Review CPP - Laws or Motion Lever -1 SECTION (A) : TYPE OF FORCES, NEWTON'S THIRD LAW, FREE BODY DIAGRAM : ‘Act. Which type of forces does a proton exerts on a proton ? A-2. Which one out of four fundamental forces is the weakest force between two protons at a distance of 1 fermi. ‘Suppose you are running fast in a field. When you suddenly find a snake in front of you, stop quickly. Which force is responsible for your deceleration ? Ablock ‘A’ exerts a force on ‘B' of magnitude 20 N. Calculate the magnitude of force exerted by ‘B on ‘K a ‘Two forces of same magnitude act on an isolated body in opposite directions to keep it at equilibrium position, Is this true according to Newton's third law? z Draw F.B.D. of the sphere of mass M placed between two vertical walls as shown in figure (All surface are smooth). AT. Ablock of mass 1 kg placed on ground is pulled by a string by applying 10 N force : (g = 10 m/s”) () Draw F.8.0. of block (i) Give action-reaction pair involved in the above problem. ‘A-8. Draw free body diagrams for masses m and M shown in figure. Identify all action-reaction pairs between two blocks. The pulley is frictionless and massless and all surfaces are smooth SECTION (B): CALCULATION OF NORMAL REACTION B41. Ablock of mass ‘m’ is placed on ground as shown in figure. Calculate YF =mg contact force between ground and block. m™ B-2, Two blocks of masses m, and m, are placed on ground as shown in figure. ‘Two forces of magnitude F act on m, and m, in opposite directions. () Draw F.B.D. of masses m, and m,. F (ii) Catcutate the contact force between m, and m, = (ii) What will be the value of action-reaction pair between m, and m, (iv) Calculate force exerted by surface on mass m, and m, ‘smooth B-3. A block of mass ‘m’ is placed on inclined plane as shown in figure. Calculate force between block and inclined plane. B-4. A sphere of mass 'm’, radius ‘R’ placed between two vertical walls having separation ‘d’ which is slightly greater than ‘2°R' : () Calculate force exerted by walls on the sphere. (i Calculate force exerted by surface on the sphere B-5. Acylinder of weight w is resting on a fixed V-groove as shown in figure. Scanned with CamScannerBs. ‘Smooth fixed groove () S oo eo" mg (2) Drawits free body diagram. (0) Calculate normal reactions between the cylinder and two inclined walls. ‘The 50 kg homogeneous smooth sphere rests on the 30° incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B. SECTION (C) : CALCULATION OF TENSION cA. c2, cs. ca. cs. SECTION (D) : CONSTRAINED MOTION Da, Astring 1 Is connected between surface and a block of mass 1 kg ‘which is pulled by another string 2 by applying force F = 10 N as 2 shown in figure. (g = 10 mis) (i) Calculate tension in string (1). (i) Calculate tension in string (2). 1 ‘Aone meter long massless string fixed with a wall is pulled horizontally by applying a force of magni- tude 10 N. Calculate : (@) the tension at 2 point 0.5m away from wall (0) the tension at a point 0.75 m away from wall (©) force exerted by string on the rigid support block of mass 1 kgis suspended by a string of mass 1 kg, length 1m as shown in figure. (g = 10 m/s?) Calculate: 1 (@ the tension in string at its lowest point. () the tension in string at its midpoint (©) force exerted by support on string. I Ablock of mass 0.2 kg is suspended from the ceiling by a light string. A second block of mass 0.3 kg is suspended from the fist block through another string, Find the tensions in the two strings. Take g = 10 mis? Ina simple Atwood machine , two unequal masses m, and m, are JMU connected bya string going over a clamped light smooth pulley. |n a typical arrangement (figure ) m, = 300 g and m, = 600g. The system is M) released from rest. (a) Find the distance