Two dimensional forces - Forces and Newton's Laws

Two dimensional forces



In this lesson, we will learn:

  • How to solve force problems when force is applied at an angle
  • How to solve force problems with inclines


  • When looking at forces in two dimensions, a force can point along the x or y axis, or at any angle in between. The net force acting on an object is found by adding all the forces acting on that object using vector addition.
    • When solving for net force it can be helpful to break angled forces into x and y components so that the forces is the x and y directions can be added separately.
  • When an object is on a slope, it tends to be pulled down the slope by gravity. We can understand why gravity pulls the object down the slope if we break the force of gravity into two components: one that is parallel to the slope, and one that is perpendicular.
    • We can redefine the x direction to be parallel to the slope and the y direction to be perpendicular to the slope for a particular problem. Essentially, we "tilt" the axes to line up with the slope. The components can then be solved like normal x and y components.
    • Fx\vec{F}_{x} represents the amount of Fg\vec{F}_{g} which is pulling the object down the slope.
    • Fy\vec{F}_{y} represents the amount of Fg\vec{F}_{g} pushing into the slope. It is balanced by the normal force from the slope pushing back on the box.
Newton's Second Law

ΣF=Fnet=ma\Sigma \vec{F} = \vec{F}_{net} = m\vec{a}

ΣF:\Sigma \vec{F}: sum of all forces, in newtons (N)

Fnet:\vec{F}_{net}: net force, in newtons (N)

m:m: mass, in kilograms (kg)

a:\vec{a}: acceleration, in meters per second squared (m/s2)(m/s^{2})

x and y Components of Force

Fxory=Fsin(θ)\vec{F}_{x or y} = \vec{F}\sin(\theta) (For the component opposite to θ\theta)

Fxory=Fcos(θ)\vec{F}_{x or y} = \vec{F}\cos(\theta) (For the component adjacent to θ\theta)

    • a)
      How to solve force problems when force is applied at an angle
    • b)
      How to solve force problems with inclines
  • 2.
    Forces on an incline
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Two dimensional forces

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