Queensland Physics

QUEENSLAND PHYSICS

CHAPTER 7BUILDING IT UP
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QUESTIONS7.3Structural stability

1.A body-builder lifts a 5 kg dumbbell while doing a biceps curl at the gym. What torque is developed if the distance between his hand and his elbow is 35 cm?

2.A particular nut securing a beam to a pillar requires a torque of 150Nm to loosen it. What is the minimum force that you will need to apply to the handle of a 30 cm long spanner if you are to loosen the nut?

3.A force of 30 N is applied to the edge of a wheel that has a radius of 45 cm. If the resulting torque produced in the wheel is 5Nm, at what angle was the force applied to the radius?

4.A labourer wishes to use a 3 m steel pole as a lever to lift a 20 kg rock. If he places a pivot 50 cm from the end of the pole that is wedged under the rock, what will be the minimum force that he will need to exert downwards on the pole to lift the rock?

5.The adventurer Tasmania Jones stands 1.5 m from the end of a narrow bridge made from a 4 m long wooden plank. If the plank has a weight of 2000 N and Tasmania has a mass of 80 kg, what is the normal force acting on the end of the plank closest to him?

6.A painter places a 3 m plank on top of two trestles as shown in the figure below.

The plank has a mass of 40 kg. If the painter, who has a mass of 50kg, stands 1 m from the end of the plank, determine the normal force acting at:

(a)the end closest to the painter

(b)the furthest end.

7.4 Trusses

7.Find the size of the force acting in each of the struts of the truss shown. Also, state whether the force is a compression force (C) or tension force (T).

Review questions

Understanding

1.Give three examples of:

(a)simply supported beams

(b)cantilever beams

(c)double cantilever beams.

2.A lintel or an arch could be used to span the opening in a building. Explain the difference in how each would support the load over the opening.

3.A ladder is leaning against a high wall. Is it more likely to slip when a person climbing it is near the ground or near the top? Explain.

4.What kind of bridge is Brisbane’s VictoriaBridge, shown below?

5.(a)What are the structural features of the railway bridge shown below?

(b)Explain how it is able to support itself and the weight of the trains that cross it.

6.Describe how the seat below supports the weight of a person sitting on it.

7.Why do you tend to lean to the left if you lift a heavy suitcase with your right hand?

8.Which of the following structures is the most stable?

(a)

(b)

(c)

(d)

9.Why are structures with wider bases harder to push over?

10.(a)What support structures can you see in use on Brisbane’s Treasury Casino?

(b)Where in these structures are compression forces at work?

11.What type of bridge is the footbridge shown in the figure below?

Application

12.The pedestrian bridge across the creek in the figure below weighs 2 kN. Calculate the reaction forces at each end when the three people are in the positions shown.

13.A wooden plank is suspended between two trestles and a load exerting a force F is placed in the middle of it, causing it to be deflected a distance of 2 mm. Assuming that the weight of the plank itself is negligible, what will be the deflection of the plank if:

(a)the load was doubled?

(b)the thickness of the plank was halved?

(c)the plank was made three times longer?

14.If the load in the figure below is acting downward on the point where struts 8 and 9 meet, which of the struts are under:

(a)compression?

(b)tension?

15.A gymnast with a mass of 50.0 kg stands on the end of a balance beam as shown in the figure below.

The beam is 5.00 m long and has a mass of 250 kg. Each of the two supports is 0.540m from their respective ends of the beam. What are the reaction forces exerted by each of the supports on the beam?

16.A door that is 820 mm wide can be opened provided that a torque of 10 Nm is applied at the hinge. How much force would be needed to open the door if it was applied perpendicularly to the door at a distance of 400 mm from the hinge?

17.To crack a walnut, a force of 40 N must act on its shell from both sides. How much force will you need to exert perpendicularly to the handles of the nutcracker in the figure below in order to crack the walnut?

18.A pair of wet jeans are hung from a clothesline as shown in the figure below.

If the wet jeans have a mass of 0.9 kg, what is the tension in the clothesline?

19.A flagpole made up of a uniform beam of length 12 m is supported by a horizontal cable at the top and a hinge from the side of a building as shown in the figure below. The tension in the cable is 400 N. Find the weight of the beam.

Challenges

20.Sean, who has a mass of 70 kg, stands on a level bridge of length L. He is at a distance equal to from one end. If the bridge is uniform and weighs 2.7 kN, what is the size of the reaction force on the end of the bridge furthest from him?

21.A sound speaker weighing 600 N is supported from the truss shown in the figure below.

What forces does the speaker cause in each strut of the truss?

22.The three-span cable-stayed bridge in the figure below must support a maximum load of 10 tonnes in the middle.
If the cables make an angle of 30 with the bridge deck, what is the magnitude of the force in:

(a)each cable?

(b)each of the towers?

23.A square trapdoor in a ceiling has a side of 0.91 m, and has a mass of 11 kg. It is hinged along one edge and has a catch on the opposite edge. If the door’s centre of gravity is located 10 cm towards the hinged edge from the centre, what will be the magnitude of the forces experienced by:

(a)the hinge?

(b)the catch?

24.The concrete wall shown in the figure below is supported on a concrete footing.

(a)Find the position of the structure’s centre of mass (consider the wall and its footing to be a single unit).

(b)Draw a diagram showing the forces that act on the structure when wind blows on it from the right.

(c)If the whole structure has a weight of 200kN and is struck by a wind gust acting at a point halfway up the wall, calculate the magnitude of the force provided by the wind gust that will just cause the wall to rotate about its base.

25.The prosthetic leg worn by a leg amputee tends to be very light so that it has good mobility. Will an amputee wearing such a leg have a lower or higher centre of mass than they had before amputation?