Forces act in two (or three!) dimensions Free Body Diagrams: Forces act in two (or three!) dimensions

Forces act in two (or three!) dimensions Free Body Diagrams: Forces act in two (or three!) dimensions Isolate the body of interest Sketch all forces that act on it Choose an appropriate coordinate system Resolve all forces into x- and y-components Apply Newton’s Second Law to each component

Example: Campers lift a food cooler with a weight of W = 192 Example: Campers lift a food cooler with a weight of W = 192.0 N out of reach of bears using two ropes hung over tree branches. Rope 1 exerts a force F1 at an angle of 47.4º above the horizontal, while rope 2 exerts a force F2 at an angle of 36.1º above the horizontal, as shown in the diagram. What are the magnitudes of the forces F1 and F2?

What’s the connection between weight and mass?

What’s the connection between weight and mass? Weight is the force of gravity between an object and the Earth

What’s the connection between weight and mass? Weight is the force of gravity between an object and the Earth Apply SF = ma to a brick in freefall

Definition of “weight” W = mg This actually comes from Newton’s Law of Universal Gravitation It is NOT F = ma It is simply a statement that weight is proportional to mass

Apparent weight You may have experienced feeling momentarily lighter or heavier in an elevator

Apparent weight You may have experienced feeling momentarily lighter or heavier in an elevator SFy = Wa – W = ma

Apparent weight You may have experienced feeling momentarily lighter or heavier in an elevator SFy = Wa – W = ma Wa = m (g + a)

Another way to interpret this is: Apparent weight You may have experienced feeling momentarily lighter or heavier in an elevator SFy = Wa – W = ma Wa = m (g + a) Another way to interpret this is: The acceleration due to gravity appears different if your reference frame is accelerating

Apparent weight Taken to an extreme – in freefall, the acceleration due to gravity appears to be zero!

When a certain person steps onto a scale on solid ground, the reading is 750 N. When the same person rides in an elevator that accelerates, the reading on the scale is different. Rank the three cases (1, 2, and 3) shown in the figure in order of increasing acceleration (from most negative to most positive) in the y-direction. A) 1, 2, 3 B) 1, 3, 2 C) 2, 1, 3 D) 2, 3, 1 E) 3, 1, 2 1 2 3

What is the apparent weight of a 5 What is the apparent weight of a 5.25 kg salmon in an elevator that is accelerating downward at 1.85 m/s2?

“Normal” means perpendicular Normal Forces “Normal” means perpendicular A normal force is a “reaction” force that occurs when something pushes on a surface

Normal forces are not always equal to weight! In this case, the normal force is less than the weight, because part of the weight is supported by the upward component of the force on the strap

Normal forces are not always equal to weight! In this case, the normal force is greater than the weight, because this dufus is pushing down on the chair

Normal forces are not always equal to weight! In this case, the normal force is less than the weight, because the surface is slanted What would the FBD look like for this situation?

What is the acceleration of the child? A child of mass m rides on a toboggan down a slick, ice-covered hill inclined at an angle q with respect to the horizontal. What is the acceleration of the child?

What is the normal force exerted on the child by the toboggan? A child of mass m rides on a toboggan down a slick, ice-covered hill inclined at an angle q with respect to the horizontal. What is the normal force exerted on the child by the toboggan?