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1 11 th Grade Phsics Workbook METU Development Foundation High School 1 Answers

2 11th Grade Chapter-1 Newton s Laws Motion Activit Applications of Newton s Laws Three blocks of masses 5 kg, 3 kg and 2 kg are tied with ropes and pulled b a horizontal force of F=60 N. The coefficient of friction between the blocks and the surface is 0,2. Calculate the acceleration of the blocks. Take all the objects as a single bod having mass of (5+3+2)=10 kg and draw a free bod diagram to show all the forces on a diagram. F f =100.0,2 F f =20 N F N =100 N F=60 N W=100 N F net =m total.a (60-20)=10.a a=4 m/s 2 60.sin30 o Two blocks are connected b a string on an inclined plane as shown in the figure. When the sstem is released, tension of the rope is measured to be 24 N. Calculate the mass of m 1. (g=10 m/s 2. Pulles are supposed to be weightless and frictionless.) F N2 60 N T 30 o 60.cos30 o 10m.sin30 o F N1 10m T-(10m.0,5)=m.a (60.0,5)-T=6.a 24-5m=m 30-24=6.a a=1 m/s 2 m=4 kg T 30 o 10m.cos30 o

3 11th Grade Chapter-1 Newton s Laws Motion Activit Applications of Newton s Laws The inclined planes given in the figure above are all frictionless. The masses of the objects are related as m K =m L <m m and β is greater than α. Compare the accelerations of the objects when the are released. F N The surfaces given in the figures above are all frictionless. The masses of objects X, Y and Z are m, 2m and 3m respectivel. When the sstems are released, the accelerations of the sstems are a 1 and a 2. The tensions in the connecting ropes are T 1 and T 2. Calculate the ratio of accelerations and tensions. (Pulles are supposed to be weightless and frictionless.).sina.sink=m.a For Figure-I; For Figure-II;.cosa k a=g.sink Acceleration depends on the gravitational acceleration and the angle of inclined plane. As the angle gets bigger acceleration gets bigger. It is independent on the mass. So; a L >a K =a M =(m+2m).a 1 =3m.a 1 a 1 =g/3 T 1 =2/3 a 1 4 = a 2 3 and =(m+3m).a 2 =4m.a 1 a 2 =g/4 T 2 =3/4 T 1 8 = T 2 9

4 11th Grade Chapter-1 Newton s Laws Motion Activit Applications of Newton s Laws When the sstem given in Figure-I is released, object Y starts to move rightward with an acceleration of a. When the sstem given in Figure-II is pulled b a horizontal force of F, object Y starts to move leftward with an acceleration of a. What is the magnitude of force F in terms of? (All the friction forces and the weight of the pulles are ignored.) For Figure-I; 2=(m+2m).a 2=3m.a a=2g/3 F=3m(2g/3)+2 F=2+2=4 For Figure-II; F-2=(m+2m).a F-2=3ma F=3ma+2 The masses of the objects K, L and M are 2 kg, 1 kg and 2 kg respectivel. The sstem given in the figure is released. After a while the rope connecting objects K and L breaks down. What can be said about the motion of object M? (All the friction forces and the weight of the pulle are ignored.) Firstl, the total weight on the right side is greater. K and L start to move downward and M starts to move upward with a constant acceleration. When the rope between K and L breaks down, the net force on the sstem will be zero. M will move at stead speed which is equal to the speed that it has while the rope breaks down.

5 11th Grade Chapter-1 Newton s Laws Motion Activit Applications of Newton s Laws Object K is fired from the bottom of an inclined plane with an initial speed of v, it can reach point X then moves downward. The magnitude of its acceleration toward point X is a 1 and the magnitude of its acceleration when it moves downward is a 2. The coefficient of friction is 0,5. What is the ratio of a 1 to a 2? An object of mass m is stationar on a horizontal surface. Then a horizontal force of F is applied on the object. The acceleration of the object versus the magnitude of the applied force graph is given above. Assume that the magnitude of the maimum static friction force is equal to the magnitude of the kinetic friction force. Calculate the mass of the object and the coefficient of friction. moving upward; F f =12 N (-.sin37 o )-(F f )=m.a 1 (-.sin37 o )-(0,5..cos37 o )=m.a 1 (-6)-(4)=a 1 then a 1 =-10 m/s 2 moving dowward; (.sin37 o )-(F f )=m.a 2 (.sin37 o )-(0,5..cos37 o )=m.a 2 a 1 (6)-(4)=a 2 then a 2 =2 m/s 2 = 5 a 2 F-F f =m.a 27-12=m.5 m=3 kg F f = µ.f N 12= µ.3.10 then µ=0,4

