MEPCO SCHLENK ENGINEERING COLLEGE, SIVAKASI – 626 005

(Autonomous)

Department of Civil Engineering

13GE201 Engineering Mechanics – Tutorial I

1. The y - component of a force F which a person exerts on the handle of the wrench box (shown in fig 1.) is 70N. Determine the x- component and magnitude of F.

2. Determine the resultant (magnitude & direction) of the two forces applied on the bolt as in fig 2.

Fig. 1 Fig. 2

3. A lamp of mass 1Kg is hung from the ceiling by a chain and is pulled aside by a horizontal chord until the chain makes an angle of 60º with ceiling. Find the tensions in chain and chord.

4. A precast concrete post weighing 50 Kg and of length 6m shown in fig. 3 is raised for placing it in position by pulling the rope attached to it. Determine the tension in the rope and the reaction at A.

Fig. 3 Fig. 5

5. The forces 20N, 30N, 40N, 50N and 60N are acting on one of the angular points of a regular hexagon, towards the other five angular points, taken in order. Find the magnitude and direction of the resultant force.

6. A fine light string ABCDE whose extremity A is fixed, has weights W1 and W2 attached to it at Band C. It passes round a small smooth peg at D carrying a weight of 40N at the free end E as shown in fig. 5. If in the position of equilibrium, BC is horizontal and AB and CD makes 150° and 120° with BC, find (i) Tension in the portion AB, BC and CD of the string and (ii) Magnitude of W1 and W2.

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Fig. 5

7. Determine the forces F1 and F2 so the particle acted upon by the system of forces as in fig.4 is in equilibrium. The angles made by the forces 4 kN, F1, 5 kN and 5.5 kN are 20, 15, 30 and 45 degrees respectively.

8. Members OA, OB and OC form a three member space truss. A weight of 10 KN is suspended at the joint ‘O’ as shown in fig. Determine the magnitude and nature of forces in each of the three members of the truss.

Fig. 6 Fig. 7

9. A couple of magnitude 5.4Nm and the three forces shown in fig.7 are applied to an angle bracket. Find a) the resultant of this system of forces and (b) Locate the points where the line of action of the resultant

intersects lines AB & BC.10. Four tugboats are used to bring an ocean liner to its pier.

Each tugboat exerts a 5000-lb force in the direction shown in fig. 8. Determine a) the equivalent force-couple system at the foremast O, b) the point on the hull where a single, more powerful tugboat should push to produce the same effect as the original four tugboats.

Fig. 8 Fig. 911. A square foundation mat supports the four columns shown in fig. 9. Determine the magnitude and point

of application of the resultant of the four loads.

Answers to TUTORIAL PROBLEMS:

A lamp of mass 1Kg is hung from the ceiling by a chain and is pulled aside by a horizontal chord until the chain makes an angle of 60º with ceiling. Find the tensions in chain and chord.

Let Tchord = Tension in chord ; Tchain = Tension in chain

W = weight of lamp = 1 × g = 9.81N

Consider point ‘C’, there are three force acting, so apply lami’s theorem at point ‘C’, as point C is in equilibrium

Tchord/sin150° = Tchain/sin90° = 9.81/sin120°

Tchord = 9.81 × sin150° /sin120°

Tchord = 5.65N .......ANS

Tchain = 9.81 × sin90° /sin120°

Tchain = 11.33N .......ANS

A precast concrete post weighing 50 Kg and of length 6m shown in fig. 3 is raised for placing it in position by pulling the rope attached to it. Determine the tension in the rope and the reaction at A.

Sol.: Apply condition of equilibrium

∑H = 0 RAH – T cos 20º = 0 RAH = T cos 20º ...(i)

∑V = 0 RAV – 50 – T sin 20º = 0 RAV = 50 + T sin 20º ...(ii)

Now taking moment about point A

T sin 20º × AC + 50 sin 45º × AE – Tcos20 × BC = 0,

AC = 4.25 m ; BC = 4.25 m ; AE = 2.25 m

T × 0.34 × 4.25 + 50 × 0.71 × 2.25 – T × 0.94 × 4.25 = 0,

1.445 T + 79.875 – 2.115 T = 0

T = 22.44 Kg .......ANS

Putting the value of T in equation (i) and (ii)

RAH = 21.1 Kg .......ANS

RAV = 57.2 Kg .......ANS

A fine light string ABCDE whose extremity A is fixed, has weights W1 and W2 attached to it at Band C. It passes round a small smooth peg at D carrying a weight of 40N at the free end E as shown in fig. 5. If in the position of equilibrium, BC is horizontal and AB and CD makes 150° and 120° with BC, find (i) Tension in the portion AB, BC and CD of the string and (ii) Magnitude of W1 and W2.

Sol.: First string ABCD is split in to two parts, and consider the joints B and C separately

Let,

T1 = Tension in String AB; T2 = Tension in String BC; T3 = Tension in String CD; T4 = Tension in String DE

T4 = T3 = 40N

Since at joint B and C three forces are acting on both points. But at B all three forces are unknown

and at point C only two forces are unknown SO Apply lamis theorem first at joint C,

T2 /sin150° = W2/sin120° = 40/sin90°

T2 = {sin150° × 40}/sin90° = 20N .......ANS

W2 = {sin120° × 40}/sin90° = 34.64N .......ANS

Now for point B, We know the value of T2 So, Again Apply lamis theorem at joint B,

T1/sin90° = W1/sin150° = T2/sin120°

T1 = {sin90° × 20}/sin120° = 23.1N .......ANS

W1 = {sin150° × 20}/sin120° = 11.55N .......ANS

The forces 20N, 30N, 40N, 50N and 60N are acting on one of the angular points of a regular hexagon, towards the other five angular points, taken in order. Find the magnitude and direction of the resultant force.

Sol.:

In regular hexagon each angle is equal to 120°, and if each angular point is joint together, then each section makes an angle of 30°.

First resolve all the forces in vertical and horizontal directions

Let ∑H = Sum of Horizontal components

∑H = 20cos 0° + 30cos 30° + 40cos 60° + 50cos 90° + 60cos 120° = 35.98N ...(i)

∑ V = Sum of Vertical components

∑ V = 20sin 0° + 30sin 30° + 40sin 60° + 50sin 90° + 60sin 120° = 151.6N ...(ii)

R = (∑H2 + ∑V2)1/2 = {(35.98)2 + (151.6)2}1/2

R = 155.81N .......ANS

Let angle made by resultant is q

Tan q = ∑V /∑H = 151.6/35.98 & q = 76.64° .......ANS