Moments, Equilibrium and Centre of Gravity: Physics 0625 (Cambridge O Level / IGCSE)

A technician tightens a bolt using a spanner. She applies a force of $25\text{ N}$ to the end of the spanner handle, and this force acts at a perpendicular distance of $40\text{ cm}$ from the bolt (the pivot). What is the moment of the force about the bolt?

A seesaw in a playground is pivoted at its centre and is balanced horizontally.

(a) State the principle of moments for an object in equilibrium. [1]

(b) A child of weight $300\text{ N}$ sits on one side of the seesaw, at a perpendicular distance of $1.5\text{ m}$ from the pivot. Calculate the moment of this child's weight about the pivot. [2]

(c) A second child sits on the other side of the seesaw, at a perpendicular distance of $1.8\text{ m}$ from the pivot, so that the seesaw is exactly balanced. Use the principle of moments to calculate the weight of the second child. [2]

(d) Explain why the weight of the seesaw itself does not need to be included when applying the principle of moments in this situation. [2]

A student investigates the centre of gravity and stability of everyday objects.

(a) State what is meant by the centre of gravity of an object. [1]

(b) The student has a flat, irregularly shaped piece of card. Describe an experiment, using a plumb line, that the student could use to find the position of the card's centre of gravity. [3]

(c) A cargo ship can be loaded so that most of its cargo is stacked low down inside the hull, or so that most of the cargo is stacked high up on the deck. Explain, in terms of centre of gravity, why loading the cargo low down makes the ship more stable. [3]

A uniform wooden plank of weight $200\text{ N}$ and length $4.0\text{ m}$ rests horizontally on two trestles (supports), one at each end of the plank, labelled A and B. A person of weight $600\text{ N}$ stands on the plank at a point $1.0\text{ m}$ from support A (and therefore $3.0\text{ m}$ from support B). The plank is in equilibrium.

(a) State the two conditions that must both be true for the plank (with the person standing on it) to be in equilibrium. [2]

(b) By taking moments about support A, calculate the moment of the plank's weight and the moment of the person's weight about A, and hence calculate the support force at B. [3]

(c) Using the condition for the resultant force on the plank, calculate the support force at A. [2]

(d) The person then walks further along the plank, away from A. State and explain what happens to the support force at B as she does this. [2]

A wooden plank rests horizontally across two supports and stays completely at rest. Which pair of conditions must both be satisfied for the plank to be in equilibrium?

A uniform metre rule is pivoted at its $50\text{ cm}$ mark so that it can turn freely. A force of $6.0\text{ N}$ pulls vertically downward on the rule at the $20\text{ cm}$ mark. A second force of $9.0\text{ N}$ pulls vertically downward on the rule at the $70\text{ cm}$ mark, on the opposite side of the pivot. What happens to the rule?

A builder uses a straight, rigid steel bar as a lever to prise up the edge of a heavy paving slab. The bar rests across a small wooden block, which acts as the pivot (fulcrum). The builder pushes down on one end of the bar with a force of $80\text{ N}$, at a perpendicular distance of $1.2\text{ m}$ from the pivot. This is just enough to lift the edge of the slab, which pushes back up on the other end of the bar with a force of $960\text{ N}$.

(a) Calculate the moment of the builder's $80\text{ N}$ force about the pivot. [2]

(b) The bar is in equilibrium at the instant the slab just begins to lift. Use the principle of moments to calculate the perpendicular distance, $d$, between the pivot and the point where the slab's $960\text{ N}$ force acts on the bar. [3]

(c) Explain, in terms of perpendicular distances from the pivot, why the builder is able to lift the heavy slab using a downward force very much smaller than the slab's own resistance force. [2]

A furniture designer is comparing two possible designs for a free-standing wooden bookcase. Both designs have the same total mass and the same overall height. Design 1 has a narrow rectangular base, with most of its mass in the upper shelves. Design 2 has a wider rectangular base, with heavy storage drawers built into the very bottom of the unit.

(a) State two features of an object's design, other than its total mass, that affect how easily it topples over. [2]

(b) Explain, in terms of the position of the centre of gravity and the width of the base, why Design 2 is less likely to topple over than Design 1. [3]

(c) The bookcase is gradually tilted to one side, for example because it is standing on a slightly uneven floor. Describe, in terms of the centre of gravity and the base of the bookcase, the condition at which it would just begin to topple over rather than settle back down. [2]

A non-uniform steel girder, of weight $480\text{ N}$ and length $6.0\text{ m}$, is used as a footbridge across a narrow stream. It rests horizontally on two concrete piers, P and Q, one at each end of the girder. Because the girder is not uniform, its centre of gravity is not at its midpoint. It lies $2.0\text{ m}$ from P. A worker of weight $720\text{ N}$ stands on the girder at a point $4.0\text{ m}$ from P. The girder is in equilibrium.

(a) State one reason why it is useful to take moments about P when finding the support force at Q. [1]

(b) By taking moments about P, calculate the support force at Q, $R_Q$. [3]

(c) Hence use the condition for the resultant force on the girder to calculate the support force at P, $R_P$. [2]

(d) Show that your answers to (b) and (c) are also consistent with the resultant moment about Q being zero. [3]

A rigid bar rests on a single pivot and is in equilibrium under three forces that act perpendicular to the bar. A downward force of $40\text{ N}$ acts $0.50\text{ m}$ to the left of the pivot; a downward force of $20\text{ N}$ acts $0.30\text{ m}$ to the left of the pivot, on the same side as the first force; and a single downward force $F$ acts $0.80\text{ m}$ to the right of the pivot. What is the value of $F$?