PHYS 1443 Section 001 Lecture 8 Monday June

PHYS 1443 – Section 001 Lecture #8 Monday, June 12, 2006 Dr. Jaehoon Yu Quiz Solutions Work done by a varying force Work and Kinetic Energy Theorem Monday, June 12, 2006 PHYS 1443 -001, Summer 2006 Dr. Jaehoon Yu 1

Announcements • Quiz result – Average: 3. 8/8 • 46/100 • Quiz 1: 76 – Top score: 7/8 • Mid-term exam – 8: 00 – 10 am, this Thursday, June 15, in class – CH 1 – 8 Monday, June 12, 2006 PHYS 1443 -001, Summer 2006 2

Work Done by Varying Force • If the force depends on the position of the object in motion – one must consider work in small segments of the position where the force can be considered constant – Then add all work-segments throughout the entire motion (xi xf) In the limit where Dx 0 – If more than one force is acting, the net work is done by the net force One of the forces depends on position is force by a spring The work done by the spring force is Hooke’s Law Monday, June 12, 2006 PHYS 1443 -001, Summer 2006 3

Kinetic Energy and Work-Kinetic Energy Theorem • Some problems are hard to solve using Newton’s second law – If forces exerting on the object during the motion are so complicated – SF Relate the work done on the object by the to theon an Suppose net force SF net wasforce exerted Mthe speed of the object M change of vi vf object for displacement d to increase its speed from on vi tothe vf. object by the net force S The work d Displacement Work Monday, June 12, 2006 Acceleration Kineti c Ener Work done by the net force gy of object’s causes change kinetic energy. PHYS 1443 -001, Summer Work-Kinetic 2006 Energy 4

Example of Work-KE Theorem A 6. 0 kg block initially at rest is pulled to East along a horizontal, frictionless surface by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3. 0 m. M F M vi=0 Work done by the force F is vf d From the work-kinetic energy theorem, we know Since initial speed is 0, the above equation becomes Solving the equation for vf, we obtain Monday, June 12, 2006 PHYS 1443 -001, Summer 2006 5

• Ffr Work and Energy Involving Kinetic Friction What do you think the work looks like if there is friction? It isn’t there when the object is moving. matter! Why? Kinetic Friction – Static friction does not – Then which friction matters? Friction force Ffr works on the object to M M slow down The work on the object by the friction Ffr is vi vf d The final kinetic energy of an object, taking into account its initial kinetic energy, friction force and other source of work, is t=0, KEi Monday, June 12, 2006 Friction, t=T, KEf Engine work PHYS 1443 -001, Summer 6 2006

Example of Work Under Friction A 6. 0 kg block initially at rest is pulled to East along a horizontal surface with coefficient of kinetic friction mk=0. 15 by a constant horizontal force of 12 N. Find the speed of the block after it has moved 3. 0 m. Fk M vi=0 F M Work done by the force F is vf d=3. 0 m Work done by friction Fk is Thus the total work is Using work-kinetic energy theorem and the fact that initial speed is 0, we obtain Solving the equation for vf, we obtain Monday, June 12, 2006 PHYS 1443 -001, Summer 2006 7

Work and Kinetic Energy Work in physics is done only when the sum of forces exerted on an object made a motion to the However much tired your arms feel, if you Whatobject. does this were just holding an object without moving it you have not done any physical work to the object. Mathematically, work is written in a product of magnitudes of the net force vector, the magnitude of the displacement vector and the angle between them. mean? Kinetic Energy is the energy associated with motion and capacity to perform work. Work causes change of energy after the completion Work-Kinetic energy theorem Nm=Joul e Monday, June 12, 2006 PHYS 1443 -001, Summer 2006 8