Transcript Chapter 6
Fundamentals of Physics Chapter 7 Kinetic Energy & Work 1. Energy 2. Work 3. Work & Kinetic Energy 4. Work Done by a Gravitational Force 5. Work Done by a Spring Force 6. Work Done by a General Variable Force 7. Power Review & Summary Questions Exercises & Problems 2009 Physics 2111 Fundamentals of Physics Chapter 7 1 Energy & Work Energy comes in many forms: • Thermal, Chemical, Atomic, Nuclear Energies • Energy is conserved. • A new tool to solve problems. • Descriptions of Energy: • Potential Energy (Chapter 7) • Kinetic Energy - motion of a massive object Kinetic Energy Units : 2009 1 2 m v2 kg m 2 1 Joule 1 s2 Physics 2111 Fundamentals of Physics Chapter 7 2 WOW! August 10, 1972, a large meteorite skipped across the atmosphere. m 4 106 kg v 15 m s KE 1 2 m v 2 0 5 1014 J KE 0.1 MT 8 WWII atomic bombs 2009 Physics 2111 Fundamentals of Physics Chapter 7 3 “Work” • Work (W) is energy transferred to or from an object by means of a force acting on the object. – Energy transferred to the object is positive work. – Stepping on the gas causes positive work to be done on a car. – Energy transferred from the object is negative work. – Stepping on the brakes causes negative work to be done on a moving car. 2009 Physics 2111 Fundamentals of Physics Chapter 7 4 Work & Kinetic Energy Consider a force acting on an object constrained to move in the x-direction: v 2 v02 2 ax d Frictionless Wire v 2 v02 2 a x d 1 2 m v 2 12 m v02 m ax d 1 2 m v 2 12 m v02 Fx d The force causes a change in kinetic energy; the force does work: "Work " Fx d F cos d Units: 1 Joule = 1 kg (m / s)2 = (1 kg m / s2) m = 1 N m 2009 Physics 2111 Fundamentals of Physics Chapter 7 5 A force acting on a particle moving along a curve: F does no work. Work FS s F does not change the velocity. cos cos 900 0 2009 Work F cos s Work F s Physics 2111 Fundamentals of Physics Chapter 7 6 “Work” W F d F cos d Work (W) is energy transferred to or from an object by means of a force acting on the object. – A force does positive work when it has a vector component in the same direction as the displacement. – A force does negative work when it has a vector component in the opposite direction as the displacement. – A force does zero work when it is perpendicular to the displacement. 2009 Physics 2111 Fundamentals of Physics Chapter 7 7 Work – Kinetic Energy Theorem W FS ds W aS s2 s1 FS ds s2 s1 m aS ds dv dv ds dv v dt ds dt ds chain rule for derivatives v dv ds m s1 ds v0 v dv 2 W 12 m v 2 12 m v0 W K f Ki W s2 mv W K Net Work Done 2009 = Change in Kinetic Energy Physics 2111 Fundamentals of Physics Chapter 7 8 Scalar (Dot) Product of Two Vectors a b a b cos Commutative Law: a b b a a b ax bx a y by az bz 2009 Physics 2111 Fundamentals of Physics Chapter 7 9 Example Work F s W Fx x Fy y W 3N 2m 4 N 5m W 14 Nm Tipler p 157 2009 Physics 2111 Fundamentals of Physics Chapter 7 10 Example: vf = ? s 57 m v0 3.6 m s m 58 kg f K 70 N Work Fnet s Fnet m g sin 250 f K m g sin 25 0 fK s 1 2 m v f 12 m v0 2 2 v f 19 m s Cutnell p 160 2009 Physics 2111 Fundamentals of Physics Chapter 7 11 Work done by the forces on the box? N F F 210 N 200 mg d 3m WF F d WF F d cos (210 N )(3 m) cos(200 ) 600 J WN N d WN N d cos(900 ) 0 Wg 2009 Physics 2111 Fundamentals of Physics Chapter 7 12 Object sliding