M.P.KEDARNATH / Asst Prof - Mechanical Page 1

MAHALAKSHMI

ENGINEERING COLLEGE

B TIRUCHIRAPALLI – 621213

Sub Code: GE 6253 Semester: II

Subject: ENGINEERING MECHANICS Unit – IV – DYNAMICS OF PARTICLES

Part-A

1. Explain the difference between kinematics and kinetics. (AU,Dec’09)

2. State the principle of work and energy. (AU,Dec’11)

3. What is D’ Alembert’s principle? (AU,Apr’11 ,Dec’12)

4. What do you mean by impact of elastic bodies? (AU,Jun’09)

5. State Newton’s law concerning equilibrium of particle. (AU,Jun’09)

6. A body moves along a straight line so that its displacement from a fixed point on the line is

given by s = 3t2+2t. Find the velocity and acceleration at the end of 3 seconds.

(AU,Jun’10,Jun’12)

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7. A point P moves along a straight line according to the equation x = 4t3-2t-5, where x is in

meters. t is in seconds. Determine the velocity and acceleration when t = 3sec

(AU,Apr’11,DEC 10)

8. A train running at 80 km/h is brought to a standing halt after 50 seconds. Find the retardation

and the distance traveled by the train before it comes to a halt. (AU,Dec’09)

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9. A particle of mass 10kg falls vertically from a height of 100m from ground. What is the change

in potential energy when it has reached a height of 50m? (AU,Jun’10, Jun’12)

10. A stone is dropped from the top of a tower. It strikes the ground after four seconds. Find the

height of the tower. (AU,Dec’11)

Part – B

1. A ball of mass I kg moving with a velocity of 6 m/s strikes another ball of mass 2kg moving with a velocity of 2m/s at the instant of impact the velocities of the two balls are parallel and inclined at 30°to the line joining their centers as shown in figure below.

If the coefficient of restitution is 0.5, find the velocity and the direction the two balls after impact. Also calculate the loss in kinetic energy due to impact and the percentage of loss.(AU, Dec’10,Jun’12)

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2. Two trains A and B leave the same station on parallel lines. A starts with a uniform

acceleration of 0.15m/s2 and attains the speed of 24 km/hour after which its speed

remains constant. B leaves 40 seconds later with uniform acceleration of 0.30 m/s2 to

attain a maximum of 48 km/hour, its speed also becomes constant thereafter. When will

B overtake A.(AU,Dec’11,JUN 12)

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3. The 10m kg block shown in figure hangs form the end of a cable wrapped around the

cylindrical drum of radius 400mm. (AU,Dec’11, JUN 10)

The system starts form rest when the block is at 1.5m above the floor. Determine the mass of

the drum which will allow the block to hit the floor at 1/4th the speed it would have attained if

the block alone were simply dropped from the same height.

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4. Car A accelerates uniformly from rest on a straight level road. Car B starting from the

same point 6 seconds later with zero initial velocity accelerates at 6m/s2 .It overtakes the

car A at 400m from the starting point. What is the acceleration of the car A? (AU, Apr’11)

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5. A stone is dropped into a well . The sound of the splash is heard 3.63 seconds later.How

far below the ground is the surface of water in the well? . Assume the velocity of sound as

331m/s. (AU, Apr’11, Dec ‘12)

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6. Block P of weight 100N and block Q of weight 50N are connected by a rope that passes

over a smooth pulley as shown in figure. Find the acceleration of the blocks and the

tension in the rope, when the system is released from rest. Neglect the mass of the pulley.

(AU, Apr’11, Dec’12)

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7. A 2000 kg automobiles is driven down a 5° inclined plane at a speed of 100km/h when

the brakes are applied causing a constant total braking force (applied by the road on the

tires) of 7KN.Determine the distance travelled by automobile as it comes to a stop.

(AU, Apr’11, Dec’12)

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8. What is impulse force and impulsive force? (AU, Jun’10)

9. A block and pulley system is shown in fig below. The coefficient of kinetic friction

between the block and the plane is 0.25. The pulley is frictionless. Find the acceleration of

the blocks and the tension in the string when the system is just released. Also find the time

required for 200kg block to come down by 2m. (AU, Jun’09,DEC 11)

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10. State the law of conservation of momentum. (AU, Jun’09, Dec12)

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11. A block of mass 50 kg slides down a 35°inclined and strikes a spring 1.5m away from

it as shown in Fig below. The maximum compression of the spring is 300mm when the

block comes to rest. If the spring constant is 1kN/m,find the coefficient of kinetic friction

between the block and the plane (AU,Jun’09)

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12. A ball of mass 2kg, moving with a velocity of 3m/s,impinges on a ball of mass 4 kg moving

with a velocity of 1m/s.The velocities of the two balls are parallel and inclined at 30°to the

line of joining their centres at the instant of impact. If the coefficient of restitution is 0.5,

find (AU,Dec’09, Jun’10)

(i) Direction, in which the 4kg ball will move after impact;

(ii) Velocity of the 4 kg ball after impact;

(iii)Direction, in which the 2kg ball will move after impact;

(iv)Velocity of the 4kg ball after impact.

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