travelled by the first block in 2 the first two seconds. (b) Find the tension in the string . (c) Find the force exerted by the clamp on the pulley. (g = 10 m/s?) In the figure shown, blocks Aand B move with velocities v, and v, along horizontal direction. Find the ratio of 2 Scanned with CamScannerD2. D3. D4. Inthe figure shown, the pulley is moving with velocity u. Calculate the velocity of the block attached with string ooo ITAA TTT The velocity of end ‘A’ of rigid rod placed between two smooth vertical walls moves with velocity ‘u’ along vertical direction. Find out the velocity of end ‘B" of that rod, rod always remains in contact with the vertical walls. If block A has a velocity of 0.6 m/s to the right, determine the velocity of block B. Al eat B Velocities of blocks A, 8 and pulley p, are shown figure. Find velocity of pulley p, and block C. ome ® m E B]f 10m zon SECTION (E) : CALCULATION OF FORCE AND ACCELERATION Et. E2 Ea, In the figure the tension in the diagonal string is 60 N. (@) Find the magnitude of the horizontal force F, and F, that must bbe applied to hold the system in the position shown. (b) _ Whatis the weight of the suspended block ? A particle of mass 50 gram moves on a straight line. The variation of speed with time is shown in figure. Find the force acting on the particle at t = 2, 4 and 6 seconds. A3.0 kg mass is ‘where x and y are in meters and tis in second. Find the magnitude of the net force acting on this mass att = 2 sec. constant force F = m,g//2is applied on the block of Scanned with CamScannermass m, as shown in figure. The string and the pulley = are light'and the surface of the table is smooth. Find the acceleration of m, E-5. _Achain consisting of five links each with mass 100gm is lifted vertically F with constant acceleration of 2m/s?. as shown. Find (g = 10 mis) (@) the forces acting between adjacent links (0) the force F exerted on the top link by the agent lifting the chain (©) thenet force on each link SECTION (F) : WEIGHING MACHINE, SPRING RELATED PROBLEMS AND SPRING BALANCE F-1, Aman of mass 60 kg is standing on a weighing machine placed in a lift moving with velocity ‘v’ and acceleration 'a’ as shown in figure. Calculate the reading of welghing machine in following situations : (g= 10 mis’) 0 0, @ 0, mis i) a=0, 2mis ®) 2mis?, ™) —2 mis? “ 2 mist, mis (wi) a= 2mist, 2mis (vi) =2 mis? 2mis F-2. What will be the readi of spring balance in the figure shown in following situations. (g = 10 m/s*) v=0 w mis i) v=-2mis ) v=o ‘ re ® 1 t w mis a= Ore i 2s wi) = 2 mis? 2mis SECTION (G) : NEWTON'S LAW FOR A SYSTEM : G-1._Amanof mass m standing on a platform of mass '2m’ a jumps horizontally with an acceleration ‘a’. Find the acceleration of platform. __ Smooth rn G-2._ Man’‘A’ of mass 60 kg pushes the other man ‘B' of Aa mass 75 kg due to which man ‘B’ starts moving with Smit acceleration 3 mis#, Calculate the acceleration of man ‘smooth surface ‘R at that instant. a SECTION (H) : PSEUDO FORCE H-1, An object of mass 2 kg moving with velocity 10] m/s is seen in a frame moving with velocity 101 mis. ‘What will be the value of ‘pseudo force’ acting on object in this frame. H-2. An object of mass 2 kg is placed at rest in a frame (S,) moving with velocity 107+] m/s and having acceleration 61+ 10] m/s*. This objects also seen by an observer standing in a frame (S,) moving with velocity 51+10] mis. () Calculate ‘Pseudo force’ acting on object. Which frame is responsible for this force. (i) Calculate net force acting on object with respect to S, frame. (ii) Calculate net force acting on object with respect to S, frame. Scanned with CamScannerH-3._ In the adjoining figure, a wedge is fixed to an elevator moving upwards with an ‘acceleration “a’ A block of mass 'm’ le