11th Grade. Review for General Exam-3. decreases. smaller than. remains the same

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1 1. An object is thrown horizontally with a speed of v from point M and hits point E on the vertical wall after t seconds as shown in the figure. (Ignore air friction.). Two objects M and S are thrown as shown in the figure. The times of flights of the objects are the same. (Ignore air friction.) If the gravitational acceleration was smaller, how would h and t change? decreases h : _ remains the same t : _ Read the following statements. If the statement is CORRECT print "C", or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) or phrase(s). C The height h 1 is one-fourth of the height h. C W The change in velocity of object M is equal to the change in velocity of object S. The speed of object M when it hits the ground is equal to the speed of object S when it hits the ground. smaller than

2 3. An object is thrown horizontally from point S with an initial speed of v and its hits point P on the wall. All the friction forces are ignored. The points on the wall are equally spaced. 4. Objects X and Y are thrown with the same initial speeds as shown in the figure. (Figure is composed of identical squares and air friction is ignored.) If the object were thrown horizontally with the same initial speed from point T, where would it hit on the wall? Prove your answer with calculations. first condition; d= v.t 5h= 1.g.t second condition; d= v.t / t / = t h / = 1.g. t = g.t = 5h 4 At which point object Y is, when object X is at point N? Prove your answer by calculations. for object X; 3h= 1.g.t and 6h= v.t for object Y; h Y = v.t - 1.g.t = 6h - 3h h Y =3h It would hit a point between points K and L. so, it would be at point M.

3 5. A plane flies horizontally with a constant speed at an altitude of h when a package is released from the plane. (Ignore friction.) 6. An object is thrown obliquely from the ground and it follows the path as shown in the figure. h max is the maximum height reached by the object. (Ignore air friction.) Read the following statements. If the statement is CORRECT print "C", or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) or phrase(s). C C W The package is freely falling with respect to the pilot of the plane. The package is thrown horizontally with respect to an observer on the ground. The velocity of the package is constant with respect to the pilot of the plane. increases uniformly What is the ratio of h to h max? h max = 1.g.4t h / = 1.g.t h= 3.g.t h h max = 3 4

4 7. Object X is thrown obliquely form the ground with an initial speed of v. After a while object Y is thrown vertically upward with the same initial speed. They collide at point O which is the maximum height reached by object X. (Ignore friction and sin37 o =0,6.) 8. Objects X, Y and Z are thrown obliquely with speeds of v 1, v and v 3 as shown in the figure. (Ignore friction. The figure is composed of identical squares.) What is the speed of object Y at point O in terms of v? for object X; h= v average.t up h= 0,6.v.0,6.v g = 0,36.v g for object Y; h= v average.t up h= v+v /. v - v / g = v -( v / ) g v / = 0,8.v Read the following statements. If the statement is CORRECT print "C", or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) or phrase(s). C C W The range of object X is equal to the range of object Z. The maximum height reached by object X is equal to the maximum height of object Y. The time of flight of object X is equal to the time of flight of object Z. Y

5 9. An object is fired from point K with an initial kinetic energy of 30 J. It can reach point L, slides down and its kinetic energy is 14 J at point K. The surface of the inclined plane has a constant friction. (sin37 o =0,6; sin37 o =0,8 ) kg and 4 kg objects are connected by an elastic spring and they are applied a vertical force of 60 N as shown in the figure. The spring constant of the spring is 7 N/m. Friction and the mass of the spring are ignored. (g=10 N/kg) Read the following statements. If the statement is ABSOLUTELY CORRECT print "A", if it is POSSIBLE print "P" or if it is WRONG then print "W". You have to correct the wrong statements by using an appropriate word(s) or phrase(s). What is the maximum elastic potential energy of the spring in J? W A P The potential energy of the object with respect to the ground is 16 J. J The work done by friction force between points K and L is -8 J. The magnitude of the friction force on the surface of the inclined plane is 10 N. 0n 4 kg object; 40 - T = 4a a= 4 m / s 0n 65 kg object; 60+T - 60=6a 40 - T = 4a T = 4 N 0n spring; F =k.x 4= 7.x max x max = 1 3 m PE max = 1.k.x = = 4 J

