2.4.1 Force & Momentum

Force & Momentum

Linear Momentum

• Linear momentum (p) is defined as the product of mass and velocity Momentum is the product of mass and velocity

• Momentum is a vector quantity – it has both a magnitude and a direction
• This means it can have a negative or positive value
• If an object travelling to the right has positive momentum, an object travelling to the left (in the opposite direction) has a negative momentum
• The negative or positive directions are defined by the observer on a case-by-case basis
• The SI unit for momentum is kg m s−1 When the ball is travelling in the opposite direction, its velocity is negative. Since momentum = mass × velocity, its momentum is also negative

Worked Example

Which object has the most momentum?  • Both the tennis ball and the brick have the same momentum
• Even though the brick is much heavier than the ball, the ball is traveling much faster than the brick
• This means that on impact, they would both exert a similar force (depending on the time it takes for each to come to rest)

Force and Momentum

• Force is defined as the rate of change of momentum on a body
• The change in momentum is defined as the final momentum minus the initial momentum
• These can be expressed as follows: • It should be noted that the force in this situation is equivalent to Newton’s second law:

F = m × a

• Only when mass is constant
• In situations where mass is not constant, Newton’s second law can only be considered to assist descriptions and not for calculations
• The force and momentum equation can be derived from Newton’s Second law and the definition of acceleration Direction of Forces

• Force and momentum are vectors so they can take either positive or negative values
• The force that is equal to the rate of change of momentum is still the resultant force
• A force on an object will be negative if it is directed in the opposite motion to its initial velocity
• This means that the force is produced by the object it has collided with The wall produces a force of -300N on the car and (due to Newton’s Third Law) the car also produces a force of 300 N back onto the wall

Worked Example

A car of mass 1500 kg hits a wall at an initial velocity of 15 m s-1.
It then rebounds off the wall at 5 m s-1 and comes to rest after 3.0 s.

Calculate the average force experienced by the car.

Exam Tip

• The direction you consider positive is your choice, as long the signs of the numbers (positive or negative) are consistent with this throughout the question
• In an exam question, carefully consider what produces the force(s) acting. Look out for words such as ‘from’ or ‘acting on’ to determine this and don’t be afraid to draw a force diagram to figure out what is going on.
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