Newton's Second Law
Newton's Laws & Momentum - OCR A-Level Physics
Key Definition
Newton's Second Law
The net (resultant) force on an object is directly proportional to its rate of change of momentum. Taking the constant of proportionality as 1 gives the defining equation below. The change in momentum (and the acceleration) is always in the same direction as the net force.
The net (resultant) force on an object is directly proportional to its rate of change of momentum. Taking the constant of proportionality as 1 gives the defining equation below. The change in momentum (and the acceleration) is always in the same direction as the net force.
Case 1 : Mass can change
Use the general form. This applies whenever mass is being added to or removed from the moving object: a rocket burning fuel, a sand conveyor belt loading material, a water jet leaving a hose.
$$\Sigma F = \frac{\Delta p}{\Delta t}$$
Case 2 : Mass is constant
If $m$ does not change, $\Delta p = m \Delta v$, so $\Sigma F = m \Delta v / \Delta t = ma$. This is the familiar special case that covers almost every A-level problem (cars, trolleys, falling objects).
$$\Sigma F = ma$$
- 1 newton is the force that gives a 1 kg mass an accelerationThe rate of change of velocity. A vector quantity. Measured in $\text{m s}^{-2}$. of 1 $\text{m s}^{-2}$.
- Worked example: a 1200 kg car accelerates from rest to 25 $\text{m s}^{-1}$ in 10 s. $a = 25/10 = 2.5 \; \text{m s}^{-2}$. $\Sigma F = (1200)(2.5) = 3000 \; \text{N}$.
- To find the acceleration of a multi-object system, use the TOTAL resultant force and the TOTAL mass: $a = \Sigma F_{\text{total}} / m_{\text{total}}$.
- The direction of acceleration is always the direction of the resultant force. They cannot point in different directions.
Common Mistake
HIGH
Wrong: Plugging a single applied force into $F = ma$ without first working out the resultant force. Or applying $F = ma$ to a rocket where fuel mass is changing.
Right: First sum all forces (with signs) to get $\Sigma F$. Then use $\Sigma F = ma$. For variable-mass problems, use the general form $\Sigma F = \Delta p / \Delta t$ instead.
Right: First sum all forces (with signs) to get $\Sigma F$. Then use $\Sigma F = ma$. For variable-mass problems, use the general form $\Sigma F = \Delta p / \Delta t$ instead.
Examiner Tips and Tricks
- If a question asks "show that $F = ma$ follows from $F = \Delta p / \Delta t$", write: $\Sigma F = \Delta (mv)/\Delta t$, then state that $m$ is constant, so $\Sigma F = m \Delta v / \Delta t = ma$. Worth 2 marks.
- When asked to "state Newton's second law", quote the momentum form. The $F = ma$ form is a special case and loses marks on its own.