If a single force is applied at an angle to the?direction of motion?it will need to be?resolved?into?components?of the force that act?perpendicular?to each other.

Why resolve a force acting at an angle?

• Resolving a force acting at an angle often helps to simplify a problem
• The components of a force parallel and perpendicular to the line of motion allows different types of problems to be solved
  • The?parallel?component of a force acting directly on a particle will be the component that causes an effect on the particle
  • The?perpendicular?component of a force acting directly on a particle will be the component that has no effect on the particle

   

• Finding the horizontal and vertical components of a force can help solve problems acting in the horizontal plane
• The two components of the force will have the same combined effect as the original force

How do you resolve a force acting at an angle?

• Use?trigonometry?to resolve a force acting at an angle
• Draw a triangle of forces by decomposing the force into its horizontal and vertical components
• The original force will be the?hypotenuse?of the triangle and the two components will make up the?opposite?and?adjacent?sides

How do we find a resultant force when two or more forces are acting at angles to each other?

• It is possible to use geometry to find the resultant force without decomposing the forces into their horizontal and vertical components
• The forces can be placed nose to tail to create a vector triangle and then the third side of the triangle can be used to calculate the?magnitude?and?direction?of the resultant force
• You will need to use?trigonometry?to find the missing side or angle in the triangle.

1. Find the vertical and horizontal components of the 10 N force.
2. Work out the acceleration of the box.
3. Calculate the magnitude of the normal reaction between the box and the floor.

How do you solve a problem involving an inclined plane?

• Problems involving inclined planes will always be acting along the?line of greatest slope?of the plane
  • The line of greatest slope is the most direct route with which it is possible to move from the bottom to the top of the plane
  • A force said to be acting in the same?vertical plane?as the line of greatest slope will be acting in the same plane as this most direct route
• It is usually easier to resolve?parallel?and?perpendicular?to the plane
• The?normal reaction force?always acts perpendicular to the plane and will not need to be resolved
• Weight (mg)?always acts vertically downwards and so it is easier to use when resolved into components perpendicular and parallel to the plane
• When an object is moving up or down the inclined plane, it has?acceleration?only in the parallel direction
  • The perpendicular forces will be equal in the positive and negative directions
  • Newton’s Second Law (F = ma) can be used in the parallel direction to determine acceleration or missing forces
• On an inclined plane?friction?will always act in the opposite direction to the direction the object is moving in or on the point of moving in