AP Physics 1: Newton's 2nd Law (F=ma)AP Physics 1: Newton's 2nd Law (F=ma)

APPHYSICS1 · UNIT2 · F O R C E S A N D N E W T O N ' S L AW S

Newton's Second Law

ΣF = ma: the engine of every force problem

Big idea. The acceleration of an object equals the net force on it divided by its mass. Net force is the vector sum of all forces. Acceleration always points in the direction of the net force. The equation

Symbol Meaning Unit

a acceleration m/s²

ΣF net (sum of) forces newtons, N (1 N = 1 kg·m/s²)

m mass (the inertia) kg

Written as a = ΣF / m it shows: more force, more acceleration. More mass, less acceleration. 5-step method for force problems

1. Draw an FBD for the object (or each object).

2. Add any forces you know (use Fg = mg).

3. Write ΣF = ma for each axis (x and y) separately.

4. Decide what you are solving for.

5. Rearrange to isolate it, then substitute numbers with units.

Sign trick. Pick the positive direction to match the acceleration. Forces in that direction are +, forces against it are −. Then ΣF = (forces with) − (forces against).

Sample problem 1: horizontal push with friction

A person pushes a 3 kg box to the left. Friction is 10 N. What push gives an acceleration of 2 m/s² to the left?

Choose left as positive. ΣFx = FA − Ff = ma

FA = ma + Ff = (3)(2) + 10 = 16 N

(Fg = 29.4 N down and FN = 29.4 N up cancel, so y has no acceleration.)

Sample problem 2: vertical motion

A 500 kg rocket produces 8000 N of thrust straight up. Find its acceleration.

Fg = 500 x 9.8 = 4900 N down. ΣFy = 8000 − 4900 = 3100 N up.

a = 3100 / 500 = 6.2 m/s² upward

Using graphs (F = ma practice with graphs)

Graph What the slope means

a (y) vs. ΣF (x) slope = 1/m. Steeper means smaller mass

ΣF (y) vs. a (x) slope = m (the mass)

a (y) vs. m (x) a curve (inverse). Doubling m halves a

v vs. t slope = a. Use ΣF = ma with that a

Test trap. Zero net force does NOT mean zero velocity. It means zero acceleration. Also, mass and weight are different. m is in kg, weight is a force in N.

Weight and apparent weight

Weight = mg. In an elevator, the scale reads the normal force: FN = m(g + a) when accelerating up, and FN = m(g − a) when accelerating down. At constant velocity FN = mg.

Quick reference

Net force 0 → a = 0 (rest or constant velocity)

Same force, double the mass → half the acceleration

Same mass, double the force → double the acceleration

Always label units: N, kg, m/s²

Practice

1. A 5 kg object has a net force of 20 N. Find a.

2. A 2 kg cart accelerates at 3 m/s². What is the net force?

3. A 1200 kg car has a net force of 3000 N. Find a.

4. A 10 kg box is pushed with 50 N. Friction is 20 N. Find a.

5. A 4 kg block has 12 N to the right and 4 N to the left. Find a.

6. Find the weight of a 6 kg object.

7. On an a vs. F graph, the slope is 0.25 kg−1. What is the mass?

8. The same force is applied to two carts. Cart B has double the mass. Compare accelerations. 9. A 500 kg rocket has 8000 N of thrust. Find a.

10. A 70 kg person is in an elevator accelerating up at 2 m/s². What does the scale read? Answers

1. a = 20/5 = 4 m/s².

2. ΣF = 2x3 = 6 N.

3. a = 3000/1200 = 2.5 m/s².

4. ΣF = 30 N, so a = 3 m/s².

5. Net = 8 N right, so a = 2 m/s² to the right. 6. 58.8 N.

7. m = 1/slope = 4 kg.

8. Cart B accelerates at half the acceleration of cart A. 9. a = (8000 − 4900)/500 = 6.2 m/s² up.

10. FN = m(g + a) = 70(11.8) = 826 N.