Moments
You must draw a
diagram for each question with forces and distances from pivot (fulcrum) added.
(g = 9.81 Nkg-1)
62 A metre rule is pivoted at its mid-point. A 0.60 N weight
is suspended from one end. How far from the other end must a 1.00 N weight be
suspended for the rule to balance? 3.5N
63 A metre rule is pivoted at its mid-point and a 50 g mass
suspended from the 20cm mark. What mass balances the rule when suspended from
the 65 cm mark? 100g
64 A lever of negligible weight is 2 m long. If a 0.80 N weight at one end balances a 0.20 N weight at the other end, how far is the fulcrum from the 0.80 N weight? 40cm
65 A metre rule is pivoted at its mid-point. A 1.0 N weight is suspended from the 30cm mark and a 2.0 N weight from the 90cm mark. Where must an upward force of 3.0 N be applied to balance the rule? 70cm
66 A uniform lever 150 cm long is pivoted at its mid-point. A 50 g mass is suspended from the left-hand end and an 80 g mass from the right- hand end. A string tied 50 cm to the right of the fulcrum passes upwards over a pulley so that the string is at 30° to the lever. What mass must be suspended from the string for the lever to balance? 90g
67 With the help of a diagram explain how you would find the weight of a metre rule using only a fulcrum and a weight which can be suspended from the rule.
64 A lever of negligible weight is 2 m long. If a 0.80 N weight at one end balances a 0.20 N weight at the other end, how far is the fulcrum from the 0.80 N weight? 40cm
65 A metre rule is pivoted at its mid-point. A 1.0 N weight is suspended from the 30cm mark and a 2.0 N weight from the 90cm mark. Where must an upward force of 3.0 N be applied to balance the rule? 70cm
66 A uniform lever 150 cm long is pivoted at its mid-point. A 50 g mass is suspended from the left-hand end and an 80 g mass from the right- hand end. A string tied 50 cm to the right of the fulcrum passes upwards over a pulley so that the string is at 30° to the lever. What mass must be suspended from the string for the lever to balance? 90g
67 With the help of a diagram explain how you would find the weight of a metre rule using only a fulcrum and a weight which can be suspended from the rule.
68 A uniform rod AB, 2 m long, weighs 0.40 N. If weights of
0.80 N and 0.40 N are suspended from A and B respectively, at what point will
it balance? 75cm from A
69 A uniform metre rule weighs 1.20 N. Weights of 0.10 N, 0.50 N, 1.00 N and 0.20 N are suspended respectively from the 10 cm, 20 cm, 60cm and 80cm marks. At which mark will the rule balance? 49cm mark
70 A non uniform rugby post 6 m long lies flat on the ground. When the narrow end only is lifted off the ground, the force needed is 140 N. When the thick end only is lifted the force needed is 280 N. Deduce the weight of the post and the distance of the centre of gravity from the thick end. 420N 2m
71 A uniform bridge AB, 30 m long and weighing 200 000 N, rests on supports at each end. Find the forces on the supports when a car of weight 10000 N is 4 m from A and a lorry of weight 100 000 N is 10 m from B. 142 kN 168 kN
72 A scaffold plank AB, 5m long, weighs 200N and its centre of gravity is 2 m from A. It rests on two bars, one 0.5 m from A, the other 0.6 m from B. Find the weight of the heaviest person who can walk from end to end without tilting the plank. 600N
73 A metre rule is suspended from two balances calibrated in Newtons. One balance is attached at the 5 cm mark, the other at the 80cm mark. If the rule weighs 1 N and downward forces of 2 N are applied at the 10cm and 60cm marks, find the readings on the balances. 2.8N 2.2N
69 A uniform metre rule weighs 1.20 N. Weights of 0.10 N, 0.50 N, 1.00 N and 0.20 N are suspended respectively from the 10 cm, 20 cm, 60cm and 80cm marks. At which mark will the rule balance? 49cm mark
70 A non uniform rugby post 6 m long lies flat on the ground. When the narrow end only is lifted off the ground, the force needed is 140 N. When the thick end only is lifted the force needed is 280 N. Deduce the weight of the post and the distance of the centre of gravity from the thick end. 420N 2m
71 A uniform bridge AB, 30 m long and weighing 200 000 N, rests on supports at each end. Find the forces on the supports when a car of weight 10000 N is 4 m from A and a lorry of weight 100 000 N is 10 m from B. 142 kN 168 kN
72 A scaffold plank AB, 5m long, weighs 200N and its centre of gravity is 2 m from A. It rests on two bars, one 0.5 m from A, the other 0.6 m from B. Find the weight of the heaviest person who can walk from end to end without tilting the plank. 600N
73 A metre rule is suspended from two balances calibrated in Newtons. One balance is attached at the 5 cm mark, the other at the 80cm mark. If the rule weighs 1 N and downward forces of 2 N are applied at the 10cm and 60cm marks, find the readings on the balances. 2.8N 2.2N
74 A metre rule is pivoted freely at its mid-point. Equal,
opposite and parallel vertical forces are applied at each end. If the direction
of these forces ALWAYS remains vertical, what will happen? Draw sketches to
clarify your explanation.
75 A tapered rod of mass 200 g is 160 cm long. It balances at its midpoint when a 150 g mass hangs from the narrow end. How far is the centre of gravity from the thick end? 20cm
76 A metal tube of length 30 cm and weight 0.45 N is fitted with a wooden handle 10 cm long and weight 0.30 N. How far is the centre of gravity from the middle of the handle? 12cm
75 A tapered rod of mass 200 g is 160 cm long. It balances at its midpoint when a 150 g mass hangs from the narrow end. How far is the centre of gravity from the thick end? 20cm
76 A metal tube of length 30 cm and weight 0.45 N is fitted with a wooden handle 10 cm long and weight 0.30 N. How far is the centre of gravity from the middle of the handle? 12cm