placed over the wedge ta Find the acceleration of the block with respect to wedge. Neglect friction. oy SECTION (I) : CIRCULAR MOTION IN HORIZONTAL PLANE Ae 14. Asphere of mass 200 gm is attached to an inextensible string of length 130 cm whose upper end is ‘ixed to the ceiling. The sphere is made to describe a horizontal circle of radius 50 cm. Calculate the period time of this conical pendulum and tke tension in the string. ur 4974) 12. Amosqulto le siting on an L.P. record ofa gramophone disc rotating on a turn table at 33 + revolvution per minute. The distance of the mosquito from the centre of the tum table is 10 em. Show that the friction coefficient between the record and the mosquito is greater than x"/ 81. Take g = 10 mis? 13. Amotorcyclist wants to drive on the vertical surface of wooden ‘wel’ of radius 5 m, with a minimum speed of ‘5,5 v/s. Find the minimum value of coefficient of fiction between the tyres and the wall ofthe well . (Lake 9 = 10 mis?) SECTION (J) : MOTION OF A VEHICLE, CENTRIFUGAL FORCE AND ROTATION OF EARTH J4, When the road is dry and ooefficient of friction is 4, the maximum speed of a car in a circular path is 10 ims“, Ifthe road becomes wet and coefficient of friction become >, whatis the maximum speed permitted? J2 Find the maximum speed at which a car can tum round a curve of 30 m radius on a level road if the Coefficient of friction between the tyres and the road is 0.4 [g = 10 m/s] IREE 1986) 43° Acyciist moving with a speed of 4.9 ms on a level road can take a sharp circular tum of radius 4 m, then find the coefficient of friction between the cycle tyres and road. J4. Atrain has to negotiate a curve of radius 400 m. By how much height should the outer rail be raised with respect to inner rail fora speed of 48 km/hr ? The distance between the rails is 1 m= 15. Apark has radius of 10 mif a vehical goes around it at an average speed of 18 km/hr, find proper angle of banking and ifthe road is horizontal (no banking) ; what should be the minimum friction coefficient 50 that a scooter going at 18 km/hr does nat skid. J6 — Acircular road of radius 1000 m has banking angle 45°. Find the maximum safe speed of a car having mass 2000 kg, if the coefficient of friction between tyre and road is 0.5, SECTION (K) : KINETIC FRICTION KA. Find the direction of friction forces on each block and the ground (Assume all surfaces are rough and all velocities are wite respect fo ground). ep ems DS te c Less > => 5m sme} A m K.2. The wheel shownis fixed al ‘O' and is in contact with a rough surface as shown . The wheel rotates with an angular velocity o. What is the direction and nature of fiction force on the wheel and on the ground. = On K3.__ Inthe following figure, find the direction of friction on the blocks and ground 2am a Feon Scanned with CamScannerk-4. Inthe following figure, find the direction and nature of friction on the block. < - ae fo k-5. —Ablock is shot with an initial velocity Sms-* on a rough horizontal plane. Find the distance covered by the block till it comes to rest. The coefficient of kinetic friction between the block and plane is 0.1, SECTION (L) : STATIC FRICTION L+1, The person applies F force on smaller block as shown in figure. The coefficient of static friction is » between the blocks and the surface. Find the force exerted by the vertical wall on mass M . Whats the value of action-reaction forces between m and M? wh L-2. The angle between the resultant contact force and the normal force exerted by a body on the others called the angle of friction. Show thal, if 2. be the angle of friction and 1 the coefficient ofstaticfriction, 4 < tan-*yt 3. Armonkey of mass mis cimbing a rope hanging from the roof with acceleration a. The coefficient of static