Physics / Unit 3: Forces and Newton's Laws
3.3 Newton's Second Law
Notes
Newton's second law: the acceleration of an object equals the net force divided by its mass: $\displaystyle a = \frac{F_{\text{net}}}{m}$, or $F_{\text{net}} = ma$.
- Acceleration points in the same direction as the net force.
- Double the net force: double the acceleration. Double the mass: half the acceleration.
- Always use the net force, not just one force.
- Example: a 1,200 kg car accelerates at $2.5 \text{ m/s}^2$. $F_{\text{net}} = 1200 \times 2.5 = 3000 \text{ N}$.
Practice
A net force of 30 N acts on a 6 kg cart. What is its acceleration?
$\displaystyle a = \frac{30}{6} = 5 \text{ m/s}^2$.
A 50 kg crate is pushed with 200 N while friction is 120 N. What is its acceleration?
$F_{\text{net}} = 200 - 120 = 80 \text{ N}$; $\displaystyle a = \frac{80}{50} = 1.6 \text{ m/s}^2$.
The same net force acts on two carts. Cart B has three times the mass of cart A. How does B's acceleration compare to A's?
$\displaystyle a = \frac{F}{m}$: tripling the mass cuts the acceleration to one third.
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