## 雅思高分作文备考攻略

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http://bailiedu.com As shown in Figure 1, the loading system consists of five forces and two couples. The two 64 N forces are parallel to each other and perpendicular to the bar. Moreover, the bar and these two forces are also in a plane which is parallel to the x-z plane. (a). Replace the loading system shown in Figure 1 by an equivalent force-couple system at point A. A diagram clearly showing the force-couple system is required. (b). Show that the resultant force is NOT perpendicular to the couple. Replace the force-couple system at A, by an equivalent wrench and state whether it is a positive or negative wrench. (c). Determine the magnitude of the moment of the wrench. (d). Find the coordinates of the point in the x-z place through which the line of action of the wrench passes.

120 mm

20 N-m 120 mm

40 N

40 N

80 mm

80 mm 30° 72 N 72 N 40 mm

60 mm 40 mm

60 mm

48 N 100 mm 100 mm 20 N-m 64 N 64 N 30°

An asymmetric bucket 1.20 m tall by 1.0 m wide as shown in Figure 2 is supported by pivots P and P′, which are vertically above the apex. Point O is the midpoint of P-P′, directly above point A (see Figure 2a). The bucket walls are non-uniform such that when empty, the centre of mass of the bucket is at point D on the line OA, 50.5 cm below point O (Figure 2b). The mass of the empty bucket is 650 kg. As the bucket fills, the centre of mass of the contents is at point E, which is NOT on line OA and as such the bucket tilts by an amount θ. Once the bucket reaches some critical angle θcrit, it will overflow at the corner C and will hold no more material than the critical volume Vcrit. If the bucket is less than full and it is desired for volume of material less than Vcrit to flow out, the bucket must be poured by attaching a cable at B and pulling vertically upward with a tension T. The density of water is ρwater=1000 kg-m-3 The density of molten iron is ρiron=7900 kg-m-3

(a) Find an expression for the volume of liquid in the bucket, V(θ), as it starts to pour as a

function of θ (see Figure 2C). Assume a straight line for the free surface of the liquid (water line).

(b) Find the position vector OE (Figure 2C) of the centre of mass of the liquid when the

bucket starts to pour, as a function of θ using the coordinate system with its origin at point O as shown,.

(c) Hence or otherwise; when the tension T in the pouring cable is zero,

I. find Vcrit and θcrit for water,

II. find Vcrit and θcrit for iron

(d) If the bucket contains iron and a tension, T, of 7700kN is required before the bucket

begins to pour, determine the volume of iron in the bucket at this moment.

(e) If the bucket containing water in part C)I, were taken to Mars (acceleration due to gravity

3.7ms-2), what would the critical volume be?  1.2 m 50.5 cm

As shown in Figure 3, the frame ABCDE is supported by a pin at point A and a roller at point B. A distributed load described by function w = 4000??3+1600??2?900??+150 (N/m) is acting on member BCD, where x, in metres, starts from point C. Assuming that the weights of the bars are negligible, a) Replace the distributed load with an equivalent point load on member BCD and indicate the point of action. b) Draw the free body diagram of the whole frame and find the reactions at point A and B. c) Draw the free body diagrams for member BCD, DE and ACE and determine the forces acting on each of the members.

+150(N/m) The ball-socket connected space truss structure shown in Figure 4 is part of a glider fuselage, and is supported by ball and socket joints at A, B and C. Forces applied at joints G, D and E are perpendicular to face/triangle DEG. The coordinates, in m, of various points are as listed in the table below. a) Find the reaction forces at A, B force. As shown in Figure 5, a horizontal wire connects the object A and the inner circle of a wheel shaft. Another wire connects the outer circle of the wheel shaft and the object C through a pulley. The inner radius of the wheel shaft is 50 mm and the outer radius is 100 mm. The weight of the object A and the wheel shaft is 500 N and 1000 N respectively. The friction coefficient between the object A and the surface is 0.5 and the friction coefficient between the wheel shaft and the surface is 0.2. The friction between the rope and the wheels is negligible. The system is stationary. (a) Draw the free body diagram of the wheel shaft, object A and object C. (b) Find the maximum weight of object C can be put before the wheel shaft slips when θ = 30°, θ = 40° or θ = 50°.

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