1. Force and Work

2. 11.1 What is Work Done?
The work done by a force is equal to the force multiplied by the distance moved in the direction of the force.
Work done = Force  Distance moved in the direction of the force

3. 11.1 What is Work Done? For work to be done:
There is a force acting on the object.
The object moves.
The movement of the object is in the direction of the force.

4. Calculating work done
The work done by a force measures the amount of energy being changed from one form to another as the work is done.
The unit of work done is the joule (J).
Work done = Force  Distance moved
1 joule = 1 newton  1 metre
1 J = 1 N m
Express

5. Calculating work done
Force = 1 N
One joule is the amount of work done when a force of one newton moves an object by one metre in the direction of the force.
Weight = 1 N
Force = 1 N
Distance = 1 m
Work done
= 1 N x 1 m
= 1 J
Weight = 1 N

6. Calculating work done
The force that you exert in lifting an object to a certain height above the ground is equal to the force of gravity acting downwards on the object.
The force exerted by gravity on the object’s mass is known as the weight of the object.
The weight of a 1 kg mass is usually taken to be 10 N.
Work done to lift an object = Lifting force  distance = Weight  distance

7. Calculating work done Express Example 1
Marie lifts a 5 kg mass from the floor and puts in on a table one metre high. What is the work done?
Solution
Work done = Force x Distance moved
= (5  10) N  1 m
= 50 N m
= 50 J
1 m

8. Calculating work done Express Example 2
Isaac carries an 8 kg pail of water up a flight of 15 steps, each 20 cm high. Calculate the amount of work done against gravity to carry the pail upstairs.
20 cm

9. Calculating work done Express Solution
The bag pulls the boy’s arm downwards. Since the pail hangs without moving on his arm, his arm must be pulling upwards with a force equal to the weight of the pail, which is 80 N. The distance moved in the direction of the force is the upward distance, not the length of the stairs.
Work done = 80 N  (15  0.2 m)
= 240 J

10. Calculating work done Express Example 3
The energy used to pull a large rock 40 m along the rough floor is 6 kJ. Find the tension in the rope used to pull the rock, if the rope is parallel to the floor.
Solution
Work done = Force  Distance moved
Force = Work done
Distance moved
= J
40 m
= 150 N

11. Calculating work done Express Example 4
The work done to pull up a bucket of 1 N filled with 23 N of water is 4.08 kJ. How far up is the bucket pulled?
Solution
Work done = Force  Distance moved
Distance moved = Work done
Force
= 4080 J
240 N
= 17 m

12. Calculating work done Express Example 5
A man tries very hard to lift a weight. His muscles strain with a force of 800 N. Finally, he collapses out of sheer exhaustion. How much work has he done against gravity?
Solution
Work done = Force  Distance moved
= 800 N x 0 m
= 0 J

13. Calculating work done Express Example 6
Marie carries her bag weighing 20 N and walks 30 m. How much work did she do against gravity while carrying her bag during her journey?
Solution
The force she exerts to carry her bag is equal to the weight of her bag. But Marie is moving sideways, while the force she exerts points up. Her movement is not in the direction of the force. Thus, no work is done against gravity.

14. 11.2 Moment of a Force Express
When we push or pull a door, we are applying a force that causes a turning effect.
This turning effect is called the moment of a force, which is used to make work easier.
The point of rotation of the moment of a force is called a fulcrum or pivot.

15. 11.2 Moment of a Force Express Moment of a force, M = F  d
= Force  Perpendicular distance from the fulcrum to the line of action of the force
S.I. unit for moment of force is newton-metre (Nm)

16. Calculation with moments
Anticlockwise moment
Clockwise moment
Express
Moments about the fulcrum F:
Moments of A’s weight = 4 N  0.60 m = 2.4 Nm
Moments of B’s weight = 12 N  0.20 m = 2.4 Nm B A
0.60 m
0.20 m F
4 N
12 N

17. Calculation with moments
Anticlockwise moment
Clockwise moment
Express B
B’s moments is called a clockwise moment because it turns the beam in the direction that a clock’s hands would move.
The moment due to A is an anti-clockwise moment.
When two moments balance, the anti-clockwise moment about any point is equal to the clockwise moment about the same point. A
0.60 m
0.20 m F
4 N
12 N

18. Calculating work done Express Example 7
Find the weight of the person A sitting on the balanced see-saw in the diagram shown. B A
1.5 m
1.0 m W
600 N

19. Calculating work done Express Solution Let the weight of A be W.
Anti-clockwise moment = Clockwise moment
W  1.5 m = 600 N  1.0 m
W  1.5 m = 600 Nm
W = 600 Nm = 400 N
1.5 m
The weight of A is 400 N.

20. Calculating work done Express Example 8
A door is held in balance by two forces – one force of 20 N acting on the handle 60 cm from the fulcrum, O, and the other of 15 N acting on the edge of the door. Find the width of the door.
20 N
60 cm
15 N O
Top view of door

21. Calculating work done Express Solution Let the width of door be D.
Taking moments about O,
Anti-clockwise moment = Clockwise moment
15 N  D = 20 N  60 m
D = 1200 Ncm = 80 cm
15 N
The width of the door is 80 cm.

22. 11.3 Levers
Express
Some examples of machines that apply moments to help us perform various tasks are pulleys, hydraulic presses and levers.
You use a lever by applying a force (called the effort) to one point of the lever.
This effort is used to overcome a force (called the load) at some other point.
In levers, the effort produces a moment, which balances the moment due to the load. The moments are taken about a point called the fulcrum (or pivot).

23. Micellaneous http://hyperphysics.phy-astr.gsu.edu/hbase/work2.html