Positive, Negative and Zero Work

1. When the force and the displacement are in the same direction (θ=0°), the work done by the force is positive.
2. When the force and the displacement are in opposite directions (θ=180°), the work done by the force is negative.
3. When the applied force does not cause any displacement or when the force and the displacement are perpendicular to each other (θ=90°), the work done by the force is zero.

Application 1:

When a person lifts a body from the ground to some higher position, the work done by the lifting force (i.e., the force applied by the person) is positive since force (vector) and displacement (vector) are along the same (vertically upward) direction and hence,
θ = 0, cos θ = 1
However, the work done by the gravity (or the force by the earth on the body) is negative since force (vector) and displacement (vector) are oppositely directed and hence
θ = 180° cos θ = −1.

Application 2:

A box is moved over a horizontal path by applying force F = 60 N at an angle θ = 30° to the horizontal. What is the work done during the displacement of the box over a distance of 0.5 km.
Solution:
By definition, W = F s cos θ
Here F = 60 N; s = 0.5 km = 500 m; θ = 30°.
W = (60)(500) cos 30° = 26 kJ

1. Aim: To study the relationship between force, displacement, and work done using a setup involving a plastic cup, thread, and nuts.

2. Requirements: plastic cup, thread, two nuts, ruler, and table.

3. Procedure

• Make a hole in the bottom of the plastic cup.
• Pass a doubled thread through the hole, tying a thick knot at the end to hold it in place.
• Attach a nut to each end of the thread.
• Place the cup on the table, keeping one nut inside the cup and letting the other nut hang down the side of the table.

Action 1 (Figure A): Observe what happens when the nut hanging down applies force on the cup.

Action 2 (Figure B): Slide the cup on the table and stop it abruptly using a ruler. Observe the effect of applying force through the ruler.

Action 3 (Figure C): Place the cup at the centre of the table, ensuring both nuts hang on opposite sides of the table. Observe if the cup moves.

Positive, negative and zero work

4. Observations

Figure A: Gravity acting on the hanging nut pulls the cup toward the edge of the table.

Figure B: The force applied by the ruler changes the motion of the cup. The displacement depends on the applied force's magnitude and direction.

Figure C: The cup remains stationary as the forces from the hanging nuts balance each other.

Types of Work Done:

• Figure A: Positive work (force and displacement in the same direction).
• Figure B: Work is done depending on the direction of force applied by the ruler relative to displacement.
• Figure C: Zero work (no displacement).

Relationship Between Force and Displacement:

Work is done when there is displacement in the direction of the applied force. If displacement is zero or the force is perpendicular to displacement, work done is zero.

5. Conclusion

• In Figure A, the gravitational force on the hanging nut pulls the cup, resulting in positive work.
• In Figure B, the force applied by the ruler changes the motion of the cup.
• In Figure C, balanced forces result in no displacement; hence, no work is done.

When force and displacement are perpendicular (e.g., in the circular motion of satellites), no work is done, as seen in the satellite analogy.