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Newton’s Second Law The acceleration of an object is directly proportional to the net force acting on it and inversely proportional r to its mass. r aα ∑ F or ∑ Fr = mar m Newton’s Third Law • If object 1 and object 2 interact, the force exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force exerted by object 2 on object 1. r r F12 = −F21 Friction Forces Contact between bodies with a relative velocity produces friction Kinetic friction: the direction of the frictional force is opposite the direction of motion. Kinetic friction is proportional to the normal force f k = µk n The coefficient of friction µ (‘mu’) depends on the surfaces in contact Static Friction ƒs Static friction acts to keep the object from moving If F increases, so does ƒs If F decreases, so does ƒs ƒs ≤ ƒs, max with ƒs, max = µs n uur uur f s = -F ƒs, max = µs n Usually, µs > µN Block on a Ramp Axes are rotated as usual on an incline The direction of impending motion would be down the plane Friction acts up the plane Opposes the motion Draw free body diagram Yada Yada Yada Chapter 5.1-5.2 Energy and Work Mechanical Energy •Kinetic (associated with motion) •Potential (associated with position) Chemical Energy Electromagnetic Energy Nuclear Energy Energy can be transformed from one form to another But not destroyed– “Energy is conserved” Work/Energy can be used in place of Newton’s laws to solve certain problems more simply Work done by a force F on an object W ≡ (F cos θ)∆x F is the magnitude of the force ∆ x is the magnitude of the object’s displacement θ is the angle between the force and the displacement Work is a scalar quantity Work by the force is zero when force and displacement are perpendicular e. g., carrying a bucket of water Displacement is horizontal Force is vertical cos 90° = 0 W ≡ (F cos θ)∆x So no work done! Work is scalar, but it can Be Positive or Negative Work done by the person on the box is positive when lifting the box Work done is negative if lowering the box force is upward, but displacement is downward Kinetic Energy Energy associated with the motion of an object 1 2 KE = mv 2 Scalar quantity with the same units as work Work is related to kinetic energy Work-Kinetic Energy Theorem Wnet = KEf − KEi = ∆KE When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object’s kinetic energy • Speed will increase if work is positive • Speed will decrease if work is negative Units of Work W ≡ (F cos θ)∆x In SI system Newton • meter = Joule N • m = J 2 / s2 J = kg • m Food calorie = 4184 J