6 11. The masses of objects K and L are 4m and m respectively. The system given in the figure is released. The pulley is frictionless and supposed to be weightless. 1. Object X and Y have masses of 4 kg and 1 kg respectively. They are tied by a massless rope as shown in the figure. When the system is released, object X starts to move downward and hits point C on the horizontal surface while object Y starts to move from point A to point B. The weight of the pulley and all the friction forces are ignored. (g=10 N/kg, sin30 o =0,5 and sin37 o =0,6) What is the maximum height reached by object L from its initial position in terms of h? 6 m 5 m 1 m Until K reaches the ground; 4mgh=mgh+E+4E E = 3mgh 5 after K hits the ground; E = 3mgh 5 = mgh / h / = 3h 5 h (from the ground)=h+ 3h 5 = 8h 5 What is the speed of object Y at point B in m/s? PE initial = KE X + KE Y = 1.4.v v 80= 54.v v = 4 m / s

7 13. A 0,5-kg mass is attached to one end of a spring and the other end is tied to a wall. The spring-mass system is pulled and released on a frictionless horizontal surface. The energy (potential & kinetic) versus displacement graph of spring-mass system is given. 14. The mass of object K is 3m and the mass of object L is m. When the system given in the figure is released, the elastic spring compresses by an amount of x. (Friction forces, the weight of the pulley and the weight of the spring are ignored.) from the graph; KE = 1 J ME = 16 J PE = 4 J a) What is the maximum speed of the mass in m/s? KE max = 16 J 16= 1.0,5.v max v max = 8 m / s b) What is the maximum compression of the spring in cm? PE max = 1.k.x max PE = 1.k.x 4 = 1.k.(0,3) x max = 0,6 m =60 cm What is the maximum elastic potential energy stored in the spring in terms of mgx? 0n K; 3mg - T =3ma a= g 0n L; T -mg=ma T -mg=ma T = 3mg F net 0n K; F net = 3mg W net = PE spring = F net.x = 3mgx

8 15. The magnitude of the net force versus displacement graph of an object that is initially at rest on a horizontal surface is given. 16. A kg object is released from the position as shown in the figure. The length of the rope is 1 m and the spring constant of the elastic spring is 1000 N/m. (g=10 N/kg, the mass of the rope is ignored.) Plot kinetic energy versus displacement graph of the object. Area of F versus x graph gives the change in KE. PE =0 What is the maximum compression of the spring in cm? ΔKE 1 = F.x ΔKE = 0 ΔKE 3 = F.x PE initial = mgh=.10.1= 0 J PE max = 1.k.x max = x max 0= x max x max = 0, m = 0 cm

9 17. The masses of objects K and L are kg and 1 kg respectively. They are moving toward each other with constant speed of 10 m/s and 5 m/s on a frictionless horizontal surface as shown in the figure. They collide and stick. 18. The masses of object K and L are m K and m L respectively. Object K is released from point A. It moves downward on the frictionless path and collides object B that is stationary at point B and stick. The combined mass can merely reach point C. What is the velocity of the combined mass in m/s? Σ P initial = Σ P final (.10)+(1.(-5))=(+1).v 0-5 =3v v = 5 m / s What is the ratio of m K to m L? for object K; 4m K gh= 1 m Kv v =8gh for combined mass; (m K + m L )gh= 1 (m K + m L )v final v final = gh PE =0 v final = v Σ P initial = Σ P final (m K.v)=(m K +m L ).v / (m K.v)=(m K +m L ). v m K m L = 1

