Quiz #6. 7) Given the following equations and m = 3kg, g = 9.81m/s 2, µ k = 0.2, and. F = 20N, calculate magnitude of the forces N and acceleration a.

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1 Quiz #6 Vector The method used in 2 Dimensions is exactly the same in 3D; just keep one more components (Pythagorean theorem also still holds in higher dimensions as long as the space is Euclidean). 1) Given A(1, 2, 3), and B( 3, 4, 1), calculate AB 2) Given AB =< 1, 2, 3 >, and AC =< 3, 5, 2 >, calculate BC 3) Given AB =< 1, 3, 1 >, calculate ê AB 4) If AB// F, A( 1, 2, 4), and B( 5, 1, 2), and F = 2, calculate F 5) Given the following equations and m = 3kg, g = 9.81m/s 2, β = 30, and α = 20, calculate the magnitude of the forces T and N. { T cosα = mgsinβ N + T sinα = mgcosβ 6) Given the following equations and m B = 3kg, m A = 4kg, g = 9.81m/s 2, and α = 20, calculate magnitude of the forces T 1, T 2, N B, and N A. T 2 m B gsinα = 0 N B m B gcosα = 0 T 1 T 2 m A gsinα = 0 N A m A gcosα = 0 7) Given the following equations and m = 3kg, g = 9.81m/s 2, µ k = 0.2, and F = 20N, calculate magnitude of the forces N and acceleration a. { F sinα µk N = ma N + F cosα mg = 0 8) Given the following equations and m = 3kg, g = 9.81m/s 2, and µ s = 0.5, α = 30, calculate magnitude of the forces N and F. { µs N + F cosα mgsinα = 0 N F sinα mgcosα = 0 1

2 Newton Given an object initially at rest on an incline plane m = 3kg, µ s = 0.6, and µ k = 0.2 as shown in Figure 1: 9) Provide a Free Body Diagram. 10) Provide all the equations obtained from your Free Body Diagrams. 11) Calculate the acceleration of the system. 12) What is the velocity of the object after it has moved 2m down the inclined plane (provide a new coordinate system that is consistent with the simplified kinematics equation you will use). Redo this problem by using a coordinate system such as: the x axis is horizontal and its positive direction is towards the right; the y axis is vertical and its positive direction is up. 13) Provide all the equations obtained from your Free Body Diagrams (no need solve, you know what the answer is... Figure 1: Given m A = 3kg, and m B = 5kg for an Atwood System of type II in Figure 2: 14) Provide a Free Body Diagram for both systems A and B. 15) Provide all the equations obtained from your Free Body Diagrams. 16) Calculate the acceleration of the system. 2

3 Figure 2: Given m A = 3kg, m B = 5kg, µ s = 0.6, and µ k = 0.2 for an Atwood System of type II in Figure 2: 17) Provide a Free Body Diagram for both systems A and B. 18) Provide all the equations obtained from your Free Body Diagrams. 19) Calculate the acceleration of the system. Given m A = 3kg, m B = 7kg, µ s = 0.6, µ k = 0.2, and given that the Atwood System of type II in Figure 2 is at rest: 20) Provide a Free Body Diagram for both systems A and B. 21) Provide all the equations obtained from your Free Body Diagrams. 22) Calculate the frictional force. 23) Deduce the maximum value the frictional force may take (if m A was increased). Given m B = 3kg, µ s = 0.6, µ k = 0.2, and given that the Atwood System of type II in Figure 2 is at rest: 24) Provide a Free Body Diagram for both systems A and B. 25) Provide all the equations obtained from your Free Body Diagrams. 26) Calculate the minimum value of m A to cause the system to move). Given m A = 3kg, and m B = 15kg for an Atwood System of type III in Figure 3: 27) Provide a Free Body Diagram for both systems A and B. 3

4 28) Provide all the equations obtained from your Free Body Diagrams. 29) Calculate the acceleration of the block B as it drops down. Figure 3: Given m A = 13kg, m B = 5kg, µ s = 0.6, and µ k = 0.2 for an Atwood System of type III in Figure 3: 30) Provide a Free Body Diagram for both systems A and B. 31) Provide all the equations obtained from your Free Body Diagrams. 32) Calculate the acceleration of the block B as it goes up. Given m A = 13kg, m B = 5kg, α = 50, and β = 30, for an Atwood System of type IV in Figure 4: 33) Provide a Free Body Diagram for both systems A and B. 34) Provide all the equations obtained from your Free Body Diagrams. 35) Calculate the acceleration of the block A as it slides down the inclined plane. Figure 4: 4

5 Given m A = 3kg, m B = 15kg, α = 50, β = 30, µ s = 0.6, and µ k = 0.2 for an Atwood System of type IV in Figure 4: 36) Provide a Free Body Diagram for both systems A and B. 37) Provide all the equations obtained from your Free Body Diagrams. 38) Calculate the acceleration of the block B as it slides down the inclined plane. 39) Provide Newton s first law in its mathematical form. 40) Provide Newton s second law in its mathematical form. 41) Provide Newton s third law in its mathematical form. 42) What is the relation between radial acceleration and tangential velocity in a circular motion? 43) What is the direction of the acceleration for a uniform circular motion? 5

6 Provide your answers here: Your Name: 1) 2) 3) 4) 5) 6) 7) 8) 6

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