Chapter 3 Kinetic Concepts for Analyzing Human Motion

Chapter 3: Kinetic Concepts for Analyzing Human Motion Basic Biomechanics, 6 th edition Susan J. Hall Created by Molly Smith

Vector Algebra • Scalar Quantity: an undirected magnitude; quantity is fully described by its magnitude. – Examples: mass, volume, density, length

Vector Algebra • Vector Quantity: a directed magnitude; quantity that is represented by an arrow. Arrow has an arrowhead (direction) and length (magnitude. – Kinetic vector quantities : force, weight, pressure, specific weight & torque – Kinematic vector quantities: displacement, velocity & acceleration

Vector Composition The composition of vectors with the same direction requires adding their magnitudes.

Vector Composition The composition of vectors with the opposite directions requires subtracting their magnitudes

Vector Composition • Resultant vector • “Tip-to-tail” vector composition Resultant vector Vector #2 Vector #1

Vector Composition The tip-to-tail method of vector composition.

Vector Composition • Sum of three original vectors: R=A + B + C • Vector B starts at the end of vector A and vector C starts at the end of vector B • Resultant begins at tail of A and ends at head of C (-1, -6).

Vector Composition • Sum of same three original vectors: R=B + A + C. • R always starts at the beginning of the first vector and terminates at the end of the last vector (-1, -6).

Vector Composition • Sum of same three original vectors: R=C + B + A. • Note that in each case, regardless of order, R has the same rectangular form (-1, -6 ).

Vector Resolution • What is vector resolution? – Operation that replaces a single vector with two perpendicular vectors such that the vector composition of the two perpendicular vectors yields the original vector.

Vector Resolution Vectors may be resolved into perpendicular components. The vector composition of each pair of components yields the original vector.

Vector Resolution Example: A ball is thrown into the air Vertical Horizontal

Graphic Solution of Vector Problems • Graphic vector manipulation may yield approximate result 1 cm = 10 N 30 N = 3 cm 35 N = 4. 5 cm

Trigonometric Solution of Vector Problems • A more accurate procedure for quantitatively dealing with vector problems hypotenuse opposite adjacent

Trigonometric Vector Resolution Two rectangular components • One directed negative x-axis (adjacent to angle) • One directed positive y-axis (opposite to angle)

Summary • This chapter introduced basic concepts related to kinetics • Vectors quantities have magnitude & direction • Vector problems may be solved by a graphic or a trigonometric approach.