10 19. The masses of object X and Y are m and m respectively. Object X moves with a constant speed of v on a frictionless horizontal surface. It collides object Y that is stationary on the horizontal surface as in Figure-1. After collision, object X moves with a constant speed of v and object Y can reach at a height of h as in Figure-. ( g is the gravitational acceleration.) 0. The masses of object K and L are m K and m L respectively. They are moving with constant velocities of +15 m/s and +10 m/s on a frictionless horizontal surface as shown in the figure. K collides L elastically and its velocity after the collision is +10 m/s. PE =0 What is the ratio of m K to m L? What is the speed of object X (v) after collision in terms of g and h? Σ P initial = Σ P final (m.v)=(m.(-v))+(m.v / ) v / = 3v for object Y; 1.m. 3v = m.g.h v = 4 gh 3 vk + u K = vl + u L = 10+u L u L = 15 m / s Σ P initial = Σ P final (m K.15)+(m L.10)=(m K.10)+(m L.15) m K m L = 1

11 1. The masses of object K and L are 8 kg and 4 kg respectively. They are placed at the two sides of an elastic spring that has spring constant of 400 N/m. Then the spring is compressed by 1 m and objects are tied by a rope as shown in the figure. (The horizontal surface is frictionless and the mass of the spring is ignored.). The masses of object K and L are kg and 3 kg respectively. They are moving with constant velocities of +0 m/s and +10 m/s on a frictionless horizontal surface as shown in the figure. They collide and stick. What is the amount of energy lost during collision in J? If the rope were cut, what would be the velocities of the objects (in m/s) after they leave the spring? PE spring = = 100 J Σ P initial = Σ P final (.0)+(3.10)=(+3).v v = 14 m / s Σ P initial = Σ P final KE initial = = 550 J (0)=(8.v K )+(4.v L ) v L = -V K 100= 1.8.v v v = 10 m / s V K = 10 m / s and V L = 0 m / s KE final = 1.(+3).14 = 490 J KE final =(550 J)-(490 J)=60 J lost

12 3. A bullet of mass m moving horizontally at a constant speed of v hits a stationary wooden block of mass 0m as in Figure-1. The bullet penetrates the wooden block and leaves with a constant speed of v as in Figure-. (The horizontal surface is frictionless. The loss of mass during penetration is ignored. ) 4. A wooden block of mass "m" is tied to the end of a m long rope and released as shown in the figure. While the wooden block passes from point A, a bullet of mass "m" hits the block with a speed of "v" and embeds. (Ignore air friction, g=10 N/kg, sin53 o =0,8 and cos53 o =0,6.) PE =0 0,8 m What is the impulse imparted by the wooden block on the bullet in terms of mv? If the wooden block had stopped after the bullet had embedded, what was the initial speed (v) of the bullet in m/s? Impulse= Δ P bullet Impulse=m.Δ v bullet for wooden block; m.g.0,8= 1.m. ( v B ) v B = 4 m / s Impulse=m.(v final v initial) Impulse=m.(v - v)=-mv Σ P initial = Σ P final (m.v)+(m.(-4))= 0 v = 4 then the initial speed of the bullet is v =8 m / s.

5. A force of magnitude of "F" is applied as shown in the figure.

(Figure is composed of identical squares.

Torque with respect to point X; τ X =(.1)+(1.1)= 3 units =3 N.m 1 unit = 1 N.

3)= 3 units τ Y = +3 N.m Torque with respect to point Z; τ Z =(.

