# Tension and pulley problems

##### Intros

###### Lessons

##### Examples

###### Lessons

**Calculating tension using Newton's second law**A train toy is made up of three carts of different masses connected by pieces of string. If string A is pulled with 7.05 N [right], find the tension in strings A, B, and C.

**Solving vertical pulley problems (Atwood machine problems)**Two boxes (5.00 kg and 7.25 kg) are tied together by a rope and hang vertically from a frictionless pulley. What is the acceleration of each box, and the tension in the rope?

**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.

**Slope with friction pulley problem using the "black box" method**Two boxes (3.50 kg and 2.00 kg) are tied together by a rope and hang from a pulley as shown. The coefficient of friction between the ground and the 3.50 kg box is 0.150. What is the acceleration of each box, and the tension in the rope?

**Three box pulley problem with slopes and friction using the "black box" method**Three boxes (3.75 kg, 5.50 kg and 12.0 kg) are tied together by two ropes and hang from a pulley as shown. The coefficient of friction between the ground and the boxes is 0.250. What is the acceleration of each box, and the tension in ropes A and B?

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###### Topic Notes

- What is tension?
- How to calculate tension
- Problem solving with tension

__Notes:____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**

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

$\Sigma \vec{F}:$ 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 $(m/s^{2})$

**Newton's Third Law**

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)

**Atwood Machine Equation**

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

$a:$ 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)

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