## Episode 202: Forces in equilibrium

Lesson for 16-19

- Activity time 105 minutes
- Level Advanced

In this episode, students will learn about the conditions for static equilibrium (excluding moments of forces).

Lesson Summary

- Demonstration and discussion: The washing line (10 minutes)
- Student experiment: Forces in different directions (15 minutes)
- Student experiment: Forces in equilibrium (20 minutes)
- Worked example and Demonstration (15 minutes)
- Student activity: An estimation (15 minutes)
- Student questions: Two problems (30 minutes)

#### Discussion and demonstrations: The washing line

Take 5 m of good strong string. Ask two pupils to take either end and pull the string taut. Hang a 1 kg mass (10 N force) from the middle of the string. The pupils will find it very difficult (impossible, in fact) to keep the string horizontal.

Drawing a vector triangle of the forces will show why the pupils have had such problems.

Student should understand that the sum of the vertical components of the tensions in the string is equal in magnitude (and of opposite sign) to the weight hanging from the middle.

Similarly, the horizontal components of the tension in the strings are also equal and opposite. Why must this be the case? (Otherwise the string would start to move horizontally.)

You could finish the discussion with a statement of the principles of equilibrium. For an object to be in equilibrium the forces on it must be balanced; we can check this by resolving in two perpendicular directions. This will give the next activity a sense of a corroborative experiment.

#### Student experiment: Forces in different directions

This activity builds upon the opening discussion. Encourage the students to discuss the questions posed on the worksheet – if they don’t it just becomes a tug-of-war. Gather the class together at the end of the activity to compare ideas and clear up misconceptions.

Episode 202-1: Forces in different directions (Word, 35 KB)

#### Student experiment: Forces in equilibrium

This activity focuses on vector triangles. The fact that the triangles the students draw won’t quite close can be a springboard for discussion but you should not allow it to dominate the thinking of the less able students – the purpose of the demonstration is to give practice in using a graphical technique to consider forces in equilibrium, and show that it works!

Episode 202-2: Forces in equilibrium (Word, 39 KB)

#### Worked example and Demonstration

You can use this worked example in conjunction with the apparatus described in the question.

This example considers forces in equilibrium in a new

situation – a trolley on a slope.

Having completed sections a – e, good students might like to resolve parallel to the runway to show that

*F*cos( θ ) = *W*sin( θ )

Episode 202-3: Trolley on a slope (Word, 27 KB)

#### Student activity: An estimation

Students can apply what they have learned to the equilibrium of a pylon supporting power lines. You may find it useful to give a lead in to the question and draw the diagram of the situation out for them. A picture can be used if you do not have pylons in the locality.

You may want to model the situation in class. In this case, a length of chain between two stools will show the students the effect and allow you to rehearse the calculations with them.

Episode 202-4: Forces acting on a power line (Word, 26 KB)

#### Student questions: Two problems

The first question should be a straightforward confidence-booster as it mirrors the algebraic analysis covered in the episode.

The second question is another scale drawing exercise. Mathematically fluent students should be encouraged to analyse the problem trigonometrically using the sine rule.

Episode 202-5: Questions on forces and equilibrium (Word, 56 KB)