13 5. A force of magnitude of "F" is applied as shown in the figure. The torque with respect to point X is "- 3 N.m". (Figure is composed of identical squares.) What are the torques with respect to point Y and Z in N.m? Torque with respect to point X; τ X =(.1)+(1.1)= 3 units =3 N.m 1 unit = 1 N.m and is chosen as " - " direction. Torque with respect to point Y; τ Y =(1.3)= 3 units τ Y = +3 N.m Torque with respect to point Z; τ Z =(.3)= 6 units τ Z = +6 N.m with respect to point K; τ 1 = Fd τ = 3Fd τ K = 3Fd τ 3 = Fd τ K = 3Fd τ L = 4Fd τ K τ L 3 4 with respect to point L; τ 1 = 8Fd τ = Fd τ L = 4Fd τ 3 = 6Fd

14 7. A plate is hinged at point O on a frictionless horizontal surface. Four forces are applied on the plate as shown in the figure. (Figure is composed of identical squares and each side of the squares is "d" for distance and "F" for forces calculations.) 8. A uniform plate is hinged at point O on a horizontal frictionless surface. Four forces having magnitudes of F, F, 3F and 4F are applied on the plate as shown in the figure. What is the net torque with respect to point O in terms of "F.d"? with respect to point 0; τ 1 = 4Fd τ = 6Fd τ net O τ 3 = 0 τ 4 = 3Fd = 5Fd What is the net torque with respect to point O in terms of "F.r"? with respect to point 0; τ 1 = Fr τ = 3Fr τ net O = 5Fr τ 3 = 8Fr τ 4 = 4Fr

15 9. A rod is hinged at point O on a horizontal fricitionless surface. Four forces are applied on the rod. Three of them are given in the figure. Their magnitudes are F, F and 3F. (The rod is composed of identical divisions.) 30. A rod is hinged at point O on a horizontal fricitionless surface. Four forces having magnitudes of F, 3F, 3F and 4 3F are applied on the rod as shown in the figure. (The rod is composed of identical divisions and the length of each division is "d".) F 1 = F 4 = x = 3d 3 3d x d If the net torque with respect ot point O is zero, what are the magnitude (in terms of F) and the direction (up or down) of the fourth force that is applied perpendicular the rod at point A? with respect to point 0; τ 1 = 4Fd τ = 3Fd τ 13 = 3Fd τ 3 = Fd τ net O = 0 τ 4 = 3Fd=F 4.d F 4 = 3F ( ) What is the net torque with respect to point O in terms of "F.d"? (sin30 o =1/, cos30 o = 3 / ) = F 3 with respect to point 0; = F τ 1 = 4 3F. 3d= 1Fd τ = F.3d=3Fd τ net τ 3 = 0 τ 4 = 3F. d = 3Fd d O = 33Fd

16 31. A rod is hinged at point O on a horizontal fricitionless surface. Four forces having magnitudes of F, F, and 5F are applied on the rod as shown in the figure. The torque applied by force having magnitude of F with respect to point O is "- 8 N.m". (The rod is composed of identical divisions and sin37 o =0,6; cos37 o =0,8) 3. A plate is hinged at point O on a horizontal fricitionless surface. Three forces having magnitudes of F 1, F and F 3 are applied on the plate as shown in the figure. The magnitudes of the torques applied by the these forces with respect to point O are equal. (Plate is composed of identical squares.) F 1 = = F 45 o α θ sinα = 1 5 cosα = 5 = F 3 sinθ = 1 10 cosθ = 10 What is the net torque with respect to point O in N.m? with respect to point 0; τ 1 = 4F.d=8Fd τ = F.3C =6Fd τ net τ 3 = F.d=Fd 6Fd=-8 Nm F.d=- 4 3 Nm τ net O = Nm O = Fd What is the decreasing order among the magnitudes of these forces? F 1. F 1. with respect to point O; τ 1 = τ = τ 3 5.1=F =F =F =F. 1 3 F >F 3 >F 1

Name & Surname:... No:... Class: 11 /...

Name & Surname:... No:... Class: 11 /... METU D. F. HIGH SCHOOL 2017-2018 ACADEMIC YEAR, 1 st SEMESTER GRADE 11 / PHYSICS REVIEW FOR GENERAL EXAM-3 UNIFORMLY ACCELERATED MOTION IN TWO DIMENSIONS, ENERGY, IMPULSE & MOMENTUM & TORQUE DECEMBER 2017