1. Section 1 – Work in Mechanical Systems
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 = 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. Example – work done to turn a crank
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

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.