• Forces can combine to produce
• • Balanced?forces
  • Unbalanced?forces

   

• Balanced?forces mean that the forces have combined in such a way that they cancel each other out and no?resultant force?acts on the body
  • For example, the?weight?of a book on a desk is balanced by the?normal?force of the desk
  • As a result,?no?resultant force?is experienced by the book, the book and the table are?equal?and?balanced

   

A book resting on a table is an example of balanced forces

• Unbalanced?forces mean that the forces have combined in such a way that they do not cancel out completely and there is a?resultant force?on the object
  • For example, imagine two people playing a game of tug-of-war, working against each other on opposite sides of the rope
  • If person?A?pulls with 80 N to the left and person?B?pulls with 100 N to the right, these forces do not cancel each other out completely
  • Since person?B?pulled with more force than person?A?the forces will be unbalanced and the rope will experience a resultant force of 20 N to the right

   

A tug-of-war is an example of when forces can become unbalanced

Unbalanced Forces, Mass & Acceleration

• When forces combine on an object in such a way that they do not cancel out, there is a?resultant force?on the object
• This resultant force causes the object to?accelerate?(i.e. change its?velocity)
  • The object might?speed up
  • The object might?slow down
  • The object might?change direction

   

• The relationship between resultant force, mass and acceleration is given by the equation:

F = m × a

• Where:
  • F?= resultant force, measured in Newtons (N)
  • m =?mass, measured in kilograms (kg)
  • a?= acceleration, measured in metres per second squared (m/s²)

   

Part (a)

Step 1: List the known quantities

• • Initial velocity = 0 m/s
  • Final velocity = 27 m/s
  • Time,?t?= 3 s

   

Step 2: Calculate the change in velocity

change in velocity = Δv?= final velocity ? initial velocity

Δv?= 27 ? 0 = 27 m/s

Step 3: State the equation for acceleration

Step 4: Calculate the acceleration

a = 27 ÷ 3 =?9 m/s²

Part (b)

Step 1: List the known quantities

• • Mass of the car,?m?= 900 kg
  • Acceleration,?a?= 9 m/s²

   

Step 2: Identify which law of motion to apply

• • The question involves quantities of?force,?mass?and?acceleration, so Newton's second law is required:

   

F?=?ma

Step 3: Calculate the force required to accelerate the car

F?= 900 × 9 =?8100 N

Part (a)

Step 1: List the known quantities

• • Initial velocity,?u?= 20 m/s
  • Final velocity,?v?= 0 m/s
  • Time,?t?= 0.1 s

   

Step 2: Calculate the change in velocity of the car (and the passenger)

change in velocity = Δv?= final velocity ? initial velocity = v ? u

Δv?= 0 ? 20

Δv?= ?20 m/s

Step 3: Calculate the deceleration of the car (and the passenger) using the equation:

Step 4: Calculate the deceleration

a?= ?20 ÷ 0.1

a?=??200 m/s²

Part (b)

Step 1: List the known quantities

• • Mass of the passenger,?m?= 70 kg
  • Acceleration (deceleration, in this case),?a?= ?200 m/s²

   

Step 2: State the relationship between resultant force, mass and acceleration

• • This question involves quantities of force, mass and acceleration, so the appropriate equation for this case is:

   

F?=?m × a

Step 3: Calculate the decelerating force

F?= 70 × ?200

F?=??14 000 N