The study of equilibrium Statics The study of equilibrium

The study of forces in equilibrium Statics The study of forces in equilibrium

Statics When forces are in equilibrium, all forces acting on a body are balanced, and the body is not accelerating.

Solving Statics Problems You must study all the forces acting on an object in the horizontal or x-direction, separately from all the forces acting in the vertical or y-direction. This means that you must take the horizontal and vertical components of these forces.

Solving Statics Problems Because the object is not accelerating, the sum of all the horizontal components must equal zero and the sum of all of the vertical components must equal zero.

Tension Tension is just a way of writing the magnitude of the force that is exerted to hold an object in place. It has the same units as any other force (N)

Wires / Strings You will work with several items that involve objects hanging from wires. Whenever this situation occurs, the sum of the vertical components of the tension in each wire is equal to the object’s weight. If the object hangs in the middle of two equal-length wires, the weight is shared equally by each wire.

Example # 1 Kelly, an exhausted gymnast, hangs from a bar by both arms in an effort to catch her breath. If Kelly has a mass of 65kg, what is the tension in each of Kelly’s arms as she hangs in place?

Example # 1 Kelly, an exhausted gymnast, hangs from a bar by both arms in an effort to catch her breath. If Kelly has a mass of 65kg, what is the tension in each of Kelly’s arms as she hangs in place? Given: Unknown m= 65 kg w g = 10m/s2 Equ w = mg = 65kg(10m/s2) = 650N Each arm shares in the force equally,therefore A tension of 325N in each arm

Example # 2 At an art auction, Jonah has acquired a painting that now hangs from a nail on his wall. If the painting has a mass of 12.6kg, what is the tension in each side of the wire supported by the painting? 90o

Example # 2 At an art auction, Jonah has acquired a painting that now hangs from a nail on his wall. If the painting has a mass of 12.6kg, what is the tension in each side of the wire supported by the painting? Given: m = 12.6kg g = 10 m/s2 Equ: w = mg (12.6kg)(10m/s2) = 126N 45o F Fy = 63N

Cos 0 = adj = Fy hyp F

Example # 3 Hannah likes to swing on a tire tied to a tree branch in her yard. If Hannah and the tire have a combined mass of 82.5kg, and Brigit pulls Hannah back far enough for her to make an angle of 30o with the vertical, what is the tension in the rope supported by Hannah and the tire?

Hannah likes to swing on a tire tied to a tree branch in her yard Hannah likes to swing on a tire tied to a tree branch in her yard. If Hannah and the tire have a combined mass of 82.5kg, and Brigit pulls Hannah back far enough for her to make an angle of 30o with the vertical, what is the tension in the rope supported by Hannah and the tire?

Example #4 After returning home from the beach, Alyssa hangs her wet .2kg bathing suit in the center of the 6m long clothesline to dry. This causes the clothesline to sag 4cm. What is the tension in the clothesline?

Example # 4 After returning home from the beach, Alyssa hangs her wet .2kg bathing suit in the center of the 6m long clothesline to dry. This causes the clothesline to sag 4cm. What is the tension in the clothesline? First convert 4cm to m 4cm = .04m Given: Unknown: m = .2kg w = mg g = 10 m/s W = .2kg ( 10m/s) = 2N

Warm- up A 1240kg wrecking ball, at Lester’s construction company LVE , is pulled back with a horizontal force of 5480N before being swung against the side of a building. a) What angle does the wrecking ball make with the vertical when it is pulled back? b) What is the tension in the ball’s supporting cable when it’s at this angle?

Warm- up A 1240kg wrecking ball, at Lester’s construction company LVE , is pulled back with a horizontal force of 5480N before being swung against the side of a building. a) What angle does the wrecking ball make with the vertical when it is pulled back? b) What is the tension in the ball’s supporting cable when it’s at this angle? θ FT 5480N mg

Warm Up θ FT 5480N mg mg FT 5480N