A uniform in shape and mass bar AB is supported by a smooth pin at point A. The orientation of the bar is given by angle theta, 0, as shown below. An external force P is applied to the bar at point B. The direction of the force is given by angle phi, p, as shown below. Both angles theta and phi are angles in standard position. Note that 0<0 < 2n and 0 < p < 2r. The weight of the bar is W; the length of the bar is L. The bar and all forces are in the plane of the page (2D case). The length is in meters and the forces are in newtons. Draw a free-body diagram for the bar AB; use the standard orientation of the Cartesian xy-plane (with positive x-axis pointing right and positive y-axis pointing up). Derive an expression for the net moment about point A in terms of given parameters like W, P, L, 0, and/or (p. Simplify the expression using an appropriate identity for trigonometric functions of sums and differences. YA sin(A + B) = sin(A) cos(B) + cos(A) sin(B) sin(A – B) = sin(A) cos(B) – cos(A) sin(B) A cos(A + B) = cos(A) cos(B) – sin(A) sin(B) cos(A – B) = cos(A) cos(B) + sin(A) sin(B)
A uniform in shape and mass bar AB is supported by a smooth pin at point A. The orientation of the bar is given by angle theta, 0, as shown below. An external force P is applied to the bar at point B. The direction of the force is given by angle phi, p, as shown below. Both angles theta and phi are angles in standard position. Note that 0<0 < 2n and 0 < p < 2r. The weight of the bar is W; the length of the bar is L. The bar and all forces are in the plane of the page (2D case). The length is in meters and the forces are in newtons. Draw a free-body diagram for the bar AB; use the standard orientation of the Cartesian xy-plane (with positive x-axis pointing right and positive y-axis pointing up). Derive an expression for the net moment about point A in terms of given parameters like W, P, L, 0, and/or (p. Simplify the expression using an appropriate identity for trigonometric functions of sums and differences. YA sin(A + B) = sin(A) cos(B) + cos(A) sin(B) sin(A – B) = sin(A) cos(B) – cos(A) sin(B) A cos(A + B) = cos(A) cos(B) – sin(A) sin(B) cos(A – B) = cos(A) cos(B) + sin(A) sin(B)
Related questions
Question
100%
Transcribed Image Text:A uniform in shape and mass bar AB is supported by a smooth pin at point A. The orientation of the bar
is given by angle theta, 0, as shown below. An external force P is applied to the bar at point B. The
direction of the force is given by angle phi, q, as shown below. Both angles theta and phi are angles in
standard position. Note that 0 <0 < 2n and 0 < p < 2r. The weight of the bar is W; the length of the bar
is L. The bar and all forces are in the plane of the page (2D case). The length is in meters and the forces
are in newtons.
Draw a free-body diagram for the bar AB; use the standard orientation of the Cartesian xy-plane (with
positive x-axis pointing right and positive y-axis pointing up). Derive an expression for the net moment
about point A in terms of given parameters like W, P, L, 0, and/or p.
Simplify the expression using an appropriate identity for
trigonometric functions of sums and differences.
B.
sin(A + B) = sin(A) cos(B) + cos(A) sin(B)
sin(A – B) = sin(A) cos(B) – cos(A) sin(B)
A
cos(A + B) = cos(A) cos(B) – sin(A) sin(B)
cos(A – B) = cos(A) cos(B) + sin(A) sin(B)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
