Transcript Chapter 3
• • C7 – Some Potential Energy Functions C8 – Force and Energy General Physics 1 Two Minute Problems – C7T.1 • • • • • The electrostatic potential energy between the proton and electron in a normal hydrogen atom (with the conventional choice of reference separation) is A. negative B. zero C. positive D. any of the above General Physics 2 Two Minute Problems – C7T.4 • • • • • • The following graph shows the potential energy function of a certain interaction. The interaction is A. always attractive B. always repulsive C. attractive for small r, repulsive for large r D. repulsive for small r, attractive for large r E. there is not enough information for a meaningful answer General Physics 3 Two Minute Problems – C8T.1 • • • • • • • Two hockey pucks are initially at rest on a horizontal plane of frictionless ice. Puck A has twice the mass of puck B. Imagine that we apply the same constant force to each puck for the same interval of time dt. How do the pucks’ kinetic energies compare at the end of this interval? A. KA = 4 KB B. KA = 2 KB C. KA = KB D. KB = 2 KA E.. KB = 4 KA F. Other General Physics 4 Two Minute Problems – C8T.5 • • When an object slides down a frictionless incline, the cotact interaction between the object and the incline does not contribute to the object’s kinetic energy, true (T) or false (F)? This means that it also does not transfer any momentum to the object, T or F? General Physics 5 Potential Energy Functions • Electromagnetic Interaction q1 q2 V r k r • Gravitational Interaction m1m2 V r G r • re fe re ncese paration: V r 0 whe nr re fe re ncese paration: V r 0 whe nr Potential Energy of a Spring 1 2 V r k s r r0 2 General Physics re fe re ncese paration: V r 0 whe nr r0 6 Attractive and Repulsive Interactions q1 q2 V r k r General Physics m1m2 V r G r 7 Interaction with a spring General Physics 8 Dot Product u w uw cos General Physics 9 Kinetic Energy • Kinetic energy is the dot product of velocity and momentum dK v dp whe ndp p dK vp cos • The kinetic energy of each interaction of the objects in the system contribute to the overall kinetic energy of the object dK v dpA v dpB v dpC ... General Physics 10 An Interaction’s contribution to dK • Impulses are small changes in momentum that contribute to the total momentum of a particle dp dpA dpB dpC ... • By analogy, k-work values are small changes in kinetic energy that contribute to the total kinetic energy of a particle dK dKA dKB dKC ... General Physics 11 K-work • Each interaction’s contribution to dK is the tiny amount of k-work the interaction contributes to the particle during the time it takes the particle to move a tiny displacement. dK F dr • F is the force exerted on the particle by the interaction and dr is the small displacement the particle moves General Physics 12 K-work and impulse are like cash transactions • • • • Momentum and kinetic energy are analogous to your bank account. Impulse and k-work analogous to cash transactions into and out of your bank account Impulse has the same units as momentum K-work has the same units as kinetic energy General Physics 13 One big difference… • • The impulse that an interaction between two particles delivers to one particle’s momentum comes directly out of the other particle’s momentum account. The k-work represents a transaction between a particle’s kinetic energy and the interaction’s potential energy, NOT the other particle’s kinetic energy • Gravitational potential – both particles are increasing their kinetic energy at the expense of the potential energy General Physics 14 Force Laws • • • The definition dK F dr Provides a link between force and energy We can determine the force an interaction exerts on a particle Gravitational force Spring force General Physics Fgz m g GmA mB Fg rˆ 2 r Fsp k s r r0 rˆ 15 Contact interactions • Perpendicular interactions don’t contribute to kinetic energy dK FN dr 0 General Physics 16 Group Problems • C8B.5 C8S.6 C8S.7 • Classroom whiteboards • • General Physics 17