Tension and pulley problems

• 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.

$\Sigma \vec{F} = \vec{F}_{net} = m\vec{a}$

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

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

$m:$ mass, in kilograms (kg)

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

For object A exerting a force on object B:

$\vec{F}_{A on B} = - \vec{F}_{B on A}$

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

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

$a = g\frac{(m_{1}-m_{2})}{(m_{1}+m_{2})}$

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

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

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

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