Trigonometry Review 5 12 a b 61

Trigonometry Review c d 7

Trigonometry Review x a x =65 sin a =3/5 cos a =4/5 y = ? y r x a tan a =3/4 y = 9 r = ? y r

F=62N Vector Review 60 o F=48N 30 o F=52N 45 o

Vector Review A swimmer pulls her hands through the water with a force of 11 pounds. Her stroke lasts a distance of 2.5 feet and takes 1 second. How much work does she do with each stroke? What power is used? Using the efficiency equation, what would the output force be if her stroke were only 60% efficient

A teacher pushes a television cart 1/8 mile (1 mile = 5,280 feet) down a hall. The television weighs 35 lbs, the cart itself weighs 30 lbs, and friction at the wheels opposes motion with a force of 2 lbs. The teacher pushes the cart at an angle of 30o downward from the horizontal. Write each of the forces acting on the cart in rectangular components. What is the resultant force acting on the cart? 65lbs 30 o 2lbs 30lbs Friction Gravity Teacher Resultant

How much does the force of gravity do to the cart? Distance =0 in the y direction Work = 0 How much work does the teacher do? How efficiently is pushing the cart? He pushes in 2 min, how much power is he using?

A radio antenna tower stands 200 meters tall. A supporting cable attached to the top of the tower stretches to the ground and makes a 30 o angle with the tower. How far is it from the base of the tower to the cable on the ground? 200m 30 o How long must the cable be?

During a storm, the wind blows against the side of the tower with a force with 300 N. The horizontal strength of the cable maintains equilibrium, what is the total force? 200m 30 o The horizontal component of resultant is 0 300N

Trigonometry and Vectors Common triangles in Geometry and Trigonometry o 2 30 o 60 o You must memorize these triangles 2 3

IOT POLY ENGINEERING 3-8 Trigonometry and Vectors SOH CAH TOA Trigonometric Functions tan A = opposite adjacent sin A = opposite hypotenuse cos A = adjacent hypotenuse

IOT POLY ENGINEERING 3-9 Trigonometry and Vectors 3.Free-body Diagram A diagram that shows all external forces acting on an object. Vectors friction force force of gravity (weight) applied force normal force WtWt F N FfFf

IOT POLY ENGINEERING 3-10 Trigonometry and Vectors Vectors – Rectangular Components y x F F x + F y + When are F x and F y Positive/Negative? F F x - F y + F F F x - F y - F x + F y -

IOT POLY ENGINEERING 3-13 Work You are pulling a wagon with a 20 lbs of force at a 60 o angle. You pull the wagon 10 feet, how much work did you do? 20 lbs 60 o Fy Fx

IOT POLY ENGINEERING 3-13 Efficiency You are pulling a wagon with a 20 lbs of force at a 60 o angle. How efficiently are you using your pulling 20 lbs 60 o Fy Fx

IOT POLY ENGINEERING 3-13 Work You are pulling a wagon with a 20 lbs of force at a 60 o angle. You pull the wagon 10 feet in 10 seconds, how much power did you use? 20 lbs 60 o Fy Fx