2.6 - Force

Force, Mass and Acceleration

A force changes an object’s state of motion.
At constant mass, acceleration is directly proportional to applied force: $a \propto F$ .
At constant force, acceleration is inversely proportional to mass: $a \propto 1/ m$ .
Graphs of $a$ against $F$ at fixed mass and $a$ against $1/ m$ at fixed force are straight lines through the origin.
A trolley investigation uses elastic strings stretched to the same length to provide comparable units of force. Changing the number of strings changes force; changing the number of trolleys changes mass. Ticker tape provides the acceleration measurements.

Combining the relationships:

a \propto \frac{F}{m} \Rightarrow F \propto ma

Newton’s Second Law of Motion: the rate of change of momentum is proportional to the applied force and occurs in its direction.
For constant mass:

F \propto ma = m \frac{v - u}{t} = \frac{m v - m u}{t}

Write $F = kma$ . In S.I. units, 1 newton is the force that gives a 1 kg mass an acceleration of $1 m s^{- 2}$ , so $k = 1$ :

F = ma, 1 N = 1 kg m s^{- 2}

Load on a smooth horizontal surface: $m = 80 kg$ , pulling force $F = 160 N$ , with no opposing resistance.

a = \frac{F}{m} = \frac{160}{80} = 2 m s^{- 2}

Braking car: $m = 1200 kg$ , initial velocity $30 m s^{- 1}$ , stopping time 5 s.

a = \frac{0 - 30}{5} = - 6 m s^{- 2}

F = 1200 (- 6) = - 7200 N

The average braking force has magnitude 7200 N and acts opposite to the initial motion.