KTU Model Question paper Answers : Engineering Mechanics

Answers :

1. Two forces of magnitude 50 KN and 80 KN are acting on a particle, such that the angle between
the two is 135°. If both the force are acting away from the particle, calculate the resultant and
find its direction ?

2. A force F=700i +1500j is applied to a bolt A. Determine the magnitude of the force and the angle it forms with the horizontal.

 Magnitude F = √ (Fx 2 +Fy 2 )
                        =√ (7002 + 15002 )
                         = 1655.29N

Angle of he force with horizontal θx = cos-1 (Fx/F) θx
                                                            = cos-1 (700/1655.29)
                                                            = 64.98

3.What is Mass moment of Inertia and state its significance ?

4. An effort of 200 N is required just to move a certain body up an inclined plane of angle 15°,
the force is acting parallel to the plane. If the angle of inclination of the plane is made 20°,
the effort required being again parallel to the plane, is found to be 230 N. Find the weight of
the body and coefficient of friction.

5. Define instantaneous center of zero velocity. State the properties of instantaneous center?

6.  Explain D’Alembert’s principle ?

7.  What is the period of oscillation of a mass of 40 kg on a spring with constant k = 10 N/m?


Answer:

We have derived that T = 2Π  . To find the period of oscillation we simply plug into this equation:

T = 2Π  = 4Π seconds

No matter what initial conditions are placed on the system ,the period of oscillation will be same. Notice again that period, frequency and angular frequency are properties of the system, not of the conditions placed on the system.

8. What is free and forced vibration ?
Answer:
free vibration
Objects which are free to vibrate will have one or more natural frequency at which they vibrate, If an object is being forced to vibrate at its natural frequency, resonance will occur and you will observe large amplitude vibrations. The resonant frequency is f_o.

Forced Viberation
This is an example of resonance - when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion. The result of resonance is always a large vibration.

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