1. Consider a water skier being towed by a light inelastic string at a constant speed of 20 mph behind a powerboat. Air resistance on the water skier is 10N and on the powerboat it is 20N. The friction of the boat on the water is 40N and of the skier on the water is 30N. If the water skier has a mass of 90 kg, find the Tension in the tow rope and the driving force of the boat. Lesson Objective Equilibrium Problems with connected particles

2. Key aspects for solving problems involving objects in equilibrium: 1)Always draw a clear diagram of the objects 2)Add all the forces acting on the objects to the diagram 3)Write down equations for each separate object by resolving the forces on each object in two perpendicular directions 4)Look at all the equations you have written down and solve them simultaneously to answer the question Note: In essence we will do this same procedure for every type of question involving forces. As the situations become more complicated (not in equilibrium for example) the equations we write down will just be adjusted as necessary.

3. The diagram shows a train consisting of a mass of 50 000kg pulling two trucks, A and B each of mass 10 000kg. The force of resistance on the engine is 2000N and that on each of the trucks 200N. The train is moving at a constant speed. a)Draw a diagram showing the horizontal forces on the train as a whole. Hence, by considering the equilibrium of the train as a whole, find the driving force provided by the engine. b)By drawing separate diagrams for the Trucks and the Engine find the tension in each of the couplings

4. Consider a pile of 3 books resting on a table. The book on the bottom has weight 1N, the middle book has weight 2N and the top book has weight 3N. a) What is the reaction force on the table? b) What is the normal contact force between the book on the top and the book on in the middle?

5. A parachutist of mass 80kg falls vertically. Air resistance on his body is 20N and he is supported by a harness that consists of 4 ropes each attached to the parachute. He is travelling at a constant speed. If the mass of the parachute is 10kg, what is the resistance force on the parachute and what is the tension force in each of the ropes?

6. A car pulls a trailer up a slope at a constant speed of 10 mph. The slope is at an angle of 10 o degrees to the horizontal The car has a mass of 2000kg and the trailer has a mass of 800kg. If the resistance force on the trailer is twice the resistance force on the car calculate the resistance force and the tension in the tow rope if the driving force is 6000N 10 o

7. 30 o Three blocks of mass M kg, 2M kg and 4M kg slide down a smooth slope at an angle of 30 o to the horizontal. Each connected by a light inextensible coupling. Each block has the same overall resistance force, R. a)Show that R = 7 / 6 Mg b)Suppose that a 4 th block of mass 8M is added to the end of the ‘train’. Find R in terms of M and g. Generalise this result. M 2M 4M