4. Static Equilibrium

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Worksheet # 4AS-level Physics 9702

Static Equilibrium

By: Umair Qureshi

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Worksheet#4 By: Umair Qureshi ASPhysics 9702

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6. Fig. 3.1 shows an arrangement used to demonstrate the principle of moments.

A uniform beam is supported on the edges of two triangular shaped wooden blocks placed on two weighing scales. The weight of the beam is 17.5 N and the distance between the wooden blocks is 800 mm. A metal object of weight 26.5 N is placed 200 mm from one of the blocks. The blocks exert upward forces A and B on the beam. (i) Calculate the force B by taking moments about wooden block 1. (ii) State the sum of the two forces A and B and explain your answer. (iii) Describe what happens to the forces A and B as the metal object is moved gradually to the centre of the beam.

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8. The diagram below shows the position of a person’s jawbones. The lower jawbone pivots at one end. The muscle that makes it move is called the masseter muscle.

During biting, the lower jawbone can be represented by the simplified model shown below. It has a horizontal part 7.0 cm in length and a part at a 50o angle from the horizontal, which is 4.0 cm long. The force from the masseter muscle is vertical at the junction of the two parts. The weight of the lower jawbone is negligible.

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During biting, there is a 55 N force on the incisors at the front of the lower jawbone.(a) Calculate the magnitude of(i) M, the force applied by the masseter muscle;(ii) F, the force at the pivot.(b) Explain why more force can be provided at the molars, during chewing, than at the incisors.9. The diagram below shows the arm of a person holding a ball in the palm of his/her hand with the forearm horizontal. The weight of the forearm is 25 N and the weight of the ball is 8.0 N.

The diagram below is a representation of the forearm showing relevant distances. B is the point where the bicep muscles are attached to the forearm.

(a) On the diagram above draw labelled arrows to represent all the forces acting on the forearm when the ball is held in the hand. (One force, namely the weight, has already been drawn for you).(b) Calculate the force that the biceps muscle exerts on the forearm.

10. A uniform, rigid rod of weight W is hinged at point P on a vertical wall. The rod is kept horizontal by means of a rope as shown in the diagram below.

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The pull of the string T on the rod and the weight W of the rod are shown on the diagram.(a) Draw an arrow on the diagram to show the direction of the reaction force N at the hinge.(b) Given that T = W = 20.0 N, determine the horizontal force that the hinge exerts on the rod.11. When a person lifts a suitcase, the spine experiences large extra forces. In a simplified model of the situation, the spine can be treated as a rigid rod.

In this model, when the suitcase is lifted, three extra forces act on the spine which need to be in equilibrium.! The additional force due to lifting the suitcase, S.! The additional force from the muscles, F.! The additional force on the base of the spine, R.The diagram below shows the directions and points of action of S and F, but not R.

(a) State the two conditions for S, F, and R to be in equilibrium.(b) Add an arrow to the diagram to show the approximate direction of R, the additional force on the base of the spine.

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(c) Write down an expression for the torque about the base of the spine due to the force S.(d) Show that the force F is approximately nine times the force S, i.e. the muscle force is nine times the weight of the suitcase being lifted.

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Questions from CIE past papers13. (a) Explain what is meant by the centre of gravity of an object.(b) A non-uniform plank of wood XY is 2.50m long and weighs 950N. Force-meters (spring balances) A and B are attached to the plank at a distance of 0.40m from each end, as illustrated in Fig. 3.1.

When the plank is horizontal, force-meter A records 570N.(i) Calculate the reading on force-meter B.(ii) On Fig. 3.1, mark a likely position for the centre of gravity of the plank.

(iii) Determine the distance of the centre of gravity from the end X of the plank. (june 2002)14. The diagram shows four forces applied to a circular object.Which of the following describes the resultant force and resultant torque on the object?

(june 2003)

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15. A spanner is used to tighten a nut as shown.

A force F is applied at right-angles to the spanner at a distance of 0.25m from the centre of the nut. When the nut is fully tightened, the applied force is 200N.What is the resistive torque, in an anticlockwise direction, preventing further tightening?A 8Nm B 25Nm C 50Nm D 800Nm (Nov 2003)16. Two parallel forces, each of magnitude F, act on a body as shown.

What is the magnitude of the torque on the body produced by these forces?A Fd B Fs C 2Fd D 2Fs (NOV 2003)17. A uniform beam of weight 50N is 3.0m long and is supported on a pivot situated 1.0m from one end. When a load of weight W is hung from that end, the beam is in equilibrium, as shown in the diagram.

What is the value of W ? A 25 N B 50N C 75N D 100N (june 2004)

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18. Two forces, each of magnitude F, form a couple acting on the edge of a disc of radius r, as shown in Fig.5.1.

(a) The disc is made to complete n revolutions about an axis through its centre, normal to the plane of the disc. Write down an expression

for(i) the distance moved by a point on the circumference of the disc,(ii) the work done by one of the two forces.(b) Using your answer to (a), show that the work W done by a couple producing a torque T when it turns through n revolutions is given byW = 2nT.

