ASSIGNMENT : NEWTON’S LAWS OF MOTIONI

1. A train with a mass of 1000 tonnes is uniformly retarded by applying brakes. In one minute, its velocitydrops from 40 km/hr to 22 km/hr. Find the braking force.

2. A motor car running at the rate of 36 km/hr can be stopped by its brakes in 10 metres prove that the totalresistance to the motion of the car when the brokes are an, is approximately half of the car’s weight.

3. What force should be applied to a real car for it to begin to move with uniform acceleration and travel adistance of 11 meters in 30 seconds? Mass of the rail car is 16000 kg. During its motion, the rail car isacted upon by a force of friction equal to 0.05 of its weight.

4. A steel wire can withstand a weight upto 4400 N. What is the maximum acceleration with a load of 3900N suspended on this wire may be lifted sot hat the wire does not break?

5. A load of mass 1 kg is suspended by a threat. Find the tension of the ghread with the load. If (i) if it islifted with an acceleration of 5 m/s2 (ii) if it is lowered with the acceleration of 5 m/s2.

6. What is the mass of the ballast to be dropped from a uniformly descending baloon to enable the latter torise up with the same velocity? The baloon together with the ballast weighs 1600 N and its liftingcapacity is 1200 N. The force of air resistance is to be taken same during both ascent and descent.g = 10%.

7. A baloon of mass m kg is rising up with an acceleration a. Show that the fraction of weight of the baloonthat must be detached in order to double its acceleration is ma/(2a + g), assuming the upthrust of air toremain the same.

8. A jet of water issuing out of a tube of cross-sectional area 10 sq.cm. Strikes horizontally, a fixed verticalwall with a velocity of 25 nc/sec. What is the force exerted on the wall by the jet (i) If the water does notrebound (ii) If the water rebounds with a horizontal velocity of 5 m/s. Assume that the velocity of waterin the tube is 25 m/s.

9. An engine driver of a train at rests observes a touch moving towards non is an incline of 1 in 60 at adistance of 0.8 km. He immediately starts his train away from the truck at a constant acceleration of 0.15m/s2. If the truck just catches the train, find its velocity when first observed. Assume that the frictionopposing the truck’s motion is 1/160 of the weight of the truck.

10. A body of mass 1 kg falls from a height of 20 m above the ground level. Find the magnitude of the totalchange in momentum of the body before it strikes the ground. Find also the corresponding averageforce experienced by it. g = 10 m/s2.

11. A particle of mass 1 kg rests on rough contact with a plane inclined at 30o to the horizontal and is justabout to slip. Find the co-efficient of friction between the plane and the particle.

12. A particle of weight W rests on a horizontal plane with which the angle of friction is . A force P inclinedat an angle to the plane is applied to the plane until it is on the point of moving. Find the value of forwhich the value of P will be least.

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JEE AdvancedPHYSICS

13. The coefficient of friction between a road and the type of a vehicle is 4/3. Find the maximum incline of theroad so that, once hard brake are applied and the wheel starts skidding the vehicle going down at aspeed of 10 m/s is stopped within 5 meters. g = 10 m/s2.

14. A bucket alongwith water of mass 25 kg is raised from a well by a 50 kg mean on two ways - (i) directlylifting the bucket through a rope fastened to it (ii) using the rope and pulley system. What is the actionon the floor by the man in these two cases. If the floor yields to a normal force of 700 N which modeshould the man adapt to lift the bucket without the floor yielding?

15. A particle of mass m, originally at rest, is subjected to a force whose direction is constant, but whose

magnitude varies with time as F = F0

21 t T

T

, where Fo, T are constants. The force acts for the

time interval 2T. Find the speed of the particle of t = 2T.

16. Having gone through a plank of thickness h, a bullet changed its velocity from Vo to V. Find the time ofmotion of the bullet in the plank, assuming the resistance force to be proportional to the square of thevelocity.

17. A particle is projected vertically upwards with speed u in a medium wherein the resistance to motion isproportional to the square of the speed. Initially net force on the particle is two times the weightdownwards. Find the time of ascent and also the distance ascended by the particle.

18. A particles of mass 1 kg which moves along the x-axis is subjected to an accelerating force whichincreases linearly with time and a retarding force which increases directly with displacements with theconstant of proportionality being one one in proper dimensions for both the cases. At time t = 0, boththe displacement and velocity are zero. Find the displacement as a function of time.

19. A charged particle of mass m and charge q is moved from rest at x = 0 by an electric field E = E0 x i

where a is a positive constant and x is the displacement of the particle in time t along x-axis. Find thedistance moved by the particle when it is again brought to rest. Find also the acceleration of the particleat that instant. Describe the motion of the particle.

20. 4 body of mass m is thrown straight up with velocity V0. Find the velocity V’ with which the body comesdown if the air drag equals KV2, where K is aconstant and V is the velocity.

21. A particle of mass 102 kg is moving along the positive x-axis under the influence of a force F(x) =K/(2x2), where K = 102 Nm2. At time t = 0, it is at x = 1 meter and its velocity is V = 0. Find (i) Velocity, whenthe it reaches x = 0.5 m (ii) Time at which it reaches t = 0.25 meters.

22. A spherical raindrop initially of radius r0 starts falling freely, recovers water particles during its fall sothat at every instant the rate of increase of volume equals times its surface are at that instant. Find (i)velocity of raindrop after t seconds, assuming no air drag. (ii) Distance that the drop has fallen in thattime.

23. A particle of mass m is fixed into a liquid at angle 0 with velocity V0, in a liquid that develops a dragresistance F = KV, where K is a positive constant and V is one particles velocity. Find the x and ycomponents of its velocity at any instant, and the maximum distance it travles.

24. A particle of mass m, moving in a straight line is acted upon by a force F = KVn, where K is a (+)veconstant. For what values of n the average velocity of the particle till it steps, is 1/3 rd of its initialvelocity? <n 1.2>.

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