not pick the 2.0 N reading, which fits 4 × 1.7 cm = 6.8 cm.

Also accept

(a) size and shape; (b) 1.5 N, 5.9 cm, anomalous: it should be 5.1 cm; (c) a ruled straight line through the origin that leaves out the anomalous point, not dot to dot; (d) to avoid parallax.

Watch for

“(b) The 2.0 N reading is anomalous, because it is only 0.9 cm more than the one before.” — Check each reading against 1.7 cm for every 0.5 N. 2.0 N should give 4 × 1.7 cm = 6.8 cm, and it does. It is the 1.5 N reading, 5.9 cm, that is too big.
“(c) Join the points dot to dot, so the line goes through every reading.” — A ruled best-fit line shows the pattern the readings share. Joining dot to dot would put a kink at the anomalous point.
“(c) Draw the line through the anomalous point as well.” — An anomalous reading does not fit the pattern of the others, so the best-fit line leaves it out.

2. SR2 · Return

Model answer. (a) The spring constant is the force per unit extension: k = F / x. (b) 6.4 cm = 0.064 m, so F = k × x = 75 N/m × 0.064 m = 4.8 N. (c) The gradient of the straight part is load ÷ extension, which is the spring constant: a steeper line means a stiffer spring. (d) The limit of proportionality is the point beyond which the extension is no longer proportional to the load. On the graph, it is where the straight line ends. (e) 3.5 N is 7 steps of 0.5 N, so if the extension were still proportional it would be 7 × 1.3 cm = 9.1 cm. It is 9.9 cm, more than that, so 3.5 N is beyond the limit of proportionality.

A full answer includes

(a) I wrote the force per unit extension.
(a) I wrote k = F / x.
(b) Method: x = 6.4 cm = 0.064 m.
(b) Method: F = k × x = 75 N/m × 0.064 m.
(b) Answer: 4.8 N.
(c) I wrote the spring constant, k.
(c) I wrote that this holds on the straight part of the line.
(d) I wrote the point beyond which the extension is no longer proportional to the load.
(e) Method: if it were proportional, 3.5 N would give 7 × 1.3 cm = 9.1 cm.
(e) I wrote yes: 9.9 cm is more than 9.1 cm, so 3.5 N is beyond the limit.
I did not write that the limit of proportionality is the biggest load the spring can hold.

Also accept

(a) force per unit extension, k = F / x; (b) 4.8 N; (c) the spring constant; (d) where the extension stops being proportional to the load; (e) yes: 9.9 cm is more than the 9.1 cm that proportion gives.

Watch for

“(b) 75 × 6.4 = 480 N.” — The spring constant is in N/m, so the extension must be in metres: 6.4 cm = 0.064 m, and 75 N/m × 0.064 m = 4.8 N.
“(d) The largest load the spring can take.” — The spring still stretches beyond the limit. It is where the extension stops being proportional to the load.
“(e) No: the spring still holds 3.5 N, so it has not passed the limit.” — Passing the limit does not mean the spring fails. It means the extension is bigger than proportion predicts, as 9.9 cm is.