6.2 Resolution of Forces / Inclines Resolution of Forces:
The process of separating a single force into two or more component forces that have the same effect.
To determine the components forces, we need to use the parallelogram method and trigonometry.
Example #1:
A tug boat pulls a barge with a force (FR) of 15,000 N at 20° S of W.
Find the component forces acting south (FS) and west (FW) on the boat.
1. A tilted surface is called an inclined plane.
2. Objects accelerate down inclined planes because of an unbalanced forces.
3. The two forces acting upon a crate which is positioned on an inclined plane (assumed to be friction-free) are the force of gravity
(FW) and the normal force (FN).
4. The force of gravity (weight) acts in a downward direction; yet the normal force acts in a direction perpendicular to the surface. 5. The force of gravity (FW ) will always be resolved into two components (FP , FV). Together, these two components can replace the force of gravity.
6. FP is the component force that is parallel to the inclined plane. This force tends to move the object down the incline (If the plane frictionless).
7. FV is the component force that is always perpendicular to the surface of the plane. This is the amount of weight supported by the incline. FW = m•g
FP = FW • sin
FV = FW • cos
FP
FV
FW Free Body Diagrams!!!! Is there gravity?
FW always acts straight down Is it sitting on a surface?
FN is always perpendicular to the surface Is something pushing or pulling it? Is there an Applied Force (FA) or a Tension Force (FT)? Is there friction (FF)?
Friction always acts in the opposite direction of motion Direction of motion Does everything lie on the X-Y axis?
Axis will be tilted to the same angle as the incline
FW will always need to be resolved into components
Example #2 A block of mass 5 kg slides down a ramp inclined at 30° to the horizontal. The frictional force is 15 N between surface and the box.
Calculate:
a. The Normal force (FN) b. The acceleration of the box
Example #3 A block with a weight of 50 N is pulled up a ramp with a 125 N force. There is a frictional force of 10 N acting between the ramp and the block. If the ramp is inclined at 20°:
Calculate:
a. The Normal force (FN) b. The acceleration of the box
Work Problem #1 A block of mass 25 kg is hauled up a plane inclined at 20° to the horizontal by a rope parallel to the plane. The frictional force is 10 N between the block and the ramp and the tension in the rope (FT) is 200 N.
Calculate:
a. The normal force (FN) (230.46 N) b. The acceleration of the block (4.24 m/s2)