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# Chapter 2 Mechanical Equilibrium

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1. Chapter 2 Mechanical Equilibrium Conceptual Physics Chapter 2

2. Scalar Quantities Can be fully described by a magnitude and appropriate units Mass Time Temperature Area Vector Quantities Requires a magnitude, appropriate units and a direction Displacement Velocity Acceleration Force Vectors and Scalars 12 mi, S 32 kg 60 s 5 m/s, upward magnitude units 28 °C -9.8 m/s2 8.4 in2 7 N, 30° E of N magnitude direction Conceptual Physics Chapter 2

3. Graphical Representation of Vectors • Vectors are represented by a line with an arrowhead attached. • The length of the vector representsthe magnitude of the quantity. • The direction of the vector indicates which way the vector points. 2V These vectors are equal in magnitude, but opposite in direction. ½V V V -V Conceptual Physics Chapter 2

4. Graphical Representation of Vectors • A vector is described completely by the length of the line and the direction of the arrow. • A vector’s position can be changed at will with no change to the vector quantity. Conceptual Physics Chapter 2

5. Force • A force is a push or pull on an object or, more specifically, any influence that causes a change in motion. • Force is a vector quantity and requires a direction. • Forces are measured in Newtons (N). • Example: F = 1250 N to the right • The combination of all forces acting on an object is called the net force. Conceptual Physics Chapter 2

6. Force • It is the net force that changes the state of motion of an object. Net Force 5 N 15 N is the same as 10 N 5 N 5 N 10 N is the same as 5 N is the same as 0 N 10 N 5 N Conceptual Physics Chapter 2

7. Force • A body can have many forces acting on it and still have a zero net force. And no net force means no change in motion! Conceptual Physics Chapter 2

8. Equilibrium • A body with no net force acting on it is said to be in equilibrium. • A body in equilibrium can either be at rest (static equilibrium) or moving with a constant velocity (dynamic equilibrium). • A body under the influence of only one force can not be in equilibrium. Conceptual Physics Chapter 2

9. Equilibrium A book resting on a table is motionless and is therefore in equilibrium. Identify all of the forces acting on the book. The earth pulls down on the book and gives us the force referred to as the weight of the book. W (weight) • Weight is a measure of the gravitational force acting on a body. • The weight of a body depends on its location and the surrounding gravity. • Weight is a vector quantity. • Weight is measured in Newtons (N). • Example: W = 85 N Conceptual Physics Chapter 2

10. Equilibrium FN (Normal Force) The table pushes up on the book with a force referred to as the normal force or support force. In this case, the normal force exactly balances the weight. W (weight) • A normal force or support force always acts between two surfaces in contact. • It keeps the two surfaces pressed together. • The normal force always acts perpendicular to the surfaces in contact. • The normal force acting on an object on an inclined plane is perpendicular to the plane, but is not opposite the vertical force of gravity. Conceptual Physics Chapter 2

11. Equilibrium There is a tension acting upward in each of the supporting ropes. The tension in each rope is half of Nellie’s weight. TA TB Tension is the stretching force that acts in a rope, cable, spring, rubber band, human arms or anything else that might be pulled on from two opposing directions. TA + TB + W = 0 The earth pulls downward on Nellie. ∑F = 0 The body is in equilibrium W Conceptual Physics Chapter 2

12. Equilibrium The tension in each rope is now one-third of Nellie’s weight. TA TB TC ∑F = 0 The earth pulls downward on Nellie. TA + TB + TC + W = 0 Nellie is still in equilibrium W Conceptual Physics Chapter 2

13. Equilibrium A rock is supported by two ropes. -W TA TB ∑F = 0 TA is found in the same way. TA + TB + W = 0 W The weight is shown acting downward. The vector sum of the tension in the two ropes must add to be equal in magnitude, but opposite in direction to the weight – the resultant must be –W! The body is in equilibrium! Construct a parallelogram which has a diagonal measuring –W and which has sides that are parallel to the supporting ropes. The tension in the rope is shown from the center of the rock, along the rope, to the intersection of the two construction lines. Conceptual Physics Chapter 2

14. Equilibrium TA and TB have increased as a result of the greater angle between the supporting ropes. The same object is then supported by ropes positioned at a flatter angle. -W TA TB ∑F = 0 Produce a vector measuring –W from the center of the hanging weight. TA + TB + W = 0 W The weight still acts straight down. The body is in equilibrium The tension in the rope is shown from the center of the rock, along the rope, to the intersection of the two construction lines. Produce all construction lines. Conceptual Physics Chapter 2

15. Equilibrium The same object is then supported by ropes positioned at an even flatter angle. -W TB TA ∑F = 0 W The weight still acts straight down. TA + TB + W = 0 The resultant of the tension vector in the two ropes must still be equal to -W The tension in the rope is shown from the center of the rock, along the rope, to the intersection of the two construction lines. The tension in the ropes is increased even further due to the flatter angle, but… Produce all construction lines. and the body is still in equilibrium Conceptual Physics Chapter 2