PHY 101 1nd Edition Lecture 15 Outline of Last Lecture I 5 2 continued II Conservative vs Nonconservative Forces III 5 3 Gravitational Potential Energy IV Gravitational Potential Energy Work V Conservation of Mechanical Energy VI 5 5 Energy Conservation Work Energy Theorem Revisted Outline of Current Lecture I Work Energy Theorem Revisited Cont II 5 6 Power III Chapter 6 Momentum Collisions IV 6 1 Momentum Impulse a Impulse Momentum Theorem b Varying Force Current Lecture Work Energy Theorem Revisted The work done by the net force is equal to the change in the system s kinetic energy o Wnet KEf KEi KE o Any forces regardless of conservative or nonconservative The work done by a nonconservative force is equal to the change in the system s mechanical energy o Wnc KEf KEi PEf PEi o Emech KE PE Example Waterslide o A 60kg person originally at rest slides down a 21 9m high waterslide He reaches a speed of 18m s at the bottom These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute o Calculate the work done by the force of friction o Solution use the bottom of the waterslide as the reference point The change in gravitational potential energy PE PEf PEi PE mg yf yi PE 60 9 8 0 21 9 12877J o Change in kinetic energy KE KEf KEi 1 2 mvf2 1 2 mvi2 Vi 0 2 1 2 60 18 9720J o Using the work energy theorem involving nonconservative force the work done by the force of friction is Wnc KE PE 9720 12877 3157J 5 6 Power Power measures the rate of work done by a force The average power done by a force during a time interval t is the work divided by the time interval o Pav W t o SI Unit Watt W 1W 1J s Other widely used units of power o Horsepower hp 1hp 746W o Kilowatt kW 1kW 1000W Widely used energy unit kilowatt hour kWh o 1kWh 1000W 3600s 3 6 x 106 J Since the work done by a force is suppose the force is along the direction of the displacement o W F x We have o Pav W t F x t FVav NOTE the power of a force is not only proportional to the force but also proportional to velocity Instantaneous power P FV Example P FV o The mass of an elevator car is 1800kg while the elevator is moving upward it experiences a friction force of 400N o If the elevator is moving upward at a constant speed of 3m s what is the power of the motor of the elevator o Analysis constant velocity equilibrium i e net force 0 o Solution since the elevator is in equilibrium the net force T Fk mg 0 T Fk mg T 4000 1800 x9 8 2 16 x 104 N o Power of the motor o P FV TV 2 16 x 104 3 6 48 x 104 N Chapter 6 Momentum Collisions Momentum P mv Impulse I F t Conservation of momentum Pi Pf 6 1 Momentum Impulse Physics an impulse of force acts on the object so it gains momentum What is momentum and what is impulse A moving object also has a certain momentum P mv o SI Unit kg m s N s Momentum is related to the impulse done on an object o I F t Both momentum and impulse are vector quantities and have same units Impulse Momentum Theorem Similar to the work energy theorem we have the impulse momentum theorem o I p p mvf mvi o Impulse delivered to an object change in the object s momentum Proof from Newton s 2nd law F ma o F t m a t vf vi a t o F t m vf vi o I p The rate of change in the momentum of an object is equal to the net force acting on it o F t p F p t During a collision the change in momentum is fixed you cannot change it o Initial momentum pi mvi o Final momentum pf mvf To minimize the injury reduce the force acting on the person s body the only thing we can do is to increase the stopping time o Seat belt increases stopping time by more than 10 times o Air bags also increase stopping time and contact area thus prevents oenetration wounds and fractures Varying Force Often the force acting on an object is not a constant the time could be very short or very long The impulse momentum still holds Need to replace the force with an average force o Fav t p