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Key Areas covered. Resolving a force into two perpendicular components. Forces acting at an angle to the direction of movement. What we will do today:. Identify how to solve problems when we have two forces acting at different angles (component of forces). Carry out problems on the above.
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Key Areas covered • Resolving a force into two perpendicular components. • Forces acting at an angle to the direction of movement.
What we will do today: • Identify how to solve problems when we have two forces acting at different angles (component of forces). • Carry out problems on the above
Any vector, x, can be resolved into two components at right angles to each other. The horizontal component xh The vertical component xv F xv is equivalent to θ xh
sin θ = xv / x xv = x sin θ cos θ = xh / x xh = x cos θ x xv θ xh
Force The vertical and horizontal components of a Force vector, F, are, respectively: Fv = F sin θ Fh = F cos θ
In the previous section, a vector was split into horizontal and vertical components. This can obviously apply to a force. is equivalent to Remember that the resultant of a number of forces is the single force which has the same effect, in both magnitude and direction, as the sum of the individual forces. Fv = F sin θ F θ Fh = F cos θ
A man pulls a garden roller of mass 100 kg with a force of 200 N acting at 30º to the horizontal. If there is a frictional force of 100 N between the roller and the ground, what is the acceleration of the roller along the ground? Solution Fh = F cos θ = 200 cos 30º = 173.2 N Fun = 173.2 N – Friction = 173.2 – 100 = 73.2 N a = Fun / m = 73.2 / 100 = 0.732 ms-2 Example 1 200 N 30º Fh Friction = 100 N
Example 2 • An oil rig is pulled by two barges as shown. Each barge applies a force of 10 kN. What is the resultant force acting on the rig? Solution: Work out Fh for one barge: Fh = F cos θ = 10 000 cos 30 = 8660N Then double this to include forces from both barges: 2 x 8660 = 17 300 N (3 sig fig)
Questions • Activity sheets: • Page 31 – 33 • Qu’s 1-5 • Resolution of forces • You should now be able to answer all questions in class jotter