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Connected Systems

Connected Systems. Action and Reaction Problems. The [towing] force the car exerts on the caravan is EQUAL TO the force the caravan exerts on the car. The forces in the coupling are equal and opposite. This fact is used to solve problems. a ms -2. R 1. R 2. T. T. 6000 N. 1200 kg.

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Connected Systems

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  1. Connected Systems

  2. Action and Reaction Problems The [towing] force the car exerts on the caravan is EQUAL TO the force the caravan exerts on the car The forces in the coupling are equal and opposite. This fact is used to solve problems.

  3. a ms-2 R1 R2 T T 6000 N 1200 kg 400 kg Weight =1200g Weight =400g Action and Reaction Problem 1200 kg The car has a driving force of 6000N. What is the acceleration? 400 kg First: Draw Force diagrams Opposite and equal force

  4. a ms-2 Resultant force = T Resultant force = 6000 - T (in direction of acceleration) (in direction of acceleration) R1 R2 T T 6000 N 1200 kg 400 kg Weight =1200g Weight =400g Action and Reaction Problem Caravan Car N2L : F = ma T = 400a N2L : F = ma 6000 - T = 1200a First: Draw Force diagrams Opposite and equal force

  5. a ms-2 R1 R2 T T 6000 N 1200 kg 400 kg Weight =1200g Weight =400g Action and Reaction Problem Caravan Substitute T 6000 - T = 1200a T = 400a Car 6000 - 400a = 1200a 6000 - T = 1200a 6000 = 1600a a= 6000 / 1600 = 3.75 ms-2 First: Draw Force diagrams Opposite and equal force

  6. a ms-2 R1 R2 200 N T T 8000 N 1500 kg 500 kg 100 N Weight =1500g Weight =500g Action and Reaction Problem 2 The car has a driving force of 8000N. 1500 kg 500 kg Forces of resistance are 200 N on the car and 100N on the caravan. What is the acceleration and tension in the coupling? First: Draw Force diagrams Opposite and equal force

  7. Resultant force = T - 100 Resultant force = 8000 - 200- T (in direction of acceleration) (in direction of acceleration) R1 R2 200 N T T 8000 N 1500 kg 500 kg 100 N Weight =1500g Weight =500g Action and Reaction Problem 2 Caravan Car N2L : F = ma T - 100 = 500a N2L : F = ma 8000 - 200- T = 1500a 7800- T = 1500a Force diagrams Opposite and equal force

  8. Action and Reaction Problem 2 Caravan Substitute T 7800- T = 1500a T - 100 = 500a 7800- (500a+ 100) = 1500a T = 500a + 100 Car 7700- 500a= 1500a 7800- T = 1500a 7700= 2000a a= 7700/ 2000 = 3.85 ms-2 T = 500a + 100 T = 500 x 3.85 + 100 T = 500 x 3.85 + 100 T = 1925+ 100 = 2025 N

  9. 120kg 120kg 30kg T1 0.1 ms-2 T2 1176 N 30kg 294N Example A crate mass 120kg is pulled vertically by a cable. A box mass 30kg is attached to the underside. They accelerate upwards at 0.1ms-2. Find the tensions in the cables. 0.1 ms-2 First: Draw Force diagrams N2L : F = ma top weight = 120g = 120 x 9.8 = 1176 N T2 N2L : F = ma bottom weight = 30g = 30 x 9.8 = 294 N

  10. Resultant force = T2- 294 Resultant force = T1- T2- 1176 120kg (in direction of acceleration) (in direction of acceleration) T1 0.1 ms-2 T2 1176 N 30kg 294N A crate mass 120kg is pulled vertically by a cable. A box mass 30kg is attached to the underside. They accelerate upwards at 0.1ms-2. Find the tensions in the cables. Top Weight First: Draw Force diagrams N2L : F = ma T1- T2- 1176= 120 x 0.1 T1- T2= 1188 Bottom Weight T2 N2L : F = ma T2- 294= 30 x 0.1 T2= 294 + 3 = 297 N

  11. 120kg T1 0.1 ms-2 T2 1176 N 30kg 294N A crate mass 120kg is pulled vertically by a cable. A box mass 30kg is attached to the underside. They accelerate upwards at 0.1ms-2. Find the tensions in the cables. Top Weight T1- T2= 1188 First: Draw Force diagrams Bottom Weight T2= 297 N T1- T2= 1188 T2 T1- 297= 1188 T1= 1485 N

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