Statics The study of equilibrium Statics The study

Statics The study of 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 ydirection. 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 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 65 kg, 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 65 kg, what is the tension in each of Kelly’s arms as she hangs in place? Given: Unknown m= 65 kg w g = 10 m/s 2 Equ w = mg = 65 kg(10 m/s 2) = 650 N Each arm shares in the force equally, therefore A tension of 325 N 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. 6 kg, what is the tension in each side of the wire supported by the painting? 90 o

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. 6 kg, what is the tension in each side of the wire supported by the painting? Given: m = 12. 6 kg g = 10 m/s 2 Equ: w = mg (12. 6 kg)(10 m/s 2) = 126 N 45 o F Fy = 63 N

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. 5 kg, and Brigit pulls Hannah back far enough for her to make an angle of 30 o 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. If Hannah and the tire have a combined mass of 82. 5 kg, and Brigit pulls Hannah back far enough for her to make an angle of 30 o 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. 2 kg bathing suit in the center of the 6 m long clothesline to dry. This causes the clothesline to sag 4 cm. What is the tension in the clothesline?

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

Warm- up A 1240 kg wrecking ball, at Lester’s construction company LVE , is pulled back with a horizontal force of 5480 N 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 1240 kg wrecking ball, at Lester’s construction company LVE , is pulled back with a horizontal force of 5480 N 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 5480 N mg

Warm Up θ FT 5480 N mg