Tension and pulley problems - Forces and Newton's Laws

Tension and pulley problems


In this lesson, we will learn:
  • What is tension?
  • How to calculate tension
  • Problem solving with tension


  • Tension is the force of a rope (or string, cable, etc.) pulling on an object.
    • Tension is always a pulling force: a rope can't push!
  • There is no formula for tension. Tension force acting on an object must be calculated from Newtons' second law.
  • If the rope is assumed to be massless and non-stretchy, then the pulling force at either end of the rope must be equal in magnitude.
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})

Newton's Third Law

For object A exerting a force on object B:

FAonB=FBonA\vec{F}_{A on B} = - \vec{F}_{B on A}

FAonB:\vec{F}_{A on B}: force A is exerting on B, in newtons (N)

FBonA:\vec{F}_{B on A}: force B is exerting on A, in newtons (N)

Atwood Machine Equation

a=g(m1m2)(m1+m2)a = g\frac{(m_{1}-m_{2})}{(m_{1}+m_{2})}

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

g:g: acceleration due to gravity, in meters per second squared (m/s2m/s^{2})

m1:m_{1}: mass of first hanging mass, in kilograms (kg)

m2:m_{2}: mass of second hanging mass, in kilograms (kg)

  • Intro Lesson
    Introduction to tension:
  • 3.
    Solving horizontal pulley problems with friction

    Two boxes (8.00 kg and 4.40 kg) are tied together by a rope and hang from a pulley as shown. The coefficient of friction between the ground and the 8.00 kg box is 0.250.

    PHYS 3 7 3
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Tension and pulley problems

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