Θ motion on an inclined plane an important type of

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θ MOTION ON AN INCLINED PLANE An important type of one –dimensional motion is one on an inclined plane or ramp. The ramp makes an angle θ to the horizontal The component of the weight (mgsin θ ) acts along the incline.
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Prepared By: ChilesheMwenyaMporokoso Page 39 Example In the figure below, the particles of mass 2.4kg is held at rest on a smooth surface AB. It is connected by a light string passing over a smooth pulley at B to a particle of mass 3.6kg. The slopping face BC is smooth and makes an angle of 30 0 with the horizontal Find; a.)the acceleration of the particles when they are released. b.)the tension in the string. Solution Consider the 2.4kg mass Since the motion of the object is horizontal, the weight (W) does not have any influence in this direction. F =ma T = ma T =2.4a…………………………(i)
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Prepared By: ChilesheMwenyaMporokoso Page 40 Now consider the 3.6kg mass F = ma mgsin θ ‐ T = ma mgsin θ ‐ T = 3.6a 3.6x9.81 x sin30 0 – T =3.6a 17.658 T = 3.6a…………………………(ii) sub (i) into (ii) 17.658 T = 3.6a becomes 17.658 – 2.4a = 3.6a 6a = 17.658 a = ଵ଻.଺ହ଼ a = 2.943m/s 2 fromeq (i) T = 2.4a T = 2.4 x 2.943
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Prepared By: ChilesheMwenyaMporokoso Page 41 T = 7.0632N T 7.1N Self Evaluation Exercise 1.State Newton’s 2 nd law of motion. A cord passing over an easily turned pulley has a 7kg mass hanging from one end and a 9kg Hanging from the other as shown. Find the acceleration of the masses and the tension in the cord. 2. A body of weight 100N rests on a plane which is inclined at 30 0 to the horizontal. Calculate the components of the weight parallel and perpendicular to the plane.
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Prepared By: ChilesheMwenyaMporokoso Page 42 UNIT 1.6: FRICTION Friction is defined as a force that opposes relative motion between two surfaces that are in sliding contact. Friction acts tangential to the two sliding surfaces. LAWS OF DRY FRICTION (applicable without lubricants) . The following are some of the laws of friction; i.)Friction force always opposes motion, i.e. it acts in the opposite direction to that of motion of an object. ii.)Friction depends on the nature of the surfaces involved (smooth or rough surfaces). iii.)Friction is proportional to the normal reaction force. A normal reaction force is a perpendicular force that a resting surface exerts on any object resting on it. iv.)Friction is independent of the area of the surfaces in contact. v.)At lower speeds, friction depends on the sliding speed. At higher speeds friction decreases. STATIC FRICTION (f s ) The magnitude of frictional force (f) increases from zero as the tendency of an object to move increases up to a limiting value (maximum). The value of this friction is called the Limiting friction . When the pushing or pulling force increases, friction also starts to act in the opposite direction. As f increases further, an instant is reached when the body just starts to slide. At this point, the value of this friction is called the limiting static friction .
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