Newton's Second Law
- Newton's second law of motion states:
The resultant force on an object is directly proportional to its acceleration
- This can also be written as:
- Where:
- F = resultant force (N)
- m = mass (kg)
- a = acceleration (m s–2)
- This relationship means that objects will accelerate if there is a resultant force acting upon then
- An unbalanced force acting on a body means it experiences a resultant force
- If the resultant force is along the direction of motion, it will speed up (accelerate) or slow down (decelerate) the body
- If the resultant force is at an angle, it will change the direction of the body
Worked example
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.
Resultant Force
- Since force is a vector, every force on a body has a magnitude and direction
- The resultant force is, therefore, the vector sum of all the forces acting on the body
- The direction is given by either the positive or negative direction as shown in the examples below
Resultant forces on a body can be positive or negative depending on their direction
- The resultant force could also be at an angle, in which case, the magnitude and direction of the resultant force can be determined using either:
- Calculation (usually simple geometry, such as Pythagoras' Theorem or the sine and cosine rules)
- Scale drawing
- This is covered further in Scale Diagrams
Acceleration
- Since acceleration is a vector, it can be either positive or negative depending on the direction of the resultant force
- If the resultant force is in the same direction as the motion of an object, the acceleration is positive
- If the resultant force is in the opposite direction to the motion of an object, the acceleration is negative
- An object may continue in the same direction however with a resultant force in the opposite direction to its motion
- This means it will slow down (decelerate) and eventually come to a stop
- If there are no drag forces, or they're negligible, the acceleration is independent of the mass of an object
- This has been shown in experiments by astronauts who have dropped a feather and a hammer on the Moon from the same height
- Both the hammer and feather drop to the Moon's surface at the same time
Worked example
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:
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
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
Worked example
A rocket produces an upward thrust of 15 MN and has a weight of 8 MN.
Calculate the magnitude and direction of the acceleration of the rocket.
Exam Tip
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.