CO-4 ASSIGNMENT QUESTIONS1a) A bullet of mass 1 kg if fired with a velocity of u m/s from a gun of mass 10 kg. Find the ratio of kinetic energies of bullet and gun.

b) Two weights P and Q are connected by the arrangement shown in Fig, neglecting friction and the inertia of the pulleys and cord, find the acceleration a of the weight Q. Assume that P=178N and Q= 133.5N.

2a) A block of mass 5 kg is thrust up a 30° inclined plane with an initial velocity of 4 m/sec. It travels a distance of 1.0 m before it comes to rest. What is the force of friction acting on it .

b) A small block of weight W=44.5N is given an initial velocity u=3m/s down the inclined plane shown in figure. If the coefficient of friction between the plane and the block is μ=0.3, find the velocity v of the block at B after it has travelled a distance x=15m.

3a) An automobile having a mass of 2000 kg cruises at a speed of 20 m/s. If all the wheels are jammed suddenly, how far will the automobile skids before it comes to a halt, assuming that the vehicle does not spin or topple? The coefficient of friction between the ground and the tyres is 0·8.

b ) A man weighing 712N stands in a boat so that he is 4.5m from a pier on the shore as shown in figure. He walks 2.4m in the boat toward the pier and then stops. How far from the pier will be at the end of this time? The boat weighs 890N, and there is assumed to be no friction between it and the water.

4a) The wheel of a small gyroscope is set spinning by pulling on a string wound around the shaft. Its moment of inertia is I=5562.5 kg-mm2 and the diameter of the shaft on which the string is wound is 12.5mm. If 750mm of string is pulled off with a constant force of 53.4N, what angular velocity will be imparted to the wheel?

b) A small block of weight W rests on an adjustable inclined plane as shown in Fig. Friction is such that sliding of the block impends when α=30o.What acceleration will the block have when α=45o Neglect any difference between static and kinetic friction.

5a) A car moving with uniform acceleration covers 450 m in a 5 second interval, and covers 700 m in the next 5 second interval. Find the acceleration of the car.

b) Weight W and 2W are supported in a vertical plane by a string and pulleys arranged as shown in Fig. Find the magnitude of an additional weight Q applied on the left which will give a download acceleration a=0.1g to the weight W. Neglect friction and inertia of pulleys.

6a) A ship being launched slips down the skids with uniform acceleration. If 10 s is required to traverse the first 4.8m, what time will be required to slide the total distance of 120m? With what velocity v will the ship strike the water?

b) A weight W= 4450N is supported in a vertical plane by a string and pulleys arranged as shown in Fig. If the free end A of the string is pulled vertically downward with constant acceleration a = 1.8 m/s2, find the tension S in the string. Neglect friction in the pulleys.

7a) A block of mass 50 kg is placed on a rough horizontal floor as shown in figure. A force P inclined at an angle of 30o is applied on the block. If the block reaches a velocity of 10 m/s in covering a distance of 10 m, what is the magnitude of the force P. Take coefficient of kinetic friction between block and floor equal to 0.25.

b) An inextensible mass less string goes over a frictionless pulley. Two weights of 100 N and 200 N are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. Find the tension in the string (in N).

8a) A 10 gm bullet is shot horizontally in a wood block of mass 1 kg. The bullet gets embedded in the block and the block is displaced on a rough horizontal table (µ=0.2) through 1 m. What was the velocity of bullet?

b) Referring to Fig., find the acceleration a of the falling weight P if the coefficient of friction between the block Q and the horizontal plane on which it slides is µ.Neglect inertia of the pulley and friction on its axle. The following numerical data are given P=44.5 N, Q= 53.4N, µ=1/3.

9 a) A 667.5 N man sits in a 333.75N canoe and fire a 0.277N rifle bullet horizontally directly over the bow of the canoe. Neglect friction of the water, find the velocity v with which the canoe will move after the shot if the rifle has a muzzle velocity of 660 m/s.

b) A ball of mass 110 gm is moving towards a batsman with a velocity of 24 m/s as shown in fig. The batman hits the ball by the bat, the ball attains a velocity of 36 m/s. If ball and bat are in contact for a period of 0.015 sec, determine the average impulsive force exerted on the ball during the impact.

10a) A vehicle of mass 600 kg and moving with a velocity of 12 m/s strikes another vehicle of mass 400 kg, moving at 9 m/s in the same direction. Both the vehicles get coupled together due to impact. Find the common velocity with which the two vehicles will move. Also find the loss of kinetic energy due to impact.

b) i)Determine the distance in which a car moving at 90 kmph can come to rest after the power is switched off if µ Between tyres and road is 0.8.