friction between the body of the monkey and the rope is yt. Find the 2 mg/(? m7 Three monkeys A, B and C with masses of 10 , 15 & 8 Kg respectively ‘are climbing up & down the rope suspended from 0 . At the instant represented , Ais descending the rope with an acceleration of 2 m/s? & Cis pulling himself up with an acceleration of 1.5 m/s? . Monkeys Bis climbing up with a constant speed of 0.8 m/s . Treat the rope and Monkeys as a complete system & calculate the tension T in the rope at D. (g= 10 m/s?) " In the figure shown Cis a fixed wedge. Ablock B is kept on the inclined surface of the wedge C. Another block Ais inserted in a slot in the block B as shown in figure. A light inextensible string passes over a light pulley which is fixed to the block B through a light rod. One end of the string is fixed and other end of the string is fixed to A.S is a fixed support on the wedge. All the surfaces are smooth. Masses of A and B are same. Find the magnitude of acceleration of Aand B. (sin 37° = 3/5) A\lift_is moving upwards with a constant acceleration a = g. A small block A of mass 'm'is kept on a wedge B of the same mass 'm'. The height of the vertical face of the wedge is “h’. Ais released from the top most point of the wedge. Find the time taken by Ato reach the bottom of B. All surfaces are smooth and B is also free to move. bead of mass mis fitted on to.a rod of a length of 2¢ and can move on it without friction. Atthe initial moment the bead is in the middle of the rod. The rod moves transiationalyyin a horizontal piane with an acceleration ‘a’ in a direction forming an angle a with the rod. Find the acceleration of the bead relative to the rod, the reaction force exerted by the rod on the bead, and the time when the bead will leave the rod. A caris speeding up on a horizontal roadwith a constant acceleration a. Calculate in the following situations in the car. () Aballis suspended from the ceiling. Find the angle made by the string ifthe ball & string remain static with respect to car. i) Ablock is kept on a smooth fixed incline and does not slip on the fixed incline with the horizontal A block is kept on the floor of an elevator at rest. The elevator starts descending with an acceleration of 12 m/ 's?Find the displacement of the block during the frst 0.2s after the start. Take g = 10 mvs*. Ablock of mass ‘m’ moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is p. The block is given an initial speed v,. As a function of the instantaneous speed ‘v' write () the normal force by the wall on the block, (ii) the frictional force by the wall and (ii) the tangential acceleration of the block. (i) obtain the speed of the block after one revolution. Scanned with CamScanner29. 30. 31, 33, 35. 37. ‘A smooth rod PQ is rotated in a horizontal plane about its mid point M which is h= 0.1 m vertically below a fixed point Aat a constant angular velocity 14 rad/s. A light elastic string of natural length 0.1 m requiring 1.47 Nlem has one end fixed at Aand its other end attached to a ring of mass m= 0.3 kg which is free to slide along the rod. When the ring is stationary relative to rod, then find inclination of string with vertical, tension. in string, force exerted by ring on the rod. A table with smooth horizontal surface is fixed in a cabin that rotates with a uniform angular velocity «in a circular path of radius R (igure). Asmooth groove AB of length L(< < R) is made on the surface of the table The groove makes an angle @ with the radius OA of the circle in which the cabin rotates. A small particle is kept at the point A in the groove and is released fo move along AB. Find the time taken by the particle to reach the point B. A uniform metallic chain with a length ¢ and whose ends are joined togethers