Answers · Moments and balance
Moments and balance — final check key
Check meaning, not exact wording. These are teaching points, not official Cambridge marks.
1. MK1 · Final check
Model answer. (a) A moment is the turning effect of a force about a pivot. It equals the force × the perpendicular distance from the pivot to its line of action. (b) 25 N × 0.40 m = 10 N m. (c) The 8.0 N weight’s moment is 8.0 N × 0.25 m = 2.0 N m, so 5.0 N × d = 2.0 N m and d = 0.40 m. (d) There is no resultant force and no resultant moment. (e) The anticlockwise moments are now 2.0 N m + 2.0 N × 0.50 m = 3.0 N m. The clockwise moments are 5.0 N × 0.40 m + 4.0 N × d = 2.0 N m + 4.0 N × d. Setting them equal, 4.0 N × d = 1.0 N m, so d = 0.25 m. (f) Balance a metre rule on its own on a knife-edge pivot. Hang masses on loops of thread on both sides, and slide one until the rule rests level. Measure each distance from the pivot to a thread, work out weight × distance for each mass, and show that the clockwise moments add up to the same as the anticlockwise moments. Repeat with other masses and positions.
A full answer includes
- (a) The moment of a force is its turning effect about a pivot: force × perpendicular distance from the pivot.
- (b) 25 N × 0.40 m = 10 N m.
- (c) 8.0 N × 0.25 m = 2.0 N m = 5.0 N × d, so d = 0.40 m.
- (d) No resultant force and no resultant moment.
- (e) Anticlockwise: 2.0 + 2.0 × 0.50 = 3.0 N m. Clockwise: 5.0 × 0.40 + 4.0 × d = 2.0 + 4.0 × d = 3.0, so d = 0.25 m.
- (f) Balance a metre rule on a pivot; hang weights on both sides and adjust one until the rule is level; measure each distance from the pivot; show that the sum of weight × distance is the same clockwise and anticlockwise; repeat.
Also accept
- (a) turning effect = force × perpendicular distance from the pivot; (b) 10 N m; (c) 0.40 m; (d) no resultant force and no resultant moment; (e) 0.25 m; (f) balance a rule, hang masses, level it, measure distances, compare the sums of moments, repeat.
Watch for
- “(e) 0.75 m, from 3.0 ÷ 4.0.” — The 5.0 N weight is still on the right and gives 2.0 N m of the clockwise total. The 4.0 N weight provides only the extra 1.0 N m.
- “(b) 1000 N cm is the same as 1000 N m.” — Use metres: 0.40 m gives 10 N m.
2. MK2 · Final check
Model answer. (a) The centre of gravity is the point through which the whole weight of an object seems to act. (b) The 0.90 N weight is 35 − 5 = 30 cm = 0.30 m from the pivot: its moment is 0.90 N × 0.30 m = 0.27 N m. The rule’s weight acts at the 50 cm mark, 0.15 m from the pivot: W × 0.15 m = 0.27 N m, so W = 1.8 N. (c) Make three holes near the edge of the lamina, well apart. Hang it from a pin through one hole so that it swings freely, and hang a plumb line from the same pin. When the lamina and the thread are still, draw a line on the lamina along the thread. Repeat from the second hole. The centre of gravity is where the two lines cross; the line from the third hole should pass through the same point. (d) The short, wide vase is more stable. Its centre of gravity is lower and its base is wider, so it can be tipped further before the vertical line from its centre of gravity passes outside its base and its weight turns it over.
A full answer includes
- (a) The point through which the whole weight of an object seems to act.
- (b) 0.90 N × 0.30 m = 0.27 N m = W × 0.15 m, so W = 1.8 N.
- (c) Holes near the edge; hang from a pin so it swings freely; plumb line; when still, draw the line; repeat from a second hole; the lines cross at the centre of gravity; check with a third hole.
- (d) The short, wide vase: its centre of gravity is lower and its base wider, so it can be tipped further before the vertical line from its centre of gravity passes outside its base.
Also accept
- (a) where the whole weight seems to act; (b) 1.8 N; (c) plumb line from two holes, crossing point, third hole as a check; (d) the short, wide vase: lower centre of gravity, wider base.
Watch for
- “(b) Measure the rule’s distance from the pivot to the end of the rule.” — The rule’s weight acts at its centre of gravity, the 50 cm mark, 0.15 m from the pivot.
- “(d) They are equally stable, because they weigh the same.” — Stability depends on how high the centre of gravity is and how wide the base is, not on the weight.