Tutorial work - 2 PDF

Preview

Summary

Download Tutorial work - 2 PDF

Description

Tutorial 2 ME101 (Engineering Mechanics) 2015-2016 Sem. II Equilibrium of Rigid Bodies Time: 8:00- 8:55 am Total: 50 Marks Q1. Figure 1 A collar B of weight W can move freely along the vertical rod shown. The constant of the spring is k, and the spring is un-stretched when =0. (a) Derive an equation in , W, k, and l that must be satisfied when the collar is in equilibrium. (b) Knowing that W=300 N, l=500 mm, and k=800 N/m, determine the value of  corresponding to equilibrium.[10 Marks] Q2. Figure 2 The rigid L-shaped member ABC is supported by a ball and socket at A and by three cables. Determine the tension in each cable and the reaction at A caused by the 1 kN load applied at G. [10 Marks] Q3. Figure 3 The uniform 10-kg rod AB is supported by a ball-and-socket joint at A and by the cord CG that is attached to the midpoint G of the rod. Knowing that the rod leans against a frictionless vertical wall at B, determine (a) the tension in the cord, (b) the reactions at A and B. [15 Marks] Q4. Figure 4 Two 2x 4 m plywood panels, each of weight 60 N, are nailed together as shown. The panels are supported by ball- and- socket joints at A and F and by the wire BH . Determine ( a ) the location of H in the xy plane if the tension in the wire is to be minimum, ( b ) the corresponding minimum tension. [15 Marks]

Figure 1

Figure 3

Figure 2

Figure 4

1/1

Solution 1

K:spring constant and T=ks s:elongtation in spring

A) From FBD of collar B

B.) 𝑡𝑎𝑛𝜃 − 𝑠𝑖𝑛𝜃 = 0.75

Solution 2.

M

A

0

=0

Equating the coefficients of unit vector to zero

Apply

F

x

 0 &  Fy  0

Solution 3

W=98.1N

AX=-36.N AY=73.6N AZ=27.6N

Solution 4:

I.

Position vector

II.

M

III.

AF

0

Projection of T on (AF rB /A ) is constant. Thus, Tmin is parallel to

1 Unit vector

5

( 2 j  k)

Tmin has no i component, wire BH is parallel to the yz plane and x=4 m. thus (x,y): (4,8)m ; Tmin=50.7...