6 11th Grade Chapter-1 Newton s Laws Motion Activit Inertial & non-inertial reference frames The coefficient of friction between the car and the bo is 0,5. What would be the minimum magnitude of the acceleration of the sstem in order to keep the bo stationar with respect to the car? The inclined plane moves with a constant acceleration. The bo of mass m is stationar with respect to the inclined plane. Epress the acceleration of the inclined plane in terms of inclination angle α. (Ignore friction.) F fictitious =ma F f F N F f = µ.f N F fictitious = ma Object is stationar; F fictitious = F N and F f = ma ma.cosα α ma.sinα nα.cosα ma.sin F N.sinα.cos Object is stationar; m.g.sinα=m.a.cosα a=g.tanα µ.m.a =m.g 0,5.m.a=m.10 a=20 m/s 2

7 11th Grade Chapter-1 Newton s Laws Motion Activit Inertial & non-inertial reference frames 3. The elevator moves upward with a constant acceleration of 3 m/s 2. What is the magnitude of the tension in the rope that connects the 2 kg object to the ceiling of the elevator? T 4. The horizontal surface is frictionless and the coefficient of friction between 1 kg object and 4 kg object is 0,3. What is the maimum magnitude of the horizontal force F in order to keep the 1 kg object stationar with respect to 4 kg object? F N =10 N ma F fictitious =ma=1.a=a F f =0,3.10=3 N object is in equilibrium; T=+ma T=(2.10)+(2.3) T=26 N F fictitious =F f a=3 m/s 2 10 N The move together. F=(1+4).3=15 N

8 11th Grade Chapter-1 Newton s Laws Motion Activit Inertial & non-inertial reference frames a) motion 5. The elevator moves upward with a constant acceleration of 2 m/s 2. a) What is the magnitude of the acceleration of object X with respect to the elevator? b) What are the magnitudes of the accelerations of objects X and Y with respect to the ground? (All the friction forces and the weight of the pulle are ignored and g=10 m/s 2.) T 20N 2a=4 N motion T 30 N 3a=6 N T-24=2.a / 36-T=3.a / 36-24=5.a / a / =2,4 m/s 2 b) a X =0,4 m/s 2 (downward) a =4,4 m/s 2 (upward) 6. A block of mass 1 kg is placed on an inclined plane of mass 3 kg. Inclined plane is pushed b a horizontal force of 40 N as shown in the figure. Calculate the acceleration of the block with respect to the inclined plane. (Ignore friction and g=10 m/s 2.) ma 0,8. 37 o 0,6.ma 0,8.ma 37 o F N 0,6. 0,8.ma - 0,6. = m.a 8-6 = 1.a a = 2 m/s 2 (upward) F=m.a sstem 40=4.a sstem a sstem =10 m/s 2

9 11th Grade Chapter-1 Newton s Laws Motion Activit Inertial & non-inertial reference frames When the car is accelerating toward right with a constant acceleration of a, boes A and B remain stationar with respect to the car. What is the magnitude of the acceleration of the car (a)? (All the friction forces and the weight of the pulle are ignored and g=10 m/s 2.) The horizontal surface is frictionless and the coefficient of friction between 2 kg object and 3 kg object is µ. When the sstem given in the figure is released, all objects move together with maimum acceleration that the can move together. Calculate the coefficient of friction (µ). (Pulle is frictionless and its weight is ignored. g=10 m/s 2.) For object B; It is stationar with respect to the car. 20-T=0 T=20 N For object A; It is stationar with respect to the car. T=m A.a sstem 20=4.a sstem a sstem =5 m/s 2 For the sstem of the objects; F net =m total.a sstem 5.10=(2+3+5). a sstem a sstem =5 m/s 2 For 2 kg object; F fictitious =F friction then m. a sstem =µ.m.g µ= (a sstem /g)=(5)/(10)=0,5