fitted onto a horizontal wooden disc as shownin the figure. The ‘isc rotates with a speed of n revolutions per second. Find the tension Tin the chain ifits mass is m. ‘A4kg block is attached to a vertical rod by means of two strings of equal length. When the system rotates about the axis ofthe rod, ’ the strings are extended as shown in figure. (@ Howmany revolutions per minute must the system make in order for the tension in the upper chord to be 20 kgf? (©) Whatis the tension in the lower chord 7 Ablock of mass mis kept on a horizontal ruler. The friction coefficient between the ruler and the block is, in, The ruler is fixed at one end and the block is at a distance L from the fixed end. The ruler is rotated about the fixed end in the horizontal plane trough the fixed enc. (A) What can the maximum angular ‘speed be for which the block does not slip ? (B) If the angular speed of the ruler is uniformly increased from zero at a constant angular acceleration a, at what angular speed will the block sip 7 Two particles A and B each of mass m are connected by amassiess (7 string. Ais placed on the rough table. The string passes over a sma, 20 with the vertical. 1um coefficient of friction between Aand the table so that during the motion of mass B. ‘The rear side of a truck is open and a box of 40 kg mass is place ‘away from the open end as shown in figure. The coefficient of friction] between the box and the surface below itis 0.18. On a straight road, the truck starts from rest and accelerates with 2 ms. Al what distance| from the starting point of the truck does the box falloff the truck? (Ignore the size of the box). oO OO Inthe figure shown below the friction between the 4 kg block and the incline as 4, and between 8 kg and incline is u,- Calculate the accelerations of the blocks when (a) 1, = 0.2 and pi, = 0.3 (b) u, = 0.3 and pi, = 0.2. (take g = 10 mis") In figure block 1 is one fourth the length / of block 2 of mass also one fourth. No friction exist between block 2 and surface on which it rests. moves when only half of block 1 is still on block 2. Block 1 and block 3 have same mass. Scanned with CamScanner33, at. a2. In the given situation it is known that when released the blocks slide. Find the accelerations of the two blocks. Also find the time when the small block wil fal off from the larger biock. Abead of mass m'is fitted onto a rod wth a length of ¢, and can move onit with friction having the coefficient of fiction u.At the inal moment the bead is in the middle of the rod. The rod moves transiationally in a horizontal plane with an ‘acceleration a’ in the direction forming an angle a wth the rod. Find the time when the bead will eave the rod : (Neglect the weight ofthe bead). M,=3kg, M,=4kg and M, = 8 kg. 1 between any two surface is 0.25, Pulleyis frictionless {and string is massless. Ais connected to the wall through a massless rigid rod.(g=10m/s") (2) find the value of F to keep C moving with constant speed J «ffc (b) if Fis 200 N then find acceleration of B What is the minimum value of force required to pull a block of mass M on a horizontal surface having Coefficient of friction 1? Also find the angle this force makes with the horizontal, Inthe figure shown, the coefficient of static friction between C and ground is 0.6, coefficient A of static friction between Aand Bis 0.25, coefficient of static friction between B and Cis, zero. Find the rrinimum value of force ‘F’ to cause sliding betweenAandB.Messes of |B_[--F ‘A Band C are respectively 2 kg, 4 kg and 5 kg. c Inthe figure shown, the coefficient of static fiction between B and the walls 213 and the coefficient of kinetic friction between B and the wall is 1/3. Other contacts are smooth. Find the minimum force ‘F' required to lif