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Dynamics Forces & Motion

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Characteristics of Force A force acting on an object will either: a. change the object’s motion b. cause a deformation in the object. Force is measured in newtons, N: 1 N = (1 kg x 1m ) / 1 s 2

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Types of Forces 1.Gravitational Force is the attraction between two bodies (objects) due to their mass. Law of Universal Attraction: F g = (G m 1 m 2 ) / r 2 Where G is the gravitational constant, 6.67 x 10 -11 Nm 2 /kg 2 m 1 is the mass of the first object in kg m 2 is the mass of the second object in kg r is the distance between the two objects in m

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Gravitational acceleration is the constant pull (acceleration) felt by a body as it falls towards the surface of the Earth (or another celestial body). On Earth, the value for the gravitational acceleration is g = 9.8 m/s 2. The gravitational force exerted by the Earth on an object can be found using F = mg. We can also use this formula to calculate the weight of an object.

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2. Normal Force The normal force is the force of resistance by an object’s surface during contact with another body. The normal force is perpendicular to the contact surface.

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In order to find a plane that is perpendicular to a spherical surface, we must use the line that passes through the center of the sphere (diameter) as a reference point. The perpendicular plane is therefore perpendicular to this line.

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The normal force is of the same magnitude as a body’s weight, but in the opposite direction. F N = - F g FNFN FgFg

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3. Force of Friction The force of friction is a force that opposes motion. Two types of friction: a.Static friction occurs when two objects touch one another, but neither moves. b.Kinetic friction occurs when two objects touch, and one slides along the other.

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Friction depends on two factors: i.The greater the normal force, the greater the friction. ii.The type of substances in contact. Each substance has its own coefficient of friction (μ). Both static and kinetic friction have their own coefficients of friction (μ S and μ K ). The μ S is always greater than μ K.

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To calculate the forces of friction: F f(static) ≤ μ S F N F f(kinetic) = μ K F N Coefficient of friction for different substances: Substance in contactμSμS μKμK Rubber on wet asphalt0.60.5 Rubber on dry asphalt1.20.8 Rubber on ice0.0060.005

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4. Tension Tension is a force exerted by a cable on an object. For calculations involving tension we assume: i. The cable has a negligible mass. ii.The cable is of negligible width. iii.The cable does not stretch. To calculate tension, the opposing force must be known.

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5. Centripetal Force The centripetal force allows an object to follow a curved path. F C = mv 2 /r The value of F c is affected by the mass and velocity of the object, as well as the radius of its path.

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The velocity vector at any point on the circular path is always tangent to the circular path and perpendicular to the radius of curvature. The centripetal force may take on a different form depending on the circumstances. In the example above, the tension in the string is equivalent to the centripetal force.

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HOMEWORK: Textbook p. 274: # 1 (a, b), 2 p. 277: # 1, 2 p. 278: # 1, 2 p. 281: #1-3

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