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 vector 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?

• Force is a?vector?quantity, so finding the?resultant?of two or more forces is the same as finding the resultant of two or more vectors
• It is possible to use geometry to find the resultant force without decomposing the forces into their horizontal and vertical components
• Use the?triangle law for vector addition?to calculate the?magnitude?and?direction?of a 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. Explain why the resultant force acting to move the box is
3. Work out the acceleration of the box.
4. 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

(i)? Find the magnitude of the reaction force acting on the box.

(ii)? Find the acceleration of the box up the slope.