Question Paper: Engineering Mechanics Question Paper - Dec 17 - First Year Engineering (Semester 1) - Mumbai University (MU)

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## Engineering Mechanics - Dec 17

### First Year Engineering (Semester 1)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

(4) Take $g=9.81m/s^2$

Q1) Attempt any four:

**1(a)**State and prove varignones theorem.

**1(b)**Find the resultant of the force system shown in fig.

**1(c)**Find the co-ordinate of the centroid of the area shown in fig.

**1(d)**A force of 500N is acting on a black of 50Kg mass resting on a horizontal surface as shown in fig. Determine the velocity after the block has traveled a distance of 10m. Coeff. of kinetic friction = 0.5.

**1(e)**The position vector of a particle which moves in the X-Y plane is given by $\bar r = (3t^3 - 4t^2)i + (0.5t^4)J m.$ Calculate velocity and acceleration at t=1 sec.

**2(a)**Find the resultant of the force acting on the bell crank level shown. Also locate its position write hinge B.

**2(b)**Determine the reaction at points of constant 1,2 and 3. Assume smooth surfaces.

**2(c)**Two balls having 20Kg and 30Kg masses are moving towards each other with velocities of 10m/s and 5m/s respectively as shown in fig. If other impact the ball having 30Kg mass is moving with 6m/s velocity to the right then determine the coefficient of restitution between the two balls.

**3(a)**Determine the centroid of the plant lamina shaded portion is removed.

**3(b)**Explain conditions for equilibrium for forces in spaces.

**3(c)**A 30N block is released from rest. If slides down a rough incline having coefficient of friction 0.25. Determine the maximum compression of the spring.

**4(a)**Find the support reaction at A and B for the beam loaded as shown in fig.

**4(b)**The V-X graph of a rectilinear moving particle is shown. Find acceleration of the particle at 20m, 80m, and 200m.

**4(c)**A bar AB 2m long slides down the plane as shown. The end A slides on the horizontal floor with a velocity of 3m/s. Determine the angular velocity of the rod AB and the velocity of end B for the position shown.

**5(a)**Referring to the truss shown in fig. Find

- i) Reaction at D and C
- ii) Zero Force members
- iii) Forces in members FE and DC by method of section.
- iv) Forces in other members by method of joints.

**5(b)**Determine the force 10 required to move the block A of 5000N weight up the inclined plane, coefficient of friction between all contact surfaces is 0.25. Neglect the weight of the wedge and the wedge angle is 15 degrees.

**5(c)**Determine the tension in a cable BC shown in fig by virtual work method.

**6(a)**A 500N crate kept on the top of a $15^0$ sloping surface is pushed down the plane with an initial velocity of 20m/s. If $\mu s = 0.5$ and $\mu k = 0.4$. Determine the distance travelled by the block and the time it will take as it comes to rest.

**6(b)**Derive the equation of the path of a prosotile and hence show that the path traced by a prosectile is a parabolic curve.

**6(c)**A particle is moving in X-Y plane and its position is defined by $\bar r = (\frac{3}{2}t^2) i + ( \frac{2}{3}t^3)J.$

Find ratio of curvature when t = 2 sec.

**6(d)**A force of 100N acts at a point P(-2, 3, 5) m has its line of action passing through Q(10,3,4)m . Calculate moment of this force about origin (0,0,0).