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Push a ball gently and it crawls; push it hard and it shoots off. A force produces acceleration — but how much? Does it depend on the object's mass too? Newton's second law answers this precisely. Let us build up to it.
- A force can start, stop or change the velocity of an object.
- A change in velocity means the object is accelerating.
- So a force produces acceleration.
In this Activity, we will pull a cart with different forces (using different falling weights) to see how the acceleration changes for a fixed mass.
2. Run the thread over a small pipe (pulley) at the table edge and attach a cup to hold weights. The falling cup pulls the cart with a constant force (Fig. 6.17).
3. Measure the mass of the cup and its contents.
4. Record the cart in slow motion as it travels a fixed distance, and find the time T 1 .
5. Double the mass in the cup (which doubles the pulling force) and repeat to get time T 2 .
- Pull a cart with a falling cup.
- Time it over a fixed distance.
- Double the force and retime.
- More force = more acceleration.
In this Activity, we will keep the force fixed but change the cart's mass to see how mass affects the acceleration.
2. Measure the cart's mass with its contents.
3. Carry out the timing steps of Activity 6.3.
- Keep the pulling force fixed.
- Double the cart's mass.
- Time it again.
- More mass = less acceleration.
- When a net force acts on an object, it accelerates in the direction of that force.
- The acceleration is proportional to the net force.
- The acceleration is inversely proportional to the mass of the object.
- Using F = ma with m = 1 kg and a = 1 m s −2 , F = 1 kg m s −2 = 1 N.
- One newton is the force that gives a 1 kg object an acceleration of 1 m s −2 .
- An object falls towards the Earth with acceleration due to gravity, g.
- The gravitational force on a mass m is F = mg.
- Near the Earth's surface g = 9.8 m s −2 (about 10 m s −2 for quick estimates).
- The acceleration due to the Earth's gravitational force (g) does not depend on the mass of the object.
A barbell has 10 kg on each side of a 10 kg bar (Fig. 6.8). How much force keeps it steady?
Total mass = 10 + 10 + 10 = 30 kg. Gravitational force, \( F = mg = 30 \times 9.8 = 294\ \text{N} \) downward.
To hold it steady, the lifter applies an equal force upward = 294 N, upward .
A 25 kg block faces a maximum friction of 50 N. Find its displacement in 2 s when pushed with (i) 50 N and (ii) 55 N.
(i) Applied force = friction = 50 N, so net force = 0. The block stays stationary .
(ii) Net force = 55 − 50 = 5 N. Acceleration \( a = \dfrac{F}{m} = \dfrac{5}{25} = 0.2\ \text{m s}^{-2} \).
Displacement \( s = ut + \dfrac{1}{2}at^2 = 0 + \dfrac{1}{2}\times0.2\times(2)^2 = 0.4\ \text{m} \) in the forward direction.
A 1500 kg sports car moves east; its velocity-time graph is shown in Fig. 6.21. Find the force during (i) 0–5 s, (ii) 5–10 s, (iii) 10–15 s.
(i) u = 0, v = 10 m s −1 , t = 5 s. Using v = u + at, \( a = \dfrac{10}{5} = 2\ \text{m s}^{-2} \). Force \( F = ma = 1500\times2 = 3000\ \text{N} \), east.
(ii) The graph is flat (constant velocity), so acceleration is zero and no force acts.
(iii) u = 10, v = 0, t = 5 s, so \( a = \dfrac{0-10}{5} = -2\ \text{m s}^{-2} \). Force \( F = 1500\times(-2) = -3000\ \text{N} \) — that is 3000 N towards the west (opposite to motion).
- Newton's second law: F = ma; acceleration is along the net force.
- One newton accelerates 1 kg at 1 m s −2 .
- Weight is the gravitational force, F = mg, with g = 9.8 m s −2 .
- In Activity 6.3, doubling the force should double the acceleration, but the increase is often a little less.
- In Activity 6.4, doubling the mass should halve the acceleration, but the value may differ slightly.
- Apart from measurement errors, friction between the wheels and the surface causes these differences.
- The more complete form of Newton's second law uses momentum — the product of mass and velocity.
- It states that the rate of change of momentum is proportional to the net force, in its direction.
- This form works even when the object's mass is not constant.
- A fielder pulls their hands back while catching a fast ball, increasing the stopping time so the force (and injury) is smaller.
- Airbags inflate into a soft cushion in a crash, increasing the time over which a passenger stops, reducing the force on them.
- Cracking a coconut works the opposite way — it stops in a very short time, so the ground exerts a very large force that breaks the shell.
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Write Newton's second law as a formula.
View Answer
F = ma (or a = F/m). -
A 2 kg object accelerates at 3 m s−². What net force acts?
View Answer
F = ma = 2 × 3 = 6 N. -
What is the value of g near the Earth's surface?
View Answer
9.8 m s−² (about 10 m s−²).
- Newton's second law of motion — net force equals mass times acceleration (F = ma); acceleration is along the net force.
- Acceleration due to gravity (g) — the acceleration of a freely falling object due to the Earth's gravitational force, 9.8 m s −2 .
