Newton's second law

Newton's second law relates the resultant force acting on a body and its acceleration:

\(F=ma\)

Because acceleration is defined as the rate of change in velocity, Newton's second law can also be expressed as the rate of change of a momentum of a body is proportional to the resultant force and is in the same direction as the force.

\(F={\Delta (mv)\over t}\)


Key Concepts

Unbalanced forces

If the forces acting on a block are unbalanced then it will accelerate, the acceleration is proportional to and in the same direction as the unbalanced (resultant) force.

\(F=ma\)

Calculating acceleration

If the force is measured in N, the acceleration in m s-2 and the mass in kg, the acceleration of a mass m by a force F will equal \(F\over m\). The constant of proportionality in this equation is 1.

\(a={F\over m}\)

Essentials

Force-time graphs

Since \(F={\Delta (mv) \over t} \Rightarrow \Delta(mv)=Ft\). Therefore, change in momentum (impulse) can be found from the area under a force - time graph.

Fluids

Water is an example of a fluid. In engineering applications, fluids typically move along pipes with a certain amount flowing past a point every second:

  • Volumetric flow rate = \({V \over t}={Av\over t}\) (m3 s-1)
  • Mass flow rate = \({m\over t} ={\rho V \over t}\) (kg s-1)

When water is made to change speed, there is a change in momentum. This requires a force related to the mass flow rate:

\(F={\Delta (mv)\over t}={m\over t}(v-u)\)

Hanging mass over a pulley

This experimental set-up can be used to verify Newton's second law.

 There are two free bodies to consider separately in this question:

  • \((\downarrow)\) The hanging mass falls because its weight is larger than the tension
  • \((\rightarrow)\) The mass on the table accelerates because the tension is larger than friction

 Applying Newtons law to both blocks gives an equation for the acceleration.

Test Yourself

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