(ii) Determine also the maximum allowable speed of a car, if it is to stop in the same distance as above on ice road where the coefficient of friction between tyres and road is 0.08. (Use work energy principle)

11a) A train is moving down a slope of 0.008 with a velocity of 48kmph. At a certain instant, the engineer applies the brakes and produces a total resistance to motion equal to one-tenth of the weight of the train. What distance x will the train travel before stopping?

b) A 750 kg hammer of a drop hammer pile driver falls from a height of 1.2 m onto the top of a pile as shown in fig. The pile is driven 100 mm into the ground. Determine the average resistance of the ground to penetration. Assume mass of pile as 2250 kg.

12a) A rotor of Turbine has an initial angular velocity of 1800 rpm. Accelerating uniformly, it doubled its velocity in 12 sec. Find the Revolutions Performed by it in this interval.

B) The driver of an automobile, travelling along a straight level highway, suddenly applies the brakes so that the car slides for 2 s, covering a distance 9.66 m, before coming to a stop. Assuming that during this time the car moved with constant deceleration; find the coefficient of friction between the tyres and pavement.

1) Change in its kinetic energy during the above period.

13a) A fly wheel weighing 60KN and having radius of gyration 1 m loses its speed from 400rpm to 280 rpm in 2 minutes. Calculate

1) The Moment (or) retarding Torque on it.

b) A solid right circular drum of radius r =0.3m and weight W=143.3N is free to rotate about its geometric axis as shown in Fig. Wound around the circumference of the drum is a flexible cord carrying at its free end a weight Q=44.5 N. If the weight Q is released from rest, (a) find the time t required for it to fall through the height h=3m. (b) With what velocity v will it strike the floor?

14a) A police investigation of tire marks shows that a car travelling along a straight level street had skidded for a total distance of 43.5 m after the brakes were applied. The coefficient of friction between the tyres and pavement is estimated to be µ=0.6. What was the probable speed of the car when the brakes were applied?

b) The 50gm bullet traveling at 600 m/s strikes the 4kg block centrally and is embedded within it. If the block slides on a smooth horizontal plane with a velocity of 12 m/s in the direction shown prior to impact, determine the velocity v2 of the block and embedded bullet immediately after impact.

15a) A solid cylindrical pulley of mass 800 kg, having 0.8 m radius of gyration and 2 m diameter, is rotated by an electric motor, which exerts a uniform torque of 60 KN-m. A body of mass 3000 kg is lifted by a wire wrapped round the pulley. Find (i) acceleration of the body; and (ii) tension in the rope.

b) Two blocks of weights P and Q are connected by a flexible but inextensible cord and supported as shown in Fig. If the coefficient of friction between the block P and the horizontal surface is µ and all other friction is negligible, find (a) the acceleration of the system and (b) the tensile force S in the cord. The following numerical data are given: P= 53.4N; Q=26.7N; µ=1/3.

16a) A mine cage of weight W= 8.9KN starts from rest and moves downward with constant acceleration, travelling a distance s = 30m in 10 s. Find the tensile force in the cable during this time.

b) A 750 N crate rests on a 500 N cart. The coefficient of friction between the crate and the cart is 0.3 and between cart and the road is 0.2. If the cart is to be pulled by a force P, such that the crate does not slip, determine (a) the maximum allowable magnitude of P and (b) the corresponding acceleration of the cart.

17a) An elevator of gross weight W=4450N when stopping, moves with constant deceleration and from the constant velocity v = 1.8m/s, comes to rest in 2 s. Determine the force P transmitted during stopping to the floor of the elevator by the feet of a man weighing 765.5N.

b) The 90kg man dives from the 40kg canoe. The velocity indicated in the figure is that of the man relative to the canoe just after loss of contact. If the man, women and canoe are initially at rest, determine the horizontal component of the absolute velocity of the canoe just after separation. Neglect drag on the canoe, and assume that the 60kg woman remains motionless relative to the canoe.

18a) The step pulley shown in fig. starts from rest and accelerates at 2 rad/sec2. How much time required for block A to move 20 m ? Find also the velocity of P and Q at the time.

b) Two bodies weighing 25N and 20 N are connected to the ends of an inextensible string, which passes over a smooth pulley. The weight 25 N is placed on a 20o inclined plane while the weight 20 N is hanging over the pulley. Determine (i) Acceleration of the system when 25 N moves up (ii) Tension in the string

20O 20 N

25 N