(june 2004)

19. An L-shaped rigid 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 30 Nm B 35Nm C 50Nm D 90Nm (june 2005)

20. A force F is applied to a beam at a distance d from a pivot. The force acts at an angle θ to a line perpendicular to the beam.

Which combination will cause the largest turning effect about the pivot?

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21. A rigid uniform bar of length 2.4 m is pivoted horizontally at its mid-point.

Weights are hung from two points of the bar as shown in the diagram. To maintain horizontal equilibrium, a couple is applied to the bar. What is the torque and direction of this couple? A 40 Nm clockwise B 40 Nm anticlockwise C 80 Nm clockwise D 80 Nm anticlockwise (june 2006)22. A rod AB is hinged to a wall at A. The rod is held horizontally by means of a cord BD, attached to the rod at end B and to the wall at D, as shown in Fig.2.1.

The rod has weight W and the centre of gravity of the rod is at C. The rod is held in equilibrium by a force T in the cord and a force F produced at the hinge.(a) Explain what is meant by(i) the centre of gravity of a body,(ii) the equilibrium of a body.(b) The line of action of the weight W of the rod passes through the cord at point P.Explain why, for the rod to be in equilibrium, the force F produced at the hinge must also pass through point P.(c) The forces F and T make angles a and ß respectively with the rod and AC = AB, as shown in Fig.2.1.Write down equations, in terms of F, W, T, a and ß, to represent

(i) the resolution of forces horizontally,(ii) the resolution of forces vertically,

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(iii)the taking of moments about A. (june 2006)23. A rigid circular disc of radius r has its centre at X. A number of forces of equal magnitude F act at the edge of the disc. All the forces are in the plane of the disc. Which arrangement of forces provides a moment of magnitude 2Fr about X?

(nov 2006)

24. Two 8.0 N forces act at each end of a beam of length 0.60m. The forces are parallel and act in opposite directions. The angle between the forces and the beam is 60 ° .

What is the torque of the couple exerted on the beam? A 2.4 Nm B 4.2Nm C 4.8Nm D 9.6Nm (june 2007)25. The diagram shows a plan view of a door which requires a moment of 12 Nm to open it.

What is the minimum force that must be applied at the door’s midpoint to ensure it opens? A 4.8 N B 9.6N C 15N D 30N (nov 2007)26. 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 which act on the ladder.

Which equation is formed by taking moments?

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A W a + Fh = 2W a B F a + W a = Fh C W a + 2W a = Fh D W a – 2W a = 2Fh

(june2008)

27. One type of weighing machine, known as a steelyard, is illustrated in Fig. 3.1.

The two sliding weights can be moved independently along the rod. With no load on the hook and the sliding weights at the zero mark on the metal rod, the metal rod is horizontal. The hook is 4.8 cm from the pivot. A sack of flour is suspended from the hook. In order to return the metal rod to the horizontal position,

the 12 N sliding weight is moved 84 cm along the rod and the 2.5 N weight is moved 72 cm.

(i) Calculate the weight of the sack of flour.

(ii) Suggest why this steelyard would be imprecise when weighing objects with a weight of about 25 N. (Nov 2008)28. A spindle is attached at one end to the centre of a lever 1.20 m long and at its other end to the centre of a disc of radius 0.20 m. A cord is wrapped round the disc, passes over a pulley and is attached to a 900 N weight.

What is the minimum force F, applied to each end of the lever, that could lift the weight?A 75 N B 150N C 300N D 950N

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29. A torque wrench is a type of spanner for tightening a nut and bolt to a particular torque, as illustrated in Fig. 3.1.

The wrench is put on the nut and a force is applied to the handle. A scale indicates the torque applied. The wheel nuts on a particular car must be tightened to a torque of 130 N m. This is achieved by applying a force F to the wrench at a distance of 45 cm from its centre of rotation C. This force F may be applied at any angle θ to the axis of the handle, as shown in Fig. 3.1. For the minimum value of F to achieve this torque, (i) state the magnitude of the angle θ that should be used, (ii) calculate the magnitude of F.

(june 2009)30. The diagram shows two pulley wheels connected by a belt.

Wheel Q is driven by a motor and rotates clockwise at a constant rate. Wheel Q puts tension in the top portion of the belt, which in turn drives the wheel P. The lower portion of the belt is slack and has no tension. The weight of the belt and frictional forces are negligible. The diameter of P is 150 mm. The diameter of Q is 100

mm. The torque applied to Q is 3.0Nm. What is the tension in the belt and the torque on wheel P?

(Nov 2009)

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ANSWERS1. (b) 7.5N2. (i) 49.05N, (iii) 87N3. (b) (iii) 15.3N4. (ii) 190N5. (2) 2.16kN6. (i), 15.4N, (ii) 44N7. (i)(3) 286N8. (a) (i) 150N, (ii) 95N9. (b) 153N10. (b) 20N13. (b) (ii) near A than B (iii) 1.08m14. D15. C16. B17. B19. A20. B21. A23. B24. B25. C26. A27. (i) 247.5N28. B29. (ii) 290N30. D

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4. Static Equilibrium