Physics 114C - Mechanics Lecture 17 (Walker: Ch. 7.3-4) Work & Power February 7, 2014

1. Physics 114C - MechanicsLecture 17 (Walker: Ch. 7.3-4)Work & PowerFebruary 7, 2014 John G. Cramer Professor of Physics B451 PAB cramer@phys.washington.edu

2. Announcements • Prof. Cramer will be back on Monday. • HW#5 is due at 11:59 PM on Thursday, February 13.HW#6 is due at 11:59 PM on Thursday, February 20. • Clicker scores as of last Friday are posted on Catalyst. • We will have Exam 2 on Friday, February 14 (Happy Valentine’s Day!). It will cover Chapters 5-8 and will be similar to Exam 1 in its structure. There will again be assigned seating. If you have not already done so and would like to request a left-handed seat, right-handed aisle seat, or front row seat, E-mail your request to Prof. Cramer ASAP. Physics 114A - Lecture 17

3. Lecture Schedule (Part 2) We are here. Physics 114A - Lecture 17

4. Work and Area If the force is constant, we can graphically interpret the work done (W = F d) as the area of a rectangleF tall and d wide: Physics 114A - Lecture 17

5. Work Done by a Variable Force If the force takes on several successive constant values we can add adjacent rectangles: Physics 114A - Lecture 17

6. Work Done by a Variable Force We can then approximate a continuously varying force by a succession of constant values. Physics 114A - Lecture 17

7. Example:Work Done by a Varying Force A force varies with x as shown. Find the work done by the force on a particle as the particle moves from x = 0.0 m to x = 6.0 m. Physics 114A - Lecture 17

8. Elastic Solids & Restoring Forces An “elastic” material is one that exhibits a restoring force, a force that acts so that it restores a system to an equilibrium position. Examples are springs and rubber bands. An elastic material stores potential energy when it is deformed and restores it when it returns to equilibrium. Microscopically, elastic solids depend on the spring-like bonds that bind atoms in a solid. rubberband Physics 114A - Lecture 17

9. Stretching a Spring The unloaded spring has a length L0. Hang a weight of mass m on it and it stretches to a new length L. Repeat the process and measure Ds=L-L0vs. the applied force Fsp=mg. We find that Fsp=kDs, wherekis the “spring constant”. Physics 114A - Lecture 17

10. Hooke’s Law The linear proportionality between force and displacement is found to be valid whether the spring is stretched or compressed, and the force and displacement are always in opposite directions. Therefore, we write the force-displacement relation as: This relation for the restoring force of a spring is sometimes called Hooke’s Law, named after Robert Hooke, a contemporary of Newton. It is not really a law or nature, but rather a rule of behavior for most springs. Physics 114A - Lecture 17

11. Clicker Question 1 The force vs. displacement curves of three springs are measured. Which spring has the largest spring constant? a) Spring 1 b) Spring 2 c) Spring 3 d) They are all the same Physics 114A - Lecture 17

12. Work and Springs The force needed to stretch a spring an amount x is F = kx. Therefore, the work done in stretching the spring is (7-8) Physics 114A - Lecture 17

13. Hooke’s Law and Work Physics 114A - Lecture 17

14. Clicker Question 2 4.0 m/s A spring-loaded gun shoots a plastic ball with a speed of 4.0 m/s. If the spring is compressed twice as much, what is the ball’s speed? a) 2.0 m/s b) 4.0 m/s c) 8.0 m/s d) 16.0 m/s e) 32.0 m/s Physics 114A - Lecture 17

15. Example: Work Doneon a Block by a Spring A 4.0 kg block on a frictionless surface is attached to a horizontal spring with k = 400 N/m. The spring is initially compressed to 5.0 cm. (a) Find the work done on the block by the spring as the block moves from x = x1 = -5.0 cm to its equilibrium position of x = x2 = 0 cm. (b) Find the speed of the block at x2 = 0 cm. Physics 114A - Lecture 17

16. Example: Dragging a Block (1) A spring is attached to a 2 kg block. The other end is pulled by a motorized toy train that moves forward at 5.0 cm/s. The spring constant is k=50 N/m and the coefficient of static friction between the block and the surface is ms=0.6. The spring is in equilibrium at t=0 s when the train starts to move. At what time does the block start to slip? Physics 114A - Lecture 17

17. Example: Dragging a Block (2) This is an example of “stick-slip motion”, which is common in nature. Example: behavior of rocks during seismic activity and earthquakes. Physics 114A - Lecture 17

18. James Watt (1736-1819) Power Power is a measure of the rate at which work is done: (7-10) SI power unit: 1 J/s = 1 watt = 1 W 1 horsepower = 1 hp = 746 W Physics 114A - Lecture 17

19. Power Physics 114A - Lecture 17

20. Power is the rate of energy flow. Power and Velocity Physics 114A - Lecture 17

21. Power and Velocity If an object is moving at a constant speed in the presence of friction, gravity, air resistance, and so forth, the power exerted by the driving force can be written: (7-13) Physics 114A - Lecture 17

22. Example:The Power of a Motor A small motor is used to operate a lift that raises a load of bricks weighing 500 N to a height of 10 m in 20 s at constant speed. The lift weighs 300 N. What is the power output of the motor? Physics 114A - Lecture 17

23. End of Lecture 17 • Before Monday, read Walker Chapter 8.1-2. • HW#5 is due at 11:59 PM on Thursday, February 13. HW#6 is due at 11:59 PM on Thursday, February 20. • Clicker scores as of last Friday have been posted on the Catalyst system. • We will have Exam 2 on Friday, February 15. It will cover Chapters 5-8 and will be similar to Exam 1 in its structure. There will again be assigned seating. If you have not already done so and would like to request a left-handed seat, a right-handed aisle seat, or a front row seat, E-mail your request to Prof. Cramer ASAP. Physics 114A - Lecture 17