# Momentum and Collisions

Computer Science I · Physics · https://tryals.app/learn/computer-science-i/momentum-and-collisions

## Quantity of Motion and Impulse

**Momentum** is an object's quantity of motion, defined as **$p = mv$** (mass times velocity). It is a vector pointing in the direction of motion.

**Impulse** links force and momentum via **$J = F \Delta t = \Delta p$**. A longer contact time softens an impact; airbags or bent knees increase **$\Delta t$** to reduce peak **$F$** for the same momentum change.

| Concept | Formula | Key Meaning |
| --- | --- | --- |
| Momentum | $p = mv$ | Vector quantity of motion |
| Impulse | $J = F \Delta t = \Delta p$ | Force over time changes $p$ |

## Conservation and Collision Types

**Conservation of momentum** states that in an isolated system, **total momentum stays constant**. Total momentum before equals total momentum after.

Collisions differ by energy conservation:

| Collision Type | Momentum | Kinetic Energy |
| --- | --- | --- |
| **Elastic** | Conserved | Conserved |
| **Inelastic** | Conserved | Lost to heat |
| **Perfect** | Conserved | Objects stick |

> **Pitfall:** Assuming **kinetic energy** is conserved in every collision. Momentum is conserved in **all** isolated collisions, but kinetic energy is conserved **only** in elastic ones.

## Practice questions

4 of this lesson's 9 practice questions, with answers. The full set is in the app.

### 1. Select every statement that is TRUE about collisions in an isolated system.

A. Total kinetic energy is the same before and after in an elastic collision
B. Total momentum is the same before and after
C. Total kinetic energy is the same