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Energy is Conserved • Energy is “Conserved” meaning it can not be created nor destroyed – Can change form – Can be transferred • Total Energy does not change with time. • This is a BIG deal! Energy • Forms – – – – Kinetic Energy Potential Energy Heat Mass (E=mc2) Motion (Today) Stored (Wednesday) later 1161 • Units Joules = kg m2 / s2 Work The definition of work, when the force is parallel to the displacement: (7-1) SI work unit: newton-meter (N·m) = joule, J 1 Typical Work Force at an Angle Work If the force is at an angle to the displacement: (7-3) Only the horizontal component of the force does any work (horizontal displacement). Where did the energy go? • You pull a 30 N chest 5 meters across the floor at a constant speed, by applying a force of 50 N at an angle of 30o. • How much work did gravity do? W = Fcos θ ∆x ∆x = 30 cos(90) x 5 90 =0 mg • How much work did friction do? T N X-Direction: ΣF = ma f T cos(30) – f = 0 mg f = T cos(30) = W = f cos(180) ∆x = (43.3 N) cos(180) x 5 = −217 Joules f ∆r 180 2 Positive & Negative Work Work done may be positive, zero, or negative, depending on the angle between the force and the displacement: Perpendicular Force and Work A car is traveling on a curved highway. The force due to friction fs points toward the center of the circular path. How much work does the frictional force do on the car? Zero! General Result: A force that is everywhere perpendicular to the motion does no work. Work Done by Gravity In lifting an object of weight mg by a height h, the person doing the lifting does an amount of work W = mgh. If the object is subsequently allowed to fall a distance h, gravity does work W = mgh on the object. W = mgh 3 ACTS: Ball Toss You toss a ball in the air. What is the work done by gravity as the ball goes up? A) Positive B) Negative C) Zero What is the work done by gravity as the ball goes down? A) Positive B) Negative C) Zero Work By Gravity When positive work is done on an object, its speed increases; when negative work is done, its speed decreases. Kinetic Energy: Motion • Apply constant net force along xdirection to an object m. W = Fx ∆x = m a ∆x = ½ m (v2 – v02) v 2 = v02 + 2a ( x − x0 ) a ⋅ ∆x = 1 2 2 ( v − v0 ) 2 • Work changes ½ m v2 • Voila – new concept: • Define Kinetic Energy K = ½ m v2 W=∆K 4 Work-Energy Theorem Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy. (7-7) Work: Energy Transfer due to Force • Force to lift trunk at constant speed – Case a Ta – mg = 0 T = mg – Case b 2Tb - mg =0 or T = ½ mg • But in case b, trunk only moves ½ distance you pull rope. • F * distance is same in both! Tb Tb Ta W = F dcos(θ) mg mg Preflight 1 FN You are towing a car up a hill with constant velocity. The work done on the car by the normal force is: T 1. positive 2. negative 3. zero V correct W “The work done on the car by the normal force is 0 because it is perpendicular” 32% 5% 63% 0% 20% 40% 60% 80% 28 5 Preflight 2 FN You are towing a car up a hill with constant velocity. The work done on the car by the gravitational forceT is: 1. positive 2. negative 3. zero correct V W The work done on the car by the gravitational force is negative because it hinders motion up the hill 7% 68% 25% 0% 20% 40% 60% 80% Preflight 3 FN You are towing a car up a hill with constant velocity. The work done on the car by the tension force is: T correct 1. positive 2. negative 3. zero W V 89% the work done on the car by the tow rope is positive because the car is moving up 6% 6% 0% 20% 40% 60% 80% 100% KE ACTS Car 1 has twice the mass of Car 2, but they both have the same kinetic energy. If the speed of Car 1 is v, approximately what is the speed of Car 2? a) 0.50 v b) 0.707 v c) v d) 1.414 v e) 2.00 v 1 1 m1v12 = m2 v22 2 2 m1 = 2m2 2m2v12 = m2v22 2v12 = v22 v2 = 2 ⋅ v1 6 Preflight 4 FN You are towing a car up a hill with constant velocity. The total work done on the car by all forces is: T 1. positive 2. negative correct 3. zero W 70% V The total work done is positive because the car is moving up the hill. (Not quite!) 4% 26% Total work done on the car is zero because the forces cancel each other out. 0% 20% 40% 60% 80% 37 Summary • Energy is Conserved • Work = transfer of energy using force – Can be positive, negative or zero – W = F d cos(θ) • Kinetic Energy (Motion) – K = ½ m v2 • Work = Change in Kinetic Energy Σ W = ∆K 50 7