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

2 11th Grade hapter-1 Vectors Activity Parallelogram & tip-to-tail methods Twelve vectors are given in the figure above. The magnitude of each vector is F. What is the magnitude of the resultant vector of them in terms of F? The magnitude of each vector given in the figure is F. What is the magnitude of the resultant vector of them in terms of F? A D B E F G H A + H =0 B + G =0 + F =0 D + E =0 Other 4 forces are all in the same direction and have the same magnitude of F. A D B F E A + E =0 D + =0 Other 2 forces (B and F) are all in the same direction and have the same magnitude of F. F R =4F F R =2F

3 11th Grade hapter-1 Vectors Activity Parallelogram & tip-to-tail methods Five vectors are acting on point K as in the figure. What is the magnitude of the resultant vector in newton? (Each square is 1 N along one side.) F 2 F 3 F 4 F 5 F R x y According to given figure decide whether the following operations correct or wrong. If the operation is correct print to the space supplied, otherwise print W. You have to correct the wrong operations. W W N -M K + L = M N + P + L = 0 M N + P - K = - M " + P " + M+ " K " = - 2 L " F R =2 N (upward)

4 11th Grade hapter-1 Vectors Activity Parallelogram & tip-to-tail methods 5. Three forces, F 2 are applied on different points of a cube as shown in the figure. All the forces have a magnitude of 5 N. What is the magnitude of the resultant force of them in newton? All the forces are perpendicular to each other. 6. The magnitude of force is 3 N and the magnitude of force F 2 is 4 N and they are applied on the same point. The angle between them is α. If 0 o α < 90 o then find the range of the magnitude of the resultant force. R 1 =3+4=7 N (when the angle is 0 o ) R 2 =5 N (when the angle is 90 o ) 7 N>R>5 N R 2 = R 2 =3.5 2 R=5 3 N

5 11th Grade hapter-1 Vectors Activity Parallelogram & tip-to-tail methods Three vectors X, Y and Z are given in the figure. The resultant vector is defined as R = Y X + Z alculate the magnitude of resultant vector R in meters. Y and Z are perpendicular to each other. the magnitude of their resultant vector is 4 2 m The resultant vector of vectors Y and Z is perpendicular to the opposite vector of vector X. Then, R=4 3 m K K and K L are vectors in the same plane. If the magnitude of vector K is increased, how will the magnitude of vector K+ L change? -L K K- L K+ L If the magnitude of vector K was increased, the magnitude of the sum of vectors K and L would increase. L

6 11th Grade hapter-1 Vectors Activity omponents method Three forces 6 N, 8 N and 10 N are acting on the same point as shown in the figure. alculate the magnitude of resultant force of these forces in N. R is the resultant force of forces and F 2. What is the ratio of the magnitude of magnitude of F 2? to the F 2.cos30 o =R F 2.sin30 o = F 2.(0,5)= F 2 = 1 2

7 11th Grade hapter-1 Vectors Activity omponents method The components of F on coordinates k and m are F k andf m. ompare the magnitudes of F, F k andf m. Three vectors K, L and M have the same magnitude of 1 N. What is the magnitude of K L M? Draw parallel lines from the tip of vector F to the axes k and m to show the components on that axes. K+L+M=0 K=-L - M R=K-L-M R=K+(-L-M)=2K F k F m = 5 2 R=2K=2.1=2 N

8 11th Grade hapter-1 Vectors Activity omponents method 5. Three vectors, F 2 are given. alculate the magnitude of the vector + F 2 + F 3. F 6. When the angle between two concurrent forces having the same magnitude is 106 o, the magnitude of their resultant force is 60 N. What would be the magnitude of the resultant of these two vectors if the angle between them is 74 o? y 53 o 53 o F x x components will cancel each other. Their resultant vector has a magnitude of 2 times of y component of one of them. R=2.F.cos53 o 60=2.F.0,6 then F=50 N y F 37 o 37 o F x R=2.F.cos37 o R=2.50.0,8 then R=80 N

9 11th Grade hapter-1 Vectors Activity omponents method 7. 8., F 2 are in the same plane. The resultant force of and F 2 is R 1, the resultant force of is R 2 and the resultant force of F 2 is R 3. If the magnitudes of R 1, R 2 and R 3 are equal, compare the magnitudes of, F 2? R 1 = R 2 = R 3 > F 3 > F 2, F 2 are forces in the same plane. An object of mass m is stationary at point O. and F 2 are applied on the object at the same time. After a while F 3 is applied on the object. What can be said about the motion of the object? The resultant vector of and F 2 is 2 units and it is directed to right. This means there is a nonzero net force acting on the object that starts the object to accelerate to right. After F 3 is applied, the net force on the object will be zero. So the object moves with its constant velocity.

10 10th Grade hapter-1 Vectors Additional Problems Four vectors are given in the scaled figure. Suppose that each side of the squares is 1 m. Answer the following questions. a) The magnitude of A+ B+ + D b) The magnitude of B+ c) The magnitude of A+ D d) The magnitude of A is m. + B D 3 2 is m. is m is m. Four vectors are given as in the figure above. In the following four different relations are given. If the relation is correct print in the space supplied, if not print W and correct it. W a) W b) c) d) X = T Z X = T Z+ T = Y T+ Y = Z X = -T Z + T = Y

11 10th Grade hapter-1 Vectors Additional Problems The resultant of vectors in Figure-I is R 1 and in Figure-II is R 2. What is the ratio of magnitude of R 1 /R 2? Five vectors and their magnitudes are given as in the figure. What is magnitude of the resultant vector in terms of F? The vector sum of three F vectors and a 2F vector has a magnitude of 2F and it is in the opposite direction of 5F vector. R = 5F - 2F = 3F R 1 R 2 = 3 3

12 10th Grade hapter-1 Vectors Additional Problems Four force vectors are given in the figure above. alculate the magnitude of resultant vector in N. Four force vectors are given in the figure above. alculate the magnitude of resultant vector in N. x y x y 2 N N N N N N N N R 6 N 0 R 4 N 3 N R=6 N (to right) R=5 N

13 10th Grade hapter-1 Vectors Additional Problems The vectors K, L and M have the same magnitude of 5 N. What is the magnitude of - L M+ 3 K? K+L=M then -K=L - M R=L-M+3K R=-K+3K=2K R=2K=2.5=10 N Object X is stationary over a frictionless horizontal surface. After the forces, F 2 are applied on X at the same time, it stays stationary. (The angle a is 45 0.) Read the following statements. Decide whether they are correct or not. Print for the correct ones, otherwise print W to the spaces supplied. You have to correct the wrong statements with the appropriate words. W W The magnitude of is equal to the magnitude of F 2. The magnitude of F 2 is equal to the magnitude of F 3. If was removed then the object X had started to move towards +x. If the angle was smaller than 45 0 then the object X had started to move towards +y. Southeast