1. 1 Applying Newton’s Laws Assumptions Assumptions Objects behave as particles Objects behave as particles can ignore rotational motion (for now) can ignore rotational motion (for now) Masses of strings or ropes are negligible Masses of strings or ropes are negligible Interested only in the forces acting on the object Interested only in the forces acting on the object can neglect reaction forces can neglect reaction forces

2. 2 Free Body Diagram Must identify all the forces acting on the object of interest Must identify all the forces acting on the object of interest Choose an appropriate coordinate system Choose an appropriate coordinate system If the free body diagram is incorrect, the solution will likely be incorrect If the free body diagram is incorrect, the solution will likely be incorrect

3. 3 Equilibrium An object either at rest or moving with a constant velocity is said to be in equilibrium An object either at rest or moving with a constant velocity is said to be in equilibrium The net force acting on the object is zero The net force acting on the object is zero

4. 4 Equilibrium cont. Easier to work with the equation in terms of its components: Easier to work with the equation in terms of its components:

5. 5 Solving Equilibrium Problems Make a sketch of the situation described in the problem Make a sketch of the situation described in the problem Draw a free body diagram for the isolated object under consideration and label all the forces acting on it Draw a free body diagram for the isolated object under consideration and label all the forces acting on it Resolve the forces into x- and y-components, using a convenient coordinate system Resolve the forces into x- and y-components, using a convenient coordinate system Apply equations, keeping track of signs Apply equations, keeping track of signs Solve the resulting equations Solve the resulting equations

6. 6 Equilibrium Example – Free Body Diagrams

7. 7 Newton’s Second Law Problems Similar to equilibrium except Similar to equilibrium except Use components Use components a x or a y may be zero a x or a y may be zero

8. 8 Solving Newton’s Second Law Problems Make a sketch of the situation described in the problem Make a sketch of the situation described in the problem Draw a free body diagram for the isolated object under consideration and label all the forces acting on it Draw a free body diagram for the isolated object under consideration and label all the forces acting on it If more than one object is present, draw free body diagram for each object If more than one object is present, draw free body diagram for each object Resolve the forces into x- and y-components, using a convenient coordinate system Resolve the forces into x- and y-components, using a convenient coordinate system Apply equations, keeping track of signs Apply equations, keeping track of signs Solve the resulting equations Solve the resulting equations

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23. 23 Inclined Planes Choose the coordinate system with x along the incline and y perpendicular to the incline Choose the coordinate system with x along the incline and y perpendicular to the incline Replace the force of gravity with its components Replace the force of gravity with its components

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45. 45 Forces of Friction When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion When an object is in motion on a surface or through a viscous medium, there will be a resistance to the motion This is due to the interactions between the object and its environment This is due to the interactions between the object and its environment This is resistance is called the force of friction This is resistance is called the force of friction

46. 46 More About Friction Friction is proportional to the normal force Friction is proportional to the normal force The force of static friction is generally greater than the force of kinetic friction The force of static friction is generally greater than the force of kinetic friction The coefficient of friction (µ) depends on the surfaces in contact The coefficient of friction (µ) depends on the surfaces in contact The direction of the frictional force is opposite the direction of motion The direction of the frictional force is opposite the direction of motion The coefficients of friction are nearly independent of the area of contact The coefficients of friction are nearly independent of the area of contact

47. 47 Static Friction, ƒ s Static friction acts to keep the object from moving Static friction acts to keep the object from moving If F increases, so does F ƒs If F increases, so does F ƒs If F decreases, so does F ƒs If F decreases, so does F ƒs F ƒs  µ F N F ƒs  µ F N

48. 48 Kinetic Friction The force of kinetic friction acts when the object is in motion The force of kinetic friction acts when the object is in motion F ƒk = µ F N F ƒk = µ F N

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53. 53 Connected Objects Apply Newton’s Laws separately to each object Apply Newton’s Laws separately to each object The acceleration of both objects will be the same The acceleration of both objects will be the same The tension is the same in each diagram The tension is the same in each diagram Solve the simultaneous equations Solve the simultaneous equations

54. 54 More About Connected Objects Treating the system as one object allows an alternative method or a check Treating the system as one object allows an alternative method or a check Use only external forces Use only external forces Not the tension – it’s internal Not the tension – it’s internal The mass is the mass of the system The mass is the mass of the system Doesn’t tell you anything about any internal forces Doesn’t tell you anything about any internal forces

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64. 64 Terminal Speed Another type of friction is air resistance Another type of friction is air resistance Air resistance is proportional to the speed of the object Air resistance is proportional to the speed of the object When the upward force of air resistance equals the downward force of gravity, the net force on the object is zero When the upward force of air resistance equals the downward force of gravity, the net force on the object is zero The constant speed of the object is the terminal speed The constant speed of the object is the terminal speed