Transcript Lecture 12
Physics I 95.141 LECTURE 12 10/18/10 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Work Done by a Spring • The force exerted by a spring is given by: Fspring kx 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Hooke’s Law Example Problem • How much work must I do to compress a spring with k=20N/m 20cm? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Exam Prep Problem • A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). Assume there is a velocity dependent drag force (FD=-10v2). REARTH 6.4 106 m , M EARTH 5.98 1024 kg – A) (5pts) What is the Force required to move the rocket at the surface of the Earth? 1,000 km above the Earth’s surface? – B) (5pts) What is the Work done by air resistance over the 1,000km? – (C) (10pts) What is the Work done by Force responsible for moving the rocket over those 1,000km? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Exam Prep Problem • A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). REARTH 6.4 106 m , M EARTH 5.98 1024 kg – A) (5pts) What is the Force required to move the rocket at the surface of the Earth? 1,000 km above the Earth’s surface? Ignore air resistance. 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Exam Prep Problem • A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). REARTH 6.4 106 m , M EARTH 5.98 1024 kg – B) (5pts) What is the Work done by air resistance over the 1,000km? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Exam Prep Problem • A 5,000 kg rocket is launched from the Earth’s surface at a constant velocity (v=50m/s). REARTH 6.4 106 m , M EARTH 5.98 1024 kg – C) (10pts) What is the Work done by Force responsible for moving the rocket over those 1,000km? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Review of Dot Products • Say we have two vectors A 6iˆ 2 ˆj 3kˆ , B 4iˆ 7 ˆj 4kˆ • What is angle between them? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Outline • • Work-Energy Theorem Conservative, non-conservative Forces • What do we know? – – – – – – – – – – – – – – – – – – – Units Kinematic equations Freely falling objects Vectors Kinematics + Vectors = Vector Kinematics Relative motion Projectile motion Uniform circular motion Newton’s Laws Force of Gravity/Normal Force Free Body Diagrams Problem solving Uniform Circular Motion Newton’s Law of Universal Gravitation Weightlessness Kepler’s Laws Work by Constant Force Scalar Product of Vectors Work done by varying Force 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Energy • One of the most powerful concepts in science, used to solve complicated problems in basically all fields of Engineering, Chemistry, Materials Science, Physics… • For the purpose of this chapter, we will define Energy as: The ability to do work. – This means something has energy if it can exert a force over a distance • We will begin by looking at translational kinetic energy 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Translational Kinetic Energy • Kinetic: associated with motion • Translational: motion in a line or trajectory (as opposed to circular/rotational motion) 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Moving Car • Say a car starts at some velocity v1, and, with a constant net Force Fnet applied to it, accelerates to a velocity v2 over a distance d. 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Kinetic Energy • The net work done on the car results in a change of the car’s kinetic energy (K). The car’s energy (also in Joules), changes by an amount equal to the net work done on the car. 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Work Energy Principle • The net work done on an object is equal to the change in the object’s kinetic energy. 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Example • What is the net Work required to accelerate a 1000kg car from rest to 20 m/s? • What about from 20 m/s to 40 m/s? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Example • What about the net Work required to stop this car when it is going 40 m/s? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Energy of a Spring • A spring (k=400N/m) is compressed 10cm, and a mass (m=2kg) is place in front of the spring. How much work does the spring do on the mass after the spring is released? x=-10cm 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Compressed Spring • What is the kinetic energy (and velocity) acquired by the mass when it separates from the released spring at x=0? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics What about Friction? • Say we assume a constant frictional force (5N) on the mass as it is pushed by the spring. Does work-energy theorem still hold? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Spring problem • Find spidey-k 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Work Done to Extend Spidey-web • d≈500m • vo=25m/s • Mtrain=181,000 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Kinetic Energy of Train 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Work-Energy Principle • Energy is the ability to do work – Train’s kinetic energy does work on Spiderman’s springs • Work and Energy have the same units • Kinetic Energy proportional to mass and the square of velocity • Both Work and Energy are scalar quantities. • Can be applied to a particle, or a mass that can be approximated by a particle…where internal motion is insignificant. • Why do we use Work/Energy here and not Kinematic equations? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Conservative and Non-Conservative Forces • A Conservative Force: – The work done by the force on an object moving from one point to another depends only on the initial and final positions of the object, and is independent of the particular path taken. • A conservative force is only a function of position 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Is Gravity a Conservative Force? • Imagine two scenarios: h dh d 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Alternative Definition • A force is conservative if the net work done by the force on an object moving around a closed path is zero. 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Conservative Forces • The work done by a conservative force is recoverable – The work done by the object (on something else) on a given path is equivalent to the work done by the something else on the object on its return trip. – This means that the net work done on the object over the closed loop is zero, which means, from the workenergy theorem, that the change in energy of the object is zero. – Energy is conserved! 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Springs • Is the Force exerted by a spring a conservative force? 95.141, F2010, Lecture 12 Department of Physics and Applied Physics What about Friction? • Is friction a conservative Force? d d 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Non-Conservative Forces • For friction, the work done by friction on an object moving around a closed loop will never be zero. • This work is not recoverable • Work done by friction (or any nonconservative Force) depends on path between two points 95.141, F2010, Lecture 12 Department of Physics and Applied Physics Non-Conservative Forces • Work done by non-conservative force depends on path 95.141, F2010, Lecture 12 Department of Physics and Applied Physics What about air resistance? • Move from point A to point B, either by path 1 or path 2, at constant velocity (FD=-bv). Path 2 R A Path 1 B 95.141, F2010, Lecture 12 Department of Physics and Applied Physics What about air resistance? • Move from point A to point B, same path, but different speeds, (FD=-bv). 2R A Path 1 B 95.141, F2010, Lecture 12 Department of Physics and Applied Physics What did we learn today? • How we can use Energy/Work to understand physical systems • Power of Work/Energy is that we don’t have to know anything about acceleration, or even the complicated kinematic equations that would go with spring/mass systems or air resistance, etc… • All we need is energy! 95.141, F2010, Lecture 12 Department of Physics and Applied Physics