on a frictionless floor Work = ? v0 0 F1 3.00 N F2 4.00 N F3 10.0 N Fnet x F1 F2 sin 500 F3 cos 350 Fnet y F2 cos 500 F3 sin 350 Fnet 2 Fnet x 2 FnetY 2 Since v0 0, d is parallel to Fnet : W Fnet d W 15.3 J 2009 Physics 2111 Fundamentals of Physics Chapter 7 13 Work Done by the Gravitational Force Going down: W F d W m g d cos 00 W m g d The work done by the gravity force increased the kinetic energy of the object. Going up: W F d W m g d cos1800 W m g d The work done by the gravity force reduced the kinetic energy of the object. 2009 Physics 2111 Fundamentals of Physics Chapter 7 14 Work Done Lifting & Lowering an Object To raise an object to a new location, an applied force, F, must act to overcome the gravity force, Fg. Consider a case where an object is at rest before and after the move. Work- Energy Theorem: Kf - Ki = Wa + Wg But Kf = Ki = 0: 0 = Wa + Wg Wa = - Wg The work done by the applied force is the negative of the work done by the gravitational force. Raising Wa m g d 2009 Lowering Wa m g d The work done by the lifter. Physics 2111 Fundamentals of Physics Chapter 7 15 Pull with constant force F. F F F F ma 2 F mg ma 0 F 1 2 mg F Is less energy expended or less work done when using a pulley (or other such device)? 2009 Physics 2111 Fundamentals of Physics Chapter 7 16 Pull with constant force F. F F F F ma 2 F mg ma 0 F 1 2 mg d 2d W ( F )(2d ) W mgd W (2 F )(d ) W mgd Same amount of work! 2009 Physics 2111 Fundamentals of Physics Chapter 7 17 An object accelerated downwards a = g/4 drops d Work by cord ? Work by gravity? Final velocity v0 0 F ma g T mg M a M 4 T 34 M g T WT 34 M g d Wg M g d aa d Wnet 14 M g d Mg Work Energy Theorem: K K 0 Wnet 1 2 M v2 0 1 4 v 2009 M gd 1 2 gd Physics 2111 Fundamentals of Physics Chapter 7 18 Work Done by a Spring Force Relaxed Hooke’s Law: F k d where k = spring constant (N/m) Stretching The force varies linearly with displacement. Compressing 2009 Physics 2111 Fundamentals of Physics Chapter 7 19 Work Done by a Spring Force F k d Hooke’s Law: Relaxed Work done by the spring force: WS xf xi F ( x ) dx WS k xf xi Stretching WS 1 2 x dx 1 2 k x 2 k xi2 WS 12 k x 2 1 2 xf xi k x 2f ( xi 0) Wa WS Compressing 2009 Physics 2111 Fundamentals of Physics Chapter 7 20 A block is dropped on a relaxed spring Wg m g d m = 250 g k = 2.5 N/cm d = 12 cm Wg ? W s? v? WS 1 2 k d 2 Wnet Wg WS Wnet K f K i mgd 1 2 k d2 0 1 2 mv 2 v d v0 2009 v k 2 d 2gd m v 35 . ms Physics 2111 Fundamentals of Physics Chapter 7 21 Work – Kinetic Energy Theorem with a Variable Force WS xf F ( x ) dx m xi xf a x dx xi dv dx a x dx dx dv v dv dt dt W m xf xi v dv 1 vf 2 mv 2 v i W KE f KEi 2009 Physics 2111 Fundamentals of Physics Chapter 7 22 Problem A 10 kg brick moves with the following variable acceleration; how much work is done on the brick in the first 8 seconds. a x 20 m s2 2.5 s 2 8m a 2.5 x WS W 2009 F ( x ) dx 2.5 m xf xi 2 .5 xf xi 8 2 m x2 0 2 .5 2 x dx (10)(8) 2 800 J Physics 2111 Fundamentals of Physics Chapter 7 23 Power Power = time rate at which Work is done due to a Force. P SI Units: dW dt 1 Watt = 1 Joule / s = 1 N m / s English Units: horsepower 1 hp = 550 ft lbs / s = 746 Watts For a constant force: d F d P F v dt Work = Power x Time 1 kW hr = 3.6 x 106 J 2009 Physics 2111 Fundamentals of Physics Chapter 7 24