PHY 101 1nd Edition Lecture 15 Outline of Last LectureI. 5.2 continuedII. Conservative vs. Nonconservative ForcesIII. 5.3 Gravitational Potential EnergyIV. Gravitational Potential Energy & WorkV. 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 PowerIII. Chapter 6: Momentum & CollisionsIV. 6.1 Momentum & Impulsea. Impulse – Momentum Theoremb. Varying ForceCurrent LectureWork – Energy Theorem Revisted- The work done by the net force is equal to the change in the system’s kinetic energyo Wnet = KEf – KEi = ΔKEo Any forces, regardless of conservative or nonconservative- The work done by a nonconservative force is equal to the change in the system’s mechanical energyo Wnc = (KEf – KEi) + (PEf – PEi)o Emech = KE + PE- Example: Waterslideo A 60kg person, originally at rest, slides down a 21.9m high waterslide. He reachesa speed of 18m/s at the bottomThese 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 frictiono Solution: use the bottom of the waterslide as the reference point. The change in gravitational potential energy ΔPE = PEf – PEi ΔPE = mg(yf – yi) ΔPE = 60(9.8)(0-21.9) = -12877Jo Change in kinetic energy ΔKE = KEf – KEi (1/2)mvf2 - (1/2)mvi2 Vi = 0 (1/2)(60)(18)2 = 9720Jo Using the work – energy theorem involving nonconservative force, the work done by the force of friction is: Wnc = ΔKE + ΔPE = 9720 – 12877 = -3157J5.6 Power- Power measures the rate of work done by a force- The average power done by a force during a time interval Δt is the work divided by the time intervalo Pav = W/ Δto SI Unit: Watt (W) 1W = 1J/s- Other widely used units of power:o Horsepower (hp) 1hp = 746Wo 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 = FΔx- We haveo Pav = W/ Δt = FΔx/ Δt = FVav- NOTE: the power of a force is not only proportional to the force, but also proportional tovelocity- Instantaneous power: P = FV- Example: P = FVo 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 = 0o 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 No Power of the motor:o P = FV = TV = (2.16 x 104)(3) = 6.48 x 104 NChapter 6: Momentum & Collisions- Momentum: P = mv- Impulse: I = FΔt- Conservation of momentum: ΣPi = ΣPf6.1 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=mvo SI Unit: kg·m/s = N·s- Momentum is related to the impulse done on an objecto I = FΔt- Both momentum and impulse are vector quantities and have same unitsImpulse – Momentum Theorem- Similar to the work – energy theorem, we have the impulse – momentum theorem:o I = Δp Δp = mvf – mvio Impulse delivered to an object = change in the object’s momentum- Proof: from Newton’s 2nd law: F = mao FΔt = m(aΔt)  vf = vi +aΔto FΔt = m(vf – vi)o I = Δp- The rate of change in the momentum of an object is equal to the (net) force acting on ito FΔt = Δp  F = Δp/Δt- During a collision, the change in momentum is fixed – you cannot change ito Initial momentum: pi = mvio 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 timeo Seat belt increases stopping time by more than 10 timeso Air bags also increase stopping time and contact area thus prevents oenetration wounds and fracturesVarying 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 forceo FavΔt =