Practise analysing centres of gravity, moments, couples and torque with force diagrams, equilibrium calculations and stability from the weight’s line of action.
The cylinder in (a) is hung from the end A of a non-uniform bar AB , as shown in Fig. 3.1.
Fig. 3.1
The bar has length 50 cm and has weight 0.25 N . The centre of gravity of the bar is 20 cm from B. The bar is pivoted at P. The pivot is 12 cm from B.
An object X is hung from end B. The weight of X is adjusted until the bar is horizontal and in equilibrium.
Explain what is meant by centre of gravity.
A pendulum consists of a solid sphere suspended by a string from a fixed point P , as shown in Fig. 3.1.
Fig. 3.1 (not to scale)
The sphere swings from side to side. At one instant the sphere is at its lowest position X , where it has kinetic energy 0.86 J and momentum 0.72 Ns in a horizontal direction. A short time later the sphere is at position Y , where it is momentarily stationary at a maximum vertical height h above position X.
The string has a fixed length and negligible weight. Air resistance is also negligible.
For the sphere at position Y , calculate the moment of its weight about point P .
Nm
Two forces act on an object.
Which diagram represents a couple?
Option A shown in diagram
Option B shown in diagram
Option C shown in diagram
Option D shown in diagram