Quiz #7. T f k m A gsinθ = m A a N m A gcosθ = 0 f k = µ k N m B g T = m B a

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Philippa Patrick
5 years ago
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1 Quiz #7 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(2, 0, 4), and B( 1, 5, 2), calculate AB 2) Given AB =< 2, 6, 3 >, calculate ê AB 3) If AB// F, A(1, 3, 6), and B(1, 0, 4), and F = 10, calculate F 4) Given the following equations and m A = 3kg, m B = 4kg, g = 9.81m/s 2, µ k = 0.2, and θ = 30, calculate the magnitude of the acceleration a. T f k m A gsinθ = m A a N m A gcosθ = 0 f k = µ k N m B g T = m B a 5) Given the following equations and m = 3kg, g = 9.81m/s 2, µ s = 0.5, β = 30, and R = 20m, calculate magnitude of the velocity v. Newton Nsinβ + f smax cosβ = ma Ncosβ f smax sinβ mg = 0 a = v2 R = µ s N f smax Given a car at rest on an incline plane held by a horizontal rope along which a tension of 5N is applied as shown in Figure 1: 6) Provide a Free Body Diagram. 7) Provide all the equations obtained from your Free Body Diagrams. 8) Calculate the mass of the system. 1

Figure 1: Find the tensions T 1, T 2, T 3 on each of the three cables supporting the traffic light, if it weighs 300N, as shown in Figure 2: 9) Provide a Free Body Diagram.

2 Figure 1: Find the tensions T 1, T 2, T 3 on each of the three cables supporting the traffic light, if it weighs 300N, as shown in Figure 2: 9) Provide a Free Body Diagram. 10) Provide all the equations obtained from your Free Body Diagrams. 11) Calculate the tensions. Figure 2: Given M = 3kg, what is the tension in the connecting string of the Atwood System in Figure 3 (no friction is present so you should be able to deduce if there is motion, what kind, and in which direction: 12) Provide a Free Body Diagram for both systems. 13) Provide all the equations obtained from your Free Body Diagrams. 2

3 14) Calculate the tension of the system. Figure 3: Given M = 0.5kg, F = 17N, µ s = 0.6, and µ k = 0.2 as shown in Figure 4: 15) Provide a Free Body Diagram for both systems. 16) Provide all the equations obtained from your Free Body Diagrams. 17) Calculate the acceleration of the suspended object as it moves up? Figure 4: 3

Figure 5: Given m A = 3kg, that the entire system is at equilibrium, and that the string between them is horizontal (Figure 6): 21) Provide a Free Body Diagram for both systems.

4 Given the mass of the sphere m = 3kg, α = 30, the fact that it is at equilibrium and that there is no friction (Figure 5): 18) Provide a Free Body Diagram. 19) Provide all the equations obtained from your Free Body Diagrams. 20) Calculate the normal forces acting on the sphere. Figure 5: Given m A = 3kg, that the entire system is at equilibrium, and that the string between them is horizontal (Figure 6): 21) Provide a Free Body Diagram for both systems. 22) Provide all the equations obtained from your Free Body Diagrams. 23) Calculate the mass of object B. 24) Calculate the tension between A and B. 25) Calculate the normal force on object A. 26) Calculate the normal force on object B. Figure 6: Given the mass of the car m = 1300kg, θ = 50, µ s = 0.6, and µ k = 0.2 and 4

5 R = 30m (Figure 7): 27) Provide a Free Body Diagram. 28) Provide all the equations obtained from your Free Body Diagrams. 29) Calculate the maximum velocity of the car so that it doesn t slip up the ramp. Figure 7: 30) Provide Newton s first law in its mathematical form. 31) Provide Newton s second law in its mathematical form. 32) Provide Newton s third law in its mathematical form. 33) What is the relation between radial acceleration and tangential velocity in a circular motion? 34) What is the direction of the acceleration for a uniform circular motion? Given the mass of the block A m = 13kg, µ s = 0.2, and µ k = 0.1 (Figure 8): 35) Provide a Free Body Diagram for block A. 36) Provide all the equations obtained from your Free Body Diagram. 37) Calculate the minimum force the person needs to apply to keep the system at equilibrium (remember the properties of a massless pulley! decoy information is provided if we use these assumptions). 5

6 Figure 8: 6

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

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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.

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. 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)