Newton’s Second Law (DP IB Physics)

It is important to understand that for an object in motion, a resultant force that opposes that motion will cause the object to decelerate, not to suddenly travel backwards. 

If no drag forces are present, then the acceleration of a falling object is independent of its mass. This unintuitive fact of physics has been proven by astronauts on the Moon, who simultaneously dropped both a hammer and a feather from equal heights and found that they hit the ground 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.

(b) The mass of the rocket is 0.8 × 10⁵ kg.

Calculate the magnitude and direction of the acceleration of the rocket.

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 × 10³ N

  • Weight (downward acting) = −8 MN = −8 × 10⁶ N

  • Thrust (upward acting) = 15 MN = 15 × 10⁶ N

Step 3: Calculate the resultant force

• 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

Step 2: Calculate the acceleration and state the direction

upwards

• Acceleration is in the same direction as the resultant force

Air resistance is a type of fluid resistance because fluids are gases or liquids. The IB specification uses fluid resistance so you should use this term when referring to air resistance in the exam. Air resistance and fluid resistance are drag forces since drag is the force exerted by the particles in a fluid on an object moving it. The symbol for fluid resistance is therefore the same as symbol for drag, F_d.

Three forces, 4 N, 8 N, and 24 N act on an object with a mass of 5 kg. Which acceleration is not possible with any combination of these three forces?

A.  1 m s^–2

B.  4 m s^–2

C.  7 m s^–2

D.  10 m s^–2

Answer: D

Step 1: List the values given

• Three possible forces at any angle of choice: 4 N, 8 N, and 24 N

• Mass of object = 5 kg

Step 2: Consider the relevant equation

• Newton's second law relates force and acceleration:

F = m × a

Step 3: Rearrange to make acceleration the focus

Step 4: Investigate the minimum possible acceleration

• The minimum acceleration would occur when the forces were acting against each other

• This is when just the 4 N force is acting on the body

• Now check the acceleration:

Step 4: Investigate the maximum possible acceleration

• The maximum acceleration would occur when all three forces are acting in the same direction

• This is a total force of

a = 4 + 8 + 24 = 36 N

• With acceleration:

Step 5: Consider this range and the options

• Since option D is higher than 7.2 m s^–2; it is not possible that these three forces can produce 10 m s^–2 acceleration for this mass

• Option D is the correct answer, as it is the only one that is not possible

The direction you consider positive is your choice, as long as the signs of the numbers (positive or negative) are consistent throughout the question.

It is a general rule to consider the direction the object is initially travelling in as positive. Therefore all vectors in the direction of motion will be positive and opposing vectors, such as drag forces, will be 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.

Answer: