① ? ① ? 2 2 1 sin 1 cos 8 a x x 8 5 3 3 2 1 sin

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+ 𝐹 𝑔 2 𝑀 2 ? − 𝑀 1 ? sin 𝜃 − 𝜇 𝐾 𝑀 1 ? cos 𝜃 = 8𝑎 ? a + x + x 𝑎 = ? 8 5 − 3 sin 30 − 0.4 3 cos 30 ∴ 𝑎 = +3.01 ? ? 2 −𝐹 𝑔 1 sin 𝜃 −? ? = 8𝑎 ? 2
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Kinetic Friction on an Inclined Plane A 3.0 kg block sitting on a 30. degree incline is attached over a frictionless pulley to a 5.0 kg mass. The surface of the incline has a coefficient of kinetic friction of u k = 0.4. Starting from rest, Q. What distance will the 3.0 kg block cover in the first 1.0 sec. Given: M 1 = 3.0kg M 2 = 5.0kg 𝜃 = 30 o t = 1.0 s Find: ∆𝒙 a M 2 n T T 𝐹 𝑔 2 = 𝑀 2 ? 𝐹 𝑔 1 = 𝑀 1 ? 𝐹 𝑔 1 cos 𝜃 𝐹 𝑔 1 sin 𝜃 𝜃 𝜃 K f a + x + y + x 𝑎 = 3.01 ? ? 2 ? = 1.0? ∆𝑥 = ? 𝑣 0 = 0 ∆𝑥 = 𝑣 0 ? + 1 2 𝑎? 2 ∆𝑥 = 0 + 1 2 3.01 1.0 2 ∴ ∆𝑥 = 1.5 ? 3
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A box of mass M is placed on a wedge with a variable angle of incline, 𝜃 , relative to the ground. Q. What is the maximum angle, 𝜃 ?𝑎? , at which the box just begins to slide down? n Mg + X + Y a S f sin 0 s Mg f max S S f n cos 0 n Mg tan S cos Mg sin Mg y y F Ma 0 Y a 0 cos n Mg x x F Ma 0 X a 0 sin S Mg f sin cos S Mg Mg At the point of slipping sin S Mg n Static Friction on an Inclined Plane 𝜇 ? = sin 𝜃 cos 𝜃 𝜃 = tan −1 𝜇 𝑆
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F a If the surface on which an object sits is accelerating, then the force of static friction can accelerate the object. How would you calculate the maximum acceleration? 𝐹 𝑆 is the static friction on the box 𝐹 is the force of static friction on the table Recap: Newton’s 3 rd Law and Static Friction S f Later
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An 80. kg box on the back of a truck is held in place by friction. If the coefficient of static friction, 𝜇 𝑆 , is 0.4, what is the acceleration of the truck when the box is on the point of slipping?
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