Push Experiment

1

Same Push on Two Boards

Shove an empty skateboard and another loaded with books using equal force.

2

Quick Check

Which board speeds up more—light or heavy? Make your choice to see.

3

What You Notice

The lighter board accelerates faster. Same push, smaller mass means greater acceleration.

Pro Tip:

Equal force causes different accelerations when masses differ—key idea of Newton’s Second Law.

Key Equation

\[\vec F = m\,\vec a\]

Variable Definitions

\( \vec F \) net force  (N)
\( m \) mass  (kg)
\( \vec a \) acceleration  (m·s\(^{-2}\))

Applications

Pushing a Trolley

Heavier trolley needs more force to gain the same acceleration.

Kicking a Football

Stronger kick gives larger acceleration to the same ball mass.

Momentum Route

1
\[ p = m v \]

Momentum is mass times velocity; here mass \(m\) stays constant.

2
\[ \vec F = \frac{d\vec p}{dt} \]

Newton's second law: force equals rate of change of momentum.

3
\[ \frac{d\vec p}{dt} = m \frac{d\vec v}{dt} \]

With constant mass, pull \(m\) outside the derivative.

4
\[ \vec F = m \frac{d\vec v}{dt} = m \vec a \]

Thus, force equals mass times acceleration—\( \vec F = m \vec a \).

Key Insight:

For constant mass, Newton’s momentum form becomes the familiar \( \vec F = m \vec a \).

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Graphical Insight

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Force–Acceleration graph for a 2 kg mass

Force ∝ Acceleration

Plotting Force (N) against Acceleration (m/s²) for a 2 kg body gives a straight line through the origin.

The line shows that for fixed mass, Force is directly proportional to Acceleration.

Key Points:

  • Slope of the line equals mass (2 kg).
  • Double the acceleration → double the force.
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Multiple Choice Question

Question

A net force of 12 N acts on a 3 kg trolley. What is its acceleration?

1
2 m/s2
2
3 m/s2
3
4 m/s2
4
6 m/s2

Hint:

Apply Newton’s second law: \(a = \frac{F}{m}\).

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Key Takeaways

Force drives change

A body accelerates only when a net external force acts.

More force, more acceleration

Acceleration is directly proportional to the applied force.

Heavier mass, slower change

Acceleration falls as mass rises for the same force.

One formula ties all

\(F = m a\) unites force, mass, and acceleration—master it.