Equilibrium of Forces (CIE AS Physics)

A uniform ladder rests against a vertical wall where there is negligible friction. The bottom of the ladder rests on rough ground where there is friction. The top of the ladder is at a height h above the ground and the foot of the ladder is at a distance 2a from the wall.

 The diagram shows the forces that act on the ladder.

Which equation is formed by taking moments?

An archer draws his bowstring back to position X. The bowstring and arrow are shown. The tension T in the string is also shown. Then he draws the bowstring back further to position Y.

The archer finds the resultant force on the arrow is greater when the arrow is released from position Y.

What is the increase in force?

The diagram shows two fixed pins, Y and Z. A length of elastic is stretched between Y and Z and around pin X, which is attached to a trolley.

X is at the centre of the elastic and the trolley is to be propelled in the direction P at right angles to YZ. The tension in the elastic is 4 N.

 What is the force accelerating the trolley in the direction P when the trolley is released?

The diagram shows a rope bridge that a student makes on an adventure training course. The student has a weight W.

Which formula gives the tension T in the rope?

A uniform beam is pivoted at P as shown. Weights of W and 2 W are attached to its ends. The beam is marked at x intervals. The weight of the beam is 10 W

At which point should a 2 W weight be attached to achieve equilibrium?

A uniform metre rule of mass 100 g is supported by a pivot and a string as shown in the diagram. The beam is marked at 2 x intervals. The string passes round a frictionless pulley and carries a mass of 20 g.

At which mark on the rule must a 50 g mass be suspended so that the rule balances?

A trailer of weight 30 kN is attached to a truck. The trailer is raised until it is held at 50˚ to the horizontal by a vertical force F as shown in the diagram.

The trailer is 2.7 m in length and the position of its centre of gravity G is a third of the length from the hinge at O.

What is the vertical force F applied to the end of the trailer?

Four beams of the same length each have three forces acting on them.

Which beam has both zero resultant force and zero resultant torque acting?

The diagram shows a child’s balancing game.

The wooden rod is uniform and all the rings are of equal mass. Two rings are hung on peg 14 and one on peg 2.

 On which hook must a fourth ring be hung in order to balance the rod?

An object, made from two equal masses joined by a light rod, falls with uniform speed through air. The rod remains horizontal.

 Which statement about this system is correct?

A man holds a 200 N load stationary in his hand. The combined weight of the forearm and hand is 25 N. The forearm is held horizontal, as shown

What is the vertical force F needed in the biceps?

A spindle is attached at one end to the centre of a lever of length 1.60 m and at its other end to the centre of a disc of radius 0.25 m. A string is wrapped round the disc, passes over a pulley and is attached to an 800 N weight.

What is the minimum force F, applied to each end of the lever, that could lift the weight?

A uniform beam of mass 1.2 kg is pivoted at P as shown. The beam has a length of 0.70 m and P is 0.40 m from one end. Loads of 5.0 kg and 7.0 kg are suspended 0.65 m and 0.35 m from the pivot as shown.

What torque must be applied to the beam in order to maintain it in equilibrium?

A rigid L-shaped lever arm is pivoted at point P.

Three forces act on the lever arm, as shown in the diagram.

 What is the magnitude of the resultant moment of these forces about point P?

A ladder is positioned on icy ground and is leant against a rough wall. At the instant of release, it begins to slide.

 Which diagram correctly shows the directions of the forces P, W and R acting on the ladder as it slides?