Equilibrium of Forces (CIE A Level Physics)

A bench consists of a plank which is resting in a horizontal position on two supports B and C. The plank is modelled as a uniform rod AD of length 2.7 m and mass 20 kg. The supports at B and C are 0.5 m from each end of the plank, as shown in Fig. 1.1. 

Fig. 1.1

Two animals sit on the plank. The rabbit has a mass of 2.5 kg and sits in the middle of the plank and the quail has a mass of 4.3 kg and sits at the end A. The plank remains horizontal and in equilibrium. The animals can be modelled as point masses. 

Calculate:

(2)

(2)

Whilst the quail stays at point A the rabbit now moves along the plank to point X. 

Given that the plank remains horizontal and in equilibrium, and that the magnitude of the normal reaction force at B is now twice the magnitude of the normal reaction force at C, calculate the distance BX.

A pole PR has a length 4 m and a weight W newton. The pole is held in a horizontal position in equilibrium by two vertical ropes attached to the pole at the points P and R where PR = 4 m, as shown in Fig. 1.2. 

Fig. 1.2

A load of weight 17 N is attached to the rod at R. The pole is uniform and the ropes are light inextensible strings. 

Given that the tension in the rope attached to the pole at Q is seven times the tension in the rope attached to the pole at P, calculate the value of W.

Q is now moved to a point further along the pole until the length QR is 0.8 m, as shown in Fig. 1.3. The pole still remains in equilibrium. The load of 17 N is now moved to a point x  metres from P. The beam remains in equilibrium in a horizontal position. 

Fig. 1.3

The rope at Q will break if its tension exceeds 202 N. The rope at P cannot break. 

Find the range of possible positions on the beam where the load can be attached without the rope at Q breaking.

A student investigates the principle of moments using the apparatus shown in Fig. 1.1.

Fig. 1.1

The scale on the forcemeter reads from 0 N to 10 N.

A 3.0 N weight is positioned so that it hangs straight downwards from the 70 cm mark on the ruler.

Describe what the student could do to ensure that the ruler is horizontal.

The student intends to investigate moments around the pivot.

The student positions the forcemeter at the 15 cm mark and uses it to hold the ruler horizontal.

He expects the reading on the forcemeter to be 14 N.

The actual reading is 10 N.

The teacher asks the student and his friend to move a table with some books on it. They carry the table as shown in Fig. 1.2.

Fig. 1.2

Use ideas about moments to explain why student A feels more force on their hands than student B.

A pole PR has a length 6.0 m and a weight W N. The pole is held in a horizontal position in equilibrium by two vertical ropes attached to the pole as shown in Fig. 1.1.

Fig. 1.1.

A load of weight 10 N is attached to the rod at R.

The tension in the rope attached at Q is six times as large as the tension in the rope attached at P. 

The pole is uniform and the ropes are light inextensible strings.

Calculate the value of W.

Q is now moved to a point further along the pole until the length QR is 0.8 m , as shown in Fig. 1.2.

Fig. 1.2

The pole remains in equilibrium. The load of 10 N is now moved to a point x metres from P.

The beam remains in equilibrium in a horizontal position.

The rope at Q will break if its tension exceeds 32 N. The rope at P cannot break.

Find the range of possible positions on the beam where the load can be attached without the rope at Q breaking.

State what is meant by the centre of gravity of an object.

A uniform plank of wood of mass 40 kg and length 5.0 m is used by a boy to help him cross a ditch.

In the ditch is a rock, which is used to support the plank horizontally 1.1 m from one end, as shown in Fig. 1.1. The other end of the plank is supported by the bank. 

Fig. 1.1

Calculate the vertical supporting force from the rock when the plank is placed in position as shown in Fig 1.1.

The boy begins to walk across the plank. The position of the boy is shown in Fig. 1.2.

Fig. 1.2

On Fig. 1.2, draw arrows to show the forces acting on the plank when the boy has crossed some of the plank. 

The boy has a mass of 50 kg.

Determine whether the boy can walk to the far end of the plank without it tipping. Support your answer with a calculation.

It is said that Archimedes used huge levers to sink Roman ships invading the city of Syracuse.

A possible system is shown in  Fig. 1.1 where a rope is hooked onto the front of the ship and the lever is pulled by several men. 

Fig. 1.1

Calculate the mass of the ship if its weight is 4.6 × 10⁴ N. Give your answer to an appropriate number of significant figures.

Calculate the moment of the ship’s weight about point P. State an appropriate unit for your answer.

Calculate the minimum vertical force T required to start raising the front of the ship. Assume the ship pivots about point P.

Calculate the minimum force F that must be exerted to start to raise the front of the ship.