Chapter 7

Work and Energy

Study Guide will is posted on webpageExam on FRIDAY, OCT 23

7-3 Work Done by a Varying Force

Example 7-5: Work done on a spring.

(a) A person pulls on a spring, stretching it 3.0 cm, which requires a maximum force of 75 N. How much work does the person do? (b) If, instead, the person compresses the spring 3.0 cm, how much work does the person do? The spring constant is K=2.5X103N/m

7-3 Work Done by a Varying Force

Example 7-6: Force as a function of x.

where F0 = 2.0 N, x0 = 0.0070 m, and x is the position of the end of the arm. If the arm moves from x1 = 0.010 m to x2 = 0.050 m, how much work did the motor do?

A robot arm that controls the position of a video camera in an automated surveillance system is manipulated by a motor that exerts a force on the arm. The force is given by

Problem 35

• (II) A spring has a constant k=65N/m. Draw a graph of the spring force F versus the stretch distance, and use it to determine the work needed to stretch the spring from x= 3cm to x= 6.5 cm where x=0cm refers to the spring’s unstretched length.

Problem 43

(II) The force needed to hold a particular spring compressed an amount x from its normal length is given by kx+ax3+bx4 . How much work must be done to compress it by an amount X, starting from X = 0.

7-3 Work Done by a Varying Force

Particle acted on by a varying force. Clearly, ·d is not constant!F

7-3 Work Done by a Varying Force

For a force that varies, the work can be approximated by dividing the distance up into small pieces, finding the work done during each, and adding them up.

7-3 Work Done by a Varying Force

In the limit that the pieces become infinitesimally narrow, the work is the area under the curve:

Or:

7-3 Work Done by a Varying Force

Work done by a spring force:

You are exerting a force Fp= kx

K is the spring constant or stifness.

The force exerted by a spring is given by: called restoring force

This is called Hooke’s law

7-3 Work Done by a Varying Force

Plot of F vs. x. Work done is equal to the shaded area.

7-4 Kinetic Energy and the Work-Energy Principle

Example 7-7: Kinetic energy and work done on a baseball.

A 145-g baseball is thrown so that it acquires a speed of 25 m/s. (a) What is its kinetic energy? (b) What was the net work done on the ball to make it reach this speed, if it started from rest?

7-4 Kinetic Energy and the Work-Energy Principle

Example 7-8: Work on a car, to increase its kinetic energy.

How much net work is required to accelerate a 1000-kg car from 20 m/s to 30 m/s?

The net work is the increase in kinetic energy

7-4 Kinetic Energy and the Work-Energy Principle

Example 7-10: A compressed spring.

A horizontal spring has spring constant k = 360 N/m. (a) How much work is required to compress it from its uncompressed length (x = 0) to x = 11.0 cm? (b) If a 1.85-kg block is placed against the spring and the spring is released, what will be the speed of the block when it separates from the spring at x = 0? Ignore friction. (c) Repeat part (b) but assume that the block is moving on a table and that some kind of constant drag force FD = 7.0 N is acting to slow it down, such as friction (or perhaps your finger).