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Work and Energy Chapter 6 Griffith Simple Machines 1. 2. 3. 4. 5. 6. ? ? ? ? ? ? Simple Machines 1. 2. 3. 4. 5. 6. Lever Pulley Inclined Plane Wedge Screw Wheel and Axle Mechanical Advantage Reduction of Friction Pulley System T T d1 T = W/2 d2 = 2d1 F=T d2 W Mechanical Advantage Less force is advantageous, even though the smaller force must act over a larger distance in order to transfer the same amount of work. Concept of Work • Work = Force × Displacement = Fd – F must be constant. – F and d must be collinear. • Work = 200 Nm = 200 Joules F = 50 N d = 4.0 meters If F and d are not collinear, F = 50 N Fy = 30 N Work = Fxd = 160 J Fx = 40 N d = 4.0 meters Work is the product of displacement and the component of force in the direction of the displacement. Work = Fd = Fd Vector or Scalar? • Note that even though force and displacement are both vectors and have direction, work has no direction. • All forms of energy have no directions either. Work and energy are scalar quantities. Work and Uniform Circular Motion v Tension F = mv2/r What is the work done on the mass by the tension in the string? Work and Uniform Circular Motion v Tension F = mv2/r The work done by tension in the string is zero!! The mass does not move toward or away from the center of the circle. Units of Work • 1.0 Joule = 1.0 Newton × meter = 1.0 kg m2/s2 • 1.0 erg = 1.0 dyne x cm = 1.0 g cm2/s2 How many dynes in 1.0 Newton? How many ergs in 1.0 Joule? Units of Work • 1.0 Joule = 1.0 Newton × meter = 1.0 kg m2/s2 • 1.0 erg = 1.0 dyne x cm = 1.0 g cm2/s2 How many dynes in 1.0 Newton? How many ergs in 1.0 Joule? 105 107 Power • In General Physics we describe average power. Pavg work done average power time taken • Units of power = J/s = Watt = kg m2/s3 – 1.0 horsepower = 746 Watts Kinetic Energy • Energy of motion • Formulated by Gottfried Wilhelm Leibniz – also developed calculus independent of Newton KE E K K mv 1 2 2 Work-Energy Theorem • The work done on a body changes the kinetic energy of the body. E Kf E Ki W • Notice that work can be positive or negative. – Positive work adds kinetic energy to the body. – Negative work takes kinetic energy away from the body. Positive and Negative Work W>0 v F W<0 v F Force does positive work on the car. The acceleration is in the direction of the velocity, and the car speeds up. Force does negative work on the car. The acceleration is opposite the direction of the velocity, and the car slows down. Work-Energy Example vi = 2.0 m/s 10 kg vf = ? F = 50 N 10 kg d = 4.0 meters A 10-kg block moving at 2.0 m/s to the right is pushed to the right by a 50-N force. The force continues as the block moves 4.0 m in a straight line. What is the final speed of the block? Work-Energy Example vi = 2.0 m/s 10 kg vf = ? F = 50 N 10 kg d = 4.0 meters E Ki W E Kf 1 2 102.02 50 4.0 12 10v 2 vf 6.6 m/s f Is the Work-Energy Theorem mysterious? E Ki W E Kf 1 2 1 2 mvi2 mv 2 vf Fd 2 f 2 vi 2 vi 1 2 mv 2f special case of constant force Fd mad 2ad third “Big 3” equation! No, the work-energy theorem is not mysterious! Potential Energy • Applies only to Conservative Forces – Gravity, Elastic forces – Friction, Applied forces • Work done against a conservative force can be later completely converted to kinetic energy. – The work is thus “stored.” Potential Energy 100 kg d = 2.0 m 100 kg Fapplied = mg = 980 N ag = 9.8 m/s2 v = constant Despite work applied to the box against gravity, the kinetic energy does not change. This means that potential energy is increasing. Fapplied Potential Energy 100 kg d = 2.0 m 100 kg W = Fappliedd = 1960 J ag = 9.8 m/s2 v = constant PEi + W = PEf PEf – PEi = 1960 J This 1960 J will be turned into kinetic energy if the box is dropped. Fapplied Potential Energy • Notice that only the change in potential energy (PEf – PEi = DPE) tells us about forces, displacements, and velocities. • The value of potential energy at any one location is completely arbitrary. Mechanical Energy • Both potential and kinetic energy are created by work, so both are types of mechanical energy. PE + KE = Emech