B, ¥ up. Now ifthe force applied on Ais siightly increased than the calculated value of minimum force, then find the acceleration of 8. Mass of Ais in, and the mass of Bis m. Take tan 0 = 3/4 plank of mass m, with a bar of mass m, placed on it lies on a smooth horizontal plane. A horizontal force ‘growing with time t as F = kt (kis constant) is applied to the bar. Find how the accelerations of the plank a, and of the bar a, depend on t, if the coefficient of fiction between the plank and the bars equal tp. Draw the approximate plots of these dependences. A block of mass 2 kg is pushed against a rough vertical wall wth a force of 40 N, coefficient of static friction being 0.5. Another horizontal force of 15 N is applied on the block in a direction parallel to the wall. Will the block move ? if yes , in which direction & what is the acceleration ? ifno, find the frictional force exerted by the wall on the block. Scanned with CamScannerANSWERS LEVEL-1I SECTION (A) AA, Gravitational. Electromagnetic, Nuclear Gravitational Frictional force, which is a type of electromag- netic force. 20N A-5. No Vertical wall does not exert force on sphere (N'= 0). w AT. () T0NGEN (N= 0), mg=10N (ii) Gravitational between earth and block N N 7 ee 7 AB Normal reaction mg Mg SECTION (B): B4. 2mg Ri, B2 () ipa ao (N=F Ms Mg (ip (ymg.mg. B.3. mgcoso B.A. (2610 mq B-5. (a) MN (b) equal magnitude w 4000 a 8 SECTION (C): CA. (I)zer0 (i) 10N C2, (a) 10N, (b) 10N, (c) 10N. ©-3. (a) 10N, (b) 15N, (c) 20N. C-4, 5N,3N. ‘500 Bs. N, N.Ny= iy 2 4 a C5. (2) P=67m () FP =4N WE =8N SECTION (D): cos, D+. cos, D2 D-3. utan6. D4, V,=3V,= 1.8 mis in downward direction. D5. Vp, = 5m/s downward V, = 25 mis upward SECTION (E) : -,_ 2, 60 60 Et. @IFI=IFI= fp N ()W= 5 N E-2. 0.25Nalong the motion, zero and 0.25 N oppo- site to the motion. IFL= (a0)? + (108)? = 112.08N mg. 2(m,+m,) E3. Lr (a) 4.8.N.3.6N,24N,1.2N (b)F=6N ()02N Scanned with CamScannerSECTION (F): Fel. ()600N, (li) GOON, (iil) 600 N, (iv), 720 N, (v) 480 N, (vi) 720N, (vl) 720 N, (vill) 480N (i) 100 N, (i) 100 N, (il) 100 N, (iv) 120 N, (v) BON, (vi) 120 N, (vil) 120 N, (vil) 80 N. SECTION (G): G+. a/2, towards left. F2, 15 G2. Pimist, opposite direction SECTION (H): HA. F=0 H-2. (i) F= -10i-20] N, Due to acceleration of frame s, (i) 10+20] NG zero. H-3. (gta) sing SECTION (I): iM ale sec., “2 N (with w(M+m)g action-reaction forces between m and M is F — mg for F > mg and 0 for F < jing LS. Upwards. = m(g+a) si L4 ostar’ > SECTION (M) Met. y,=0.60, 4,=0.52 M2. (a) a,=3mis,a,=0,{,=0, f,=0 (b) a= 1 mis? a =0, f, = 25N., f, = 25N (0) a, =5 mist 2, = 10 mis? ; 1, = 25N ; mis? ay = m/s? f, = 5N 2Mgcoso 2 1+sin?0 " os! ee ee a Load ~ 1+sin?@ ® “ s Scanned with CamScanner10. 12. 14. 15, 16. 47. 18. 20. 24. 22. 23. Moe = Ma 49. ,=Mg and T,= 2 = Mo rey Between 70/N and 105 N a @ 7 5 ae 1. Dim 60cm 13, 12 mis. 2gsindcosd Agsin?0 8° 4a3sint0 143sin70* a, = 1 mis? (1), a, = Im/s? (7) = 4 mis? () 19. 1.5 mis. (@) T=mg- ‘;(o)tengthof spring wilbecome less than'‘¢’ and T = 0 in string. For the system = 33g =m,a,4m,a, + m2, = 10(-2) + 15 (0) +8 (312) = T=93g-8=322N In(1+ sin? 9) 2gsin’ 2 i eng)? +(masina)? 28. 29. 30. 32, 33. 88 37. 38. 45. IMgsino + #mgeos0 ws migeos0 tan'(a/g) ineach case] 27. 20 cm 2 2 oe w vem (iy > yew 147 cos 0= 9/5, T=9.8N,N =< > =2.94N 50 a coe ‘o*Reosd Sh. Toate (a) 9% per min = 30. permin, (1508 2 (A) Vig7l (8) (3 -2c0s6 20m (@) 24 mis*both ; (b) 3.2 mis?, 2.4 mis? Tune %2* 82-314) ,=asino- # goose; aa +1 Viens oar tan. yr <2 -2 Fg = 5 9 (b= When 1 < t,, the accelerations a, =a, =kt/(m, +m, ;whent > t, a, = pgm, /m,, a, = (at pm,g) /m,, Here t, =iigm, (m, + m,) km. ‘ It wil move at an angle of 53° with the 15N force and with acceleration 5/2 m/s. Scanned with CamScanner