Work and Kinetic Energy PHYS116 A01 91914 Lecture

Work and Kinetic Energy PHYS-116 A-01, 9/19/14, Lecture 12 Momchil Velkovsky

Consider the vectors shown. What is the dot product C. D ? ¡ ¡ ¡ A. (120 m 2 ) cos 78. 0° B. (120 m 2 ) sin 78. 0° C. (120 m 2 ) cos 62. 0° D. (120 m 2 ) sin 62. 0° E. none of these

Consider the two vectors What is the dot product ¡ ¡ ¡ A. zero B. 14 C. 48 D. 50 E. none of these ?

Work, a force through a distance l As in the illustration, pushing in the same direction that the object moves

Use the parallel component if the force acts at an angle

How can it be such a great “workout” with no work? • When positive and negative work cancel, the net work is zero even though muscles are exercising.

Stepwise solution of work done by several forces . . . Fg

A 6. 00 -kg block and an 8. 00 -kg block are connected as shown. When released, the 6. 00 -kg block accelerates downward and the 8. 00 -kg block accelerates to the right. After each block has moved 2. 00 cm, gravity has done ¡ ¡ A. more work on the 8. 00 -kg block than on the 6. 00 -kg block. B. the same amount of work on both blocks. C. less work on the 8. 00 -kg block than on the 6. 00 -kg block. D. not enough information given to decide

A 6. 00 -kg block and an 8. 00 -kg block are connected as shown. When released, the 6. 00 -kg block accelerates downward and the 8. 00 -kg block accelerates to the right. After each block has moved 2. 00 cm, the total work done on the 8. 00 -kg block ¡ ¡ A. is greater than the total work done on the 6. 00 -kg block. B. is the same as the total work done on the 6. 00 -kg block. C. is less than the total work done on the 6. 00 -kg block. D. not enough information given to decide

The work-energy theorem • Work done on an object will change its velocity.

A nonzero net force acts on an object. Which of the following quantities could be constant? ¡ ¡ A. the object’s kinetic energy B. the object’s velocity C. both of the above D. none of the above

How fast will be our sled moving? l l Fx=800 N m=2000 kg 3. 0

Two iceboats (one of mass m, one of mass 2 m) hold a race on a frictionless, horizontal, frozen lake. Both iceboats start at rest, and the wind exerts the same constant force on both iceboats. Which iceboat crosses the finish line with more kinetic energy (KE)? 1. 2. 3. 4. 5. the iceboat of mass m: it has twice as much KE as the other the iceboat of mass m: it has 4 times as much KE as the other the iceboat of mass 2 m: it has twice as much KE as the other the iceboat of mass 2 m: it has 4 times as much KE as the other they both cross the finish line with the same kinetic energy

Physics trivia ¡ Ernest Rutherford used the following way to select assistants. When someone came to him for the first time, he’ll give him a task. If afterwards the assistant came to ask what to do next, he’ll fire him.

Work for composite systems x 1 F s/b x 0 Fw/s x 1 moves, x 0 does not! Fs/b does work, Fw/s does not, although they may have the same magnitude.

Work by forces acting on composite objects ¡ ¡ ¡ The static friction force F is the net force. It creates the acceleration. It is not doing work! Still the kinetic energy of the motorcycle changes! a F

Work and energy with varying force

The stretch of a spring and the force that caused it

Motion with a varying force ¡ ¡ ¡ k=2. 25 N/m m=1 kg At the point where the spring is un-stretched v 1 =2 m/s mk= 0. 408 What is the distance traveled to the point where v=0 ?

Motion on a curved path h

Watt about power? 1 hp=746 W P=d. W/dt=F. dr/dt P=F. v