Class 9 > Unit # 03: Dynamics > Momentum & Safety Devices

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Unit No. 3 Dynamics - Momentum & Safety Devices

Q. Define Momentum, write its formula and unit. Also define momentum in terms of Force.

Definition

"The quantity or quality of motion contained in a body is called momentum, and it is denoted by $P$."

Mathematical Definition

It is the product of mass and velocity.

$P = m \times v$

Where:
• $P$ = Momentum
• $m$ = Mass of body
• $v$ = Velocity of body

SI Unit of Momentum

A mass unit multiplied by a velocity unit gives the unit of momentum:

$\text{Momentum} = \text{mass} \times \text{velocity} = \text{kg} \cdot \text{m/s} = \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \times \text{s} = \text{N} \cdot \text{s}$

Thus, the SI unit of momentum is kilogram meter per second ($\text{kg}\cdot\text{m/s}$) or Newton-second ($\text{N}\cdot\text{s}$).

Momentum in Terms of Force

The rate of change of momentum of a body is equal to the applied net force. Consider a body of mass $m$ moving with an initial velocity $v_i$. A force $F$ acts on the body to produce acceleration $a$, so that its final velocity after time $t$ becomes $v_f$.

Initial momentum ($P_i$) and final momentum ($P_f$):

$P_i = m v_i \quad \text{--- (i)}$

$P_f = m v_f \quad \text{--- (ii)}$

Subtracting equation (i) from equation (ii) to find the change in momentum:

$\Delta P = P_f - P_i = m v_f - m v_i = m(v_f - v_i)$

Dividing by time $t$ on both sides:

$\frac{\Delta P}{t} = \frac{m(v_f - v_i)}{t}$

Since acceleration $a = \frac{v_f - v_i}{t}$, we can write:

$\frac{\Delta P}{t} = m \cdot a$

Since $F = m \cdot a$, it follows that:

$F = \frac{\Delta P}{t} \quad \implies \quad F \cdot t = \Delta P$

This shows that the change in momentum ($F \cdot t$, also known as impulse) is equal to the force multiplied by the time interval.

Q. Describe the principle used in safety devices with examples.

Principle of Safety Devices

The relation $F \cdot t = \Delta P$ (or $F = \frac{\Delta P}{t}$) is fundamental in designing safety features. To stop a moving body, a certain change in momentum ($\Delta P$) must be produced. According to this equation, if the time interval ($t$) of impact is increased, the impact force ($F$) acting on the object or person is significantly reduced, preventing severe injuries.

Examples

• Car Bumpers and Grills: Designed to crumple slowly upon impact, increasing the collision time and reducing the force transmitted to the passengers.
• Seat Belts, Cushions, and Airbags: They hold passengers from moving forward suddenly and provide extra cushioning time to change momentum during a crash, lowering the impact force.
• Fragile Packaging: Glassware and sensitive electronic components are packed in Styrofoam and safety bags to absorb shocks by increasing the stopping time during drops.
• Helmets: Protect the head from direct strikes by increasing the stopping time during an impact, thereby reducing the peak force experienced by the skull.

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