10 11th Grade Chapter-1 Newton s Laws of Motion Additional Problems 1. The sstem given in the figure is frictionless. When the sstem is pulled b a vertical force F, the acceleration of the pulle and 1 kg object would be 2 m/s 2 and 6 m/s 2 respectivel. Calculate the magnitude of the force F in newtons. (Ignore friction, pulle is not rotating and g=10 m/s 2.) 2. The objects move with a constant acceleration of 3 m/s 2 when a horizontal force F is applied on 6 kg object. The horizontal surface is frictionless and the coefficient of friction between 4 kg object and 6 kg object is 0,3. Calculate the magnitude of the horizontal force F in newtons. (Pulle is frictionless and its weight of the pulle is ignored. g=10 m/s 2.) For 1 kg object; For pulle For 4 kg object; For 6 kg object; T-=m.a T-10=1.6 F-2T-m pulle.g=m pulle.a pullle F-32-5=0,5.2 T-F f =m 1.a T-(0,3.40)=4.a T=4a+12 F-T-F f =m 2.a F-T-12=6.a F-24=(6.3)+12 T=16 N F=38 N T=(4.3)+12=24 N F=54 N

11 11th Grade Chapter-1 Newton s Laws of Motion Additional Problems The sstems given above are frictionless. The ratio of the tensions T 1 /T 2 = 3/5 when the sstems are moving. What is the ratio of the masses m 1 /m 2? (Pulles are frictionless and weights of the pulles are ignored.) When a horizontal force F is applied on 2 kg object, 2 kg and 4 kg objects move together. The horizontal surface is frictionless and the coefficient of friction between 4 kg object and 2 kg object is 0,5. Calculate the maimum magnitude of the horizontal force F to move the objects together. For Figure-I; m 2.g=(m 1 +m 2 ).a 1 T 1 =m 1.a 1 For Figure-II; 2m 2.g=(m 2 +2m 2 ).a 2 2m 2.g=3m 2.a 2 T 1 T 2 = 3 5 = m 2.g m 1. (m 1 +m 2 ) 2m 2.g 3 3.m 1 2.(m 1 +m 2 ) For 2 kg object; For 4 kg object; F-F f =2.a F f =4.a F-(0,5.20)=2.a 10=4.a F=2a+10 a=2,5 m/s 2 F=(2.2,5)+10 F=15 N a 2 =2g/3 T 2 =m 2.a 2 =2m 2 g/3 m 1 m 2 = 2 3

12 11th Grade Chapter-1 Newton s Laws of Motion Additional Problems 5. When the wagon moves rightward with a constant acceleration of a, the ball inside the wagon is in equilibrium with respect to the wagon as shown in the figure. Calculate the magnitude of the acceleration of the wagon. 6. The bo of mass 70 kg measures his weight as 490 N when the elevator moves downward. What is the magnitude of the acceleration of the elevator? Is the elevator speeding up or slowing down? T.cos37 o F fictitious =ma 37 o T T.sin37 o F N ma F N +ma= ma=t.sin37 o =T.cos37 o a=3g/4 490=700-(70.a) a=3 m/s 2

13 11th Grade Chapter-1 Newton s Laws of Motion Additional Problems 7. F N The elevator moves downward and decelerates at 3m/s 2. An object of mass 4 kg is pulled b a horizontal force of F and it accelerates at 2 m/s 2 with respect to the elevator. If the coefficient of friction between the mass and the elevator s floor is 0,4 then what is the magnitude of the force F? F f =0,4.( ) F f =20,8 N 8. Three objects A, B and C are stationar on horizontal surfaces. Horizontal forces are applied to move the objects. The acceleration versus applied force graphs of the objects are given above. Answer the following questions. a) Compare the frictions forces on the objects. b) Compare the masses of the objects. c) Compare the coefficients of friction of the horizontal surfaces where B and C move. d) Compare the coefficients of friction of the horizontal surfaces where A and B move. a) C>B=A F f F fictitious =ma F F-F f =m.a B using the graphs; forces that are applied to start the motion of the objects are compared. b) A<B=C The reciprocal of the slope of acceleration versus time graph gives the mass of the object. c) B<C F-20,8=4.2 F=28,8 N Masses of B and C are equal and the friction forces on them are related as C>B. The same relation must be among the coefficient of frictions. d) A<B The friction forces on A and B are the same. Mass and the coefficient of friction are inversel proportional.

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