Investigating Forces

Activities to try

1. 1

   Hooke's Law practical with real apparatus

   Why it works: Force is measured in newtons; extension (not total length) is the quantity that responds to force; controlling variables and repeating readings is what makes the relationship trustworthy.

   1. Clamp a spring, measure and record its natural (unstretched) length first.
   2. State the variables before starting: independent = force applied (added in equal steps), dependent = extension, control = the same spring throughout.
   3. Add weight one equal step at a time (hang slotted masses and convert to weight using W = m × g, or read force directly in newtons from a newton meter), letting the spring settle each time.
   4. Measure the new length at each load and read the ruler squarely — line your eye level with the mark, or use a set square against the ruler to avoid parallax error.
   5. Calculate extension at each step: extension = current length − natural length.
2. 2

   Plotting force vs extension and drawing a line of best fit

   Why it works: A best-fit line averages real measurement scatter rather than connecting individual points; the force–extension relationship is proportional only up to a limit of proportionality, after which it bends (and, at still greater loads beyond the elastic limit, the spring may deform permanently).

   1. Plot Force (newtons) on the y-axis against Extension on the x-axis using your recorded data.
   2. Draw a single straight line of best fit through the scattered points — do NOT join the dots point-to-point; aim for a line with roughly equal numbers of points on each side.
   3. Describe the pattern in words: up to the limit of proportionality, equal steps of force add the SAME extension each time (not 'the length doubles'), and with zero extension at zero force this means extension is directly proportional to force — a straight line through the origin.
   4. Continue adding load in a second investigation (or extend the dataset) until the once-straight line starts to bend, and mark that point where proportionality ends — the limit of proportionality.
   5. Separately, note that if the spring is loaded past its elastic limit (which for many springs is at or only a little beyond the limit of proportionality) it may be permanently stretched and no longer return to its natural length; this is a distinct idea from the limit of proportionality.
3. 3

   Testing Newton's Second Law with a trolley

   Why it works: A measured applied force on a known total moving mass (trolley plus any hanging masses) predicts an acceleration via a = F/m when friction is small; more precisely, it is the resultant force (applied force minus friction) that determines acceleration — a change in motion, not an instant speed or direction. Because real friction makes the resultant smaller than the applied force, the observed acceleration is usually a little below F/m, and comparing prediction with real motion tests Newton's Second Law.

   1. Apply a measured force to a trolley of known mass (include a risk assessment for any hanging masses).
   2. State the trolley's starting condition (e.g. starting from rest) before describing how its motion changes.
   3. Calculate the predicted acceleration using a = F / m, where F is the applied (driving) force and m is the total mass being accelerated (the trolley plus any hanging masses that move with it), assuming friction is small.
   4. Measure the trolley's actual acceleration (e.g. with light gates or a motion sensor/data logger) and compare it with the calculated acceleration.
   5. Discuss sources of difference (e.g. friction opposing the applied force, measurement error) between prediction and observation.