Momentum and Impulse

Momentum and Impulse

MEDI11002 Physics for Health Sciences
Week 2 Lecture 1
CQU

Goals for this Session

• Define key terms:

  • Momentum

  • Impulse

• Relate the magnitude of momentum of an object to its mass and velocity.

• Differentiate between momentum and inertia.

• Relate the impulse experienced by an object to the magnitude of force and the time over which the force is applied to the object.

• Integrate the concepts of acceleration, force, inertia, momentum, and impulse in discussing stationary and moving objects.

• Perform simple calculations involving force, acceleration, momentum, and impulse.

• Review of Week 2 learning goals:

  1. Understanding momentum and impulse

  2. Application of Newton’s laws

  3. Practical applications in health sciences

  4. Integrative analysis of motion and forces

  5. Analytical calculations of physical quantities

  6. Conceptual differentiation between similar principles

Momentum

Definition

• Momentum is defined as the 'inertia of motion.'

• It refers to the tendency of a moving object to resist changes in its state of motion.

• Mathematically, momentum is represented as: $p = mv$ where

  • p = momentum

  • m = mass of the object

  • v = velocity of the object

Properties

• Momentum is directly proportional to both mass and velocity:

  • $p ext{ is proportional to } m$

  • $p ext{ is proportional to } v$

• For example, a stationary object has zero momentum:

  • Stationary objects can’t have momentum because their velocity is zero.

  • $ext{Velocity} = 0 <br>ightarrow ext{Momentum} = 0$

• A moving object with mass has non-zero momentum.

  • Example:

  • A massive mountain (large mass) that is stationary has momentum = 0.

  • A tiny bird (small mass) in motion has momentum greater than 0.

Momentum and Net Force

• Net force causes acceleration, which leads to changes in velocity, subsequently causing changes in momentum.

• According to Newton’s Second Law:

  • $F = ma$

  • Forces acting on an object do not cancel out when the velocity is changing.

  • As per the momentum formula, since momentum $p = mv$ and mass remains constant, changing velocity alters momentum.

• For momentum change:

  • The greater the net force applied, the greater the change in momentum:

  • $rac{d p}{dt} ext{ (change in momentum)} ext{ is proportional to } F$

  • Mathematically,

  • $rac{d p}{dt} <br>ightarrow ext{acceleration} <br>ightarrow ext{change in velocity}$

Change in Momentum and Time

• Newton’s Second Law can be expressed in terms of momentum:

  • $F = rac{d p}{dt}$

  • Rearranging gives:

  • $ext{Change in momentum (Δp)} = F imes t$

• If the time (t) remains constant while force changes, the change in momentum is directly proportional to the force:

  • $ext{Δp} ext{ is proportional to } F$

• If net force is applied for longer duration, the change in momentum increases:

  • $ext{Δp is proportional to } t$

Impulse

• Impulse is defined as the product of the net force and the time it acts.

• Since change in momentum (Δp) is proportional to both net force (F) and elapsed time (t):

  • $ext{Impulse} (Ft) = ext{Δp}$

• Impulse represents the change in momentum experienced by an object under a force applied over time.

Impulse and Momentum Change

• Recall that:

  • Impulse can also be represented as:

  • $Ft = ext{Δmv}$

• Impulse relates to change in momentum:

  • $ext{Impulse} = ext{change in momentum}$

  • This connection helps understand how to manage changes in motion and the repercussions of forces applied.

Practical Examples

Example 1: Tennis

• In tennis, players aim to maximize the ball’s momentum to achieve a high velocity.

• To do this:

  • Maximize the change in momentum (Δp) by maximizing the product of force and time (Ft).

  • Use the largest possible force and maintain contact for the longest time.

Tennis Swing Mechanics

• A player swings the racquet quickly along the intended path of the ball:

  • This technique increases contact time with the racquet, maximizing the impulse (Ft).

• Comparison:

  • Stopping the racquet immediately after hitting the ball yields less significant momentum change and lower ball velocity.

Example 2: Airbags

• Airbags in automobiles are designed to reduce the force experienced during impacts by decelerating the occupant more gradually.

• A car with mass (m) moving at velocity (v) has momentum represented as:

  • $p = mv$

• Upon collision, the car’s velocity decreases, leading to a change in momentum characterized by:

  • $ext{Δp is proportional to } Ft$

Example 3: Catching a Ball

• Catching a ball at high velocity can be painful if done improperly:

• Technique:

  • If the hand remains still, the ball is decelerated rapidly causing a high impact force which results in pain.

• Improved technique:

  • Moving the hand in the direction of the ball during contact extends contact time, reducing the peak force of impact, which minimizes pain.

Summary

• After this session, you should be able to:

  • Define key terms:

  • Momentum

  • Impulse

  • Relate momentum's magnitude to mass and velocity.

  • Differentiate between momentum and inertia.

  • Relate impulse to the magnitude of force and time over which it is applied.

  • Apply concepts of inertia, momentum, and impulse in discussing both stationary and moving objects.