2.9 Force & Acceleration

• Newton's First Law states:

A body will remain at rest or move with constant velocity unless acted on by a resultant force

• The law is used to explain why things move with a constant (or uniform) velocity
• If the forces acting on an object are balanced, then the resultant force is zero
• The forces to the left = the forces to the right
• The forces up = the forces down
• The velocity (i.e. speed and direction) can only change if a resultant force acts on the object

Worked Example

Step 1: Identify the prompt (or 'clue') word in the question to choose which rules to apply

• • The clue in this question is 'constant velocity'
  • This means that forces are perfectly balanced in every direction

 

Step 2: Calculate the missing force

• • For constant velocity sum of forces, 

 ΣF = 0

 F = D

 Step 3: Write the answer including units

F = 6 k N

• Newton's Second Law states that:

The acceleration of an object with constant mass is directly proportional to the resultant force on it

• An unbalanced force on a body means it experiences a resultant force
  • If the resultant force is along the direction of motion, the body will speed up (accelerate) or slow down (decelerate)
  • If the resultant force is at an angle, the body will change direction

• Since resultant force is being considered, the equation is often written 

ΣF = ma

• • The use of Σ (Sigma) signifies that F is the sum of the forces rather than just one force acting alone

Worked Example

Step 1: Write down the known quantities

• • Mass, m = 750 g = 0.750 kg
  • Acceleration, a =  11 m s⁻².

Step 2: Identify the equation needed and substitute in the values

ΣF = ma = 0.75 × 11 = 8.25

Step 3: Write the final answer using the correct significant figures and units

ΣF = 8.3 N

• In reality moving bodies always do have some resultant force acting on them, for example, due to friction caused by;
  • Movement through air or water (drag forces)
  • Movement across a surface (such as tyres on the road)
  • Moving parts within the object itself (such as the engine of a car, or the bearings in a wheel)

• When the drag forces become equal to the driving force the velocity reaches its maximum value and the object is said to be moving at terminal velocity
  • 'Terminal' means final, meaning there can be no more increases in velocity after it has been reached

• Terminal velocity is reached when the forces in the direction of motion are balanced by the forces opposing motion
  • This is often used in relation to the case of a skydiver falling in freefall, although it can apply to any situation where drag forces apply
• In the case of the skydiver the force in the direction of motion is their weight, which remains constant
  • As the skydiver accelerates air resistance increases, until the opposing forces balance

Worked Example

Step 1: Identify exactly what the question is asking for

• • The question asks about 'maximum' (terminal) velocity, this occurs when all forces are balanced
  • To increase the terminal velocity the car either needs to
    • Increase the forces in the forwards direction, or
    • Decrease the forces in the backwards direction (the ones which are opposing motion)

Step 2: Write down the forces affecting the motion

• • In the forwards direction the only force is the thrust from the engine
  • The forces opposing motion include:
    • Friction between the tyres and the road
    • Air resistance
    • Friction in the moving parts of the engine
    • Friction in the moving parts of the wheel system (bearings)

Step 3: Suggest changes the designer could make

• • Increase the forwards thrust by increasing power from the engine 
  • Reduce opposing forces by 
    • Using tyres with less grip
    • Making the car body more streamlined
    • Reducing friction in the engine (using better oil for example)
    • Reduce friction in the moving parts with smoother surfaces or better lubricants

Exam Tip