Newton's Second Law (AQA A Level Physics): Revision Note

Remember that a resultant force opposing an object's motion makes it decelerate; it doesn't suddenly travel backwards. If there are no drag forces, the acceleration of a falling object doesn't depend on its mass, which astronauts showed on the Moon by dropping a hammer and a feather from the same height and watching them land together at the same time. (Because there is no air resistance on the Moon.)

A rocket produces an upward thrust of 15 MN and has a weight of 8 MN.

(a) When in flight, the force due to air resistance is 500 kN. Determine the resultant force on the rocket. [2]

(b) The mass of the rocket is 0.8 × 10⁵ kg. Calculate the acceleration of the rocket, and state the direction of the acceleration. [3]

Answer:

Part (a)

Step 1: Draw a force diagram of the situation

Step 2: Convert the forces into newtons and assign directions

• The direction of motion is upwards, therefore upwards is the positive direction

  • Air resistance (downward acting) = −500 kN = $-500\times {10}^3\mathrm{N}$

  • Weight (downward acting) = −8 MN = $-8\times {10}^6\mathrm{N}$

  • Thrust (upward acting) = 15 MN = $15\times {10}^6\mathrm{N}$ [1 mark]

Step 3: Calculate the resultant force

$F=\left(15\times {10}^6\right)+\left(-8\times {10}^6\right)+\left(-500\times {10}^3\right)$

$F=6.5\times {10}^6\mathrm{N}=6.5\mathrm{MN}$ [1 mark]

• The positive value indicates that the resultant force acts in the direction of motion i.e. upwards 

Part (b)

Step 1: State the equation for Newton's second law and rearrange to make acceleration the subject

$F=ma\Rightarrow a=\frac{F}{m}$

Step 2: Calculate the acceleration and state the direction

$a=\frac{6.5\times {10}^6}{0.8\times {10}^5}$ [1 mark]

$a=81\mathrm{m}{\mathrm{s}}^{-2}\left(2\mathrm{s}.\mathrm{f}.\right)$ upwards [1 mark]

• Acceleration is in the same direction as the resultant force [1 mark]

It is a general rule to consider the direction of the object's motion as positive. Therefore, all vectors in the direction of motion will be positive, and opposing vectors, such as drag forces, will be negative. For stationary objects, you can choose which direction is positive or negative as long as you are consistent throughout your calculations. However, it is generally assumed that forward, upwards, and to the right are positive and backward, downwards, and to the left are negative.

A girl is riding her skateboard down the road and increases her speed from 1 m s^-1 to 4 m s^-1 in 2.5 s.

The force driving her forward is 72 N.

Calculate the combined mass of the girl and the skateboard.

[2]

Answer:

Step 1: List the known quantities

• Initial speed, $u=1\mathrm{m}{\mathrm{s}}^{-1}$

• Final speed, $v=4\mathrm{m}{\mathrm{s}}^{-1}$

• Time, $t=2.5\mathrm{s}$

• Force, $F=72\mathrm{N}$

Step 2: Use Newton's second law in terms of momentum to calculate mass

 $F=m\frac{∆v}{∆t}$

 $m=\frac{F∆t}{∆v}=\frac{72\times 2.5}{\left(4-1\right)}$ [1 mark]

$m=60\mathrm{kg}$ [1 mark]