Fnet = ma

Forming the N2L equation is the first step to solving many dynamics problems.

  1. Choose your mass.
  2. Include each and every force acting on that mass.
  3. Exclude each and every force not acting on that mass.

Example
Block A, B and C of mass 4.0 kg, 6.0 kg and 2.0 kg respectively are pushed along a smooth horizontal surface by an external force of 24 N.

fnet1Calculate

  1. a) the contact force between block A and B
  2. b) the contact force between block B and C

Solution

Using Fxy to denote the contact force that block X exerts on Y,

fnet2

Considering all three blocks as a combined 12 kg mass,

fnet3

\displaystyle \begin{aligned}({{F}_{net}}&=ma)\\24&=(2+6+4)a\text{ }\\a&=2.0\text{ m }{{\text{s}}^{\text{-2}}}\end{aligned}

a)

Let’s consider blocks B and C as a combined 8 kg mass,

fnet4

\displaystyle \begin{aligned}({{F}_{net}}&=ma)\\{{F}_{AB}}&=(6+2)(2.0)\\&=16\text{ N}\end{aligned}


Alternatively, we can consider block A by itself as a 4 kg mass.

fnet5

\displaystyle \begin{aligned}({{F}_{net}}&=ma)\\24-{{F}_{BA}}&=(4)(2.0)\\{{F}_{BA}}&=16\text{ N}\end{aligned}

b)

Considering block C by itself as a 2 kg mass,

fnet7
\displaystyle \begin{aligned}({{F}_{net}}&=ma)\\{{F}_{BC}}&=(2)(2.0)\\&=4.0\text{ N}\end{aligned}


Alternatively, we can consider blocks A and B as a combined 10 kg mass.
fnet6

\displaystyle \begin{aligned}({{F}_{net}}&=ma)\\24-{{F}_{CB}}&=(4+6)(2)\\{{F}_{CB}}&=4.0\text{ N}\end{aligned}

Fully solved,

fnet8

See more worked examples:

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