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Unit 2 Statics of Particles EGR 140 Engineering Mechanics: Statics Professor Mun

Learning Objectives Upon successful completion of this learning module, students will be able to: Using the Parallelogram Law, Force Triangle Method, or Method of Components, determine the resultant force R for a coplanar force system, including the magnitude, angle of inclination, and sense. 2. For a particle under a coplanar force system, construct a free-body diagram that includes all the known forces acting on the particle, indicating a magnitude, line of action, and sense. Indicate the desired unknown forces with a symbol. 3. For a three-dimensional force equilibrium problem, compute the x-, y-, and z-components of the force acting on a particle and their respective angles defining the direction of the force.

For the following two-force coplanar system, determine the resultant force, R . 150 N 100 N 15  10  x y ) ) O

Method of Components Resolve the force into its component forces along the axes. Find the sum of the component forces in each direction. Find the magnitude of the resultant force R. Find the direction and sense.

Review of Right Triangle and Trigonometry Creative Commons: scherer.wikispaces.com/ Right + Triangle + Trigonometry +SOH+-+CAH+-+TOA - SOH CAH TOA

1. Resolve the force into its component forces along the axes: x- axis. 150 N 100 N 15  10  x y ) ) O 100 x 100 y 100 N 15  ) O 100 x 100 y Fx = F(cos  ) Fy = F(sin  ) 100 x = 100N (cos15 °) = 96.5926 N 100 y = 100N (sin15 °) = 25.8819 N

1. Resolve the force into its component forces along the axes: y- axis. 150 N 100 N 15  10  x y ) ) O 150 x 150 y Fx = F(sin  ) Fy = F(cos  ) 150 x = 150N (sin10 °) = 26.0472 N 150 y = 150N (cos10 °) = 147.7212 N 150 N 10  ) 150 x 150 y

2. Find the sum of the component forces in each direction. R x =  F x = 100 x + 150 x = 100N (cos15°) + 150N (sin10°) = 96.5926 N + 26.0472 N =122.6398 N R y =  F y = 100 y + 150 y = 100N (sin15°) + 150N (cos10°) = 25.8819 N + 147.7212 N = 173.6031 N

3. Find the magnitude of the resultant force R . R =  R x 2 + R y 2 =   F x 2 +  F y 2 =  (122.6398 N) 2 + (173.6031 N) 2 =  45178.5569 N 2 = 212.5525 N = 213 N

4. Find the direction and sense. x y O R x = 122.6398 N R y = 173.6031 N R = 213 N )  x Angle of Inclination tan  x = R y /R x = 173.6031 N 122.6398 N tan  x = 1.4156  x = tan -1 (1.4156)  x = 54.8º )  x R Sense

Mun unit5 cdp_slide_share

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