Chapter 2 - Work

1. Chapter 2 - Work Section 1 – Work in Mechanical Systems

2. Objectives • Define work by a force or torque in a mechanical system. • Explain the relationship between work, force and distance. • Solve work problems given force and distance in English or SI units. • Explain efficiency in terms of work in & work out

3. Objectives – cont. • Define radian measure of angles. • Explain the relationship between work, torque and angle moved. • Solve work problems given torque and angle in English or SI units.

4. Work done by a force • Work = force times distance • W = Fd • If the object does not move, no work is done.

5. Units • English units are foot-pounds (ft-lb) or inch pounds (in-lb) • SI units are newton-meters (N-m). • 1N-m = 1 Joule (J). • Work can be positive or negative depending upon the direction of the displacement.

6. Work changes energy • Work changes the kinetic or potential energy of an object. • The amount of work done equals the change in the energy of an object. • W = DKE + DPE

7. Efficiency • Efficiency equals the output work divided by the input work, usually expressed as a percentage. • Eff= (Wout / Win ) x 100%

8. Measuring angles in radians

9. Radians • The angle, q is defined as the ratio of the arc length, s to the radius, r. q = s / r. • Since both the radius and the arc length are measured in meters, the units of the angle cancel out. The “unit” for the angle is called radians (rad). • One radian is the angle marked out by an arc length equal to the radius of the circle.

10. Converting to Radians • The circumference of a circle is 2pr. The angle marked out by going the entire circumference would be 2pr / r or 2p rad. • Thus 2p rad = 360o or p rad = 180o • 1 rad = 360o / 2p rad = 57.3o • 1o = 2p rad / 360o = 0.017 rad • 1 revolution (rev) = 360o = 2p rad

11. Convert the following • 90o to radians • 20 radians to revolutions • 45o to revolutions • 10 revolutions to radians • 5 radians to degrees

12. Work done by a torque • Torque = force times lever arm t = Fr • Thus F=t / r • W = Fd = (t/r)d • W = t (d/r) where d = arc length • Thus work = torque times the angle (in radians) through it moves. • W = tq

13. 20 lb of force is needed to turn a 1.5 ft crank 5 revolutions. Calculate the work First, find the torque – t = Fl = 20 lb x 1.5 ft = 30 ft-lb Convert the angle to radians – 5 rev X 2p rad/rev = 10p rad Now compute the work W =tq = 30 ft-lb x 10p rad = 944 ft-lb Example – work done to turn a crank

14. Summary • Mechanical systems use force and torque to cause movement and do work. • Work is done when a force or torque moves an object. Work is done when the force or torque is applied in the direction of motion. • Work equals force times distance (W = fd) or torque times angle (W = tq) . Units are ft-lb or N-m.

15. Summary - cont • Efficiency is the ratio of output work to input work. Eff = Wout / Win . This is usually expressed as a percentage. • In calculations of work, angles must be in radians. A radian is a dimensionless ratio and thus not a unit. • 1 revolution = 360o = 2p rad.