6-4 Connected Objects • If there is a pulley, it is easiest to have the coordinate system follow the string: Similar to CH06 HW, # 6.38 Choose + x along the direction of acceleration. The same magnitude 1 1 Tensions and are the same. Common acceleration. 2 2 28 Object x - component Mass1: 𝑚 ∑𝐹  𝑇  𝑚 𝑎 (1) x - component ∑𝐹  𝑚 𝑔  𝑇  𝑚 𝑎 Mass 2: 𝑚 Note: I have not considered any forces along y direction (𝑎𝑦  0󰇜. Algebraic expressions (1) +(2)      (2) +  29 • If you know the force masses,      (1)       If you know masses, you can find the numerical values for tension and the acceleration. 30 Example 6: A mug rests on an inclined surface, as shown. (a) What is the magnitude of the frictional force exerted on the mug? (b) What is the minimum coefficient of static friction required to keep the mug from sliding? y The angle 𝜃  16°. Similar to CH06 HW, # 6.11 𝑠 Equilibrium condition. F F x 0 y 0 x 31 Force x component 0  0 𝑠 𝑠 y component +N    𝑚𝑔 sin 𝜃  𝑓  0 𝑓  𝑚𝑔 sin 𝜃 N  𝑚𝑔 cos 𝜃  0 N  𝑚𝑔 cos 𝜃 a) What is the magnitude of the frictional force exerted on the mug?  𝑓  𝑚𝑔 sin 𝜃  0.27 kg 9.8  sin 16  0.73 N 32 (b) What is the minimum coefficient of static friction required to keep the mug from sliding?      33 Example 7: A loudspeaker of mass 21.0 kg is suspended a distance of h = 2.40 mm below the ceiling by two cables that make equal angles with the ceiling. Each cable has a length of l = 3.70 mm y Similar to CH06 HW, # 1 1 2 x Equilibrium condition. sin 𝜃  ℎ 2.40 mm   0.649 𝑙 3.70 mm F x 0 F y 0 𝜃  sin 󰇛 0.649 󰇜  40.4° 34 𝑇1 x component 𝑇1 cos 𝜃 y component 𝑇1 sin 𝜃 𝑓𝑠 𝑇2 cos 𝜃 𝑇1 sin 𝜃 𝑊  𝑚𝑔 0 𝑚𝑔 F ∑𝐹  0 𝑇1 cos 𝜃  𝑇1 cos 𝜃  0 𝑇  𝑇 ∑𝐹  0 𝑇1 sin 𝜃  𝑇1 sin 𝜃  𝑚𝑔 0 Force 1 1 1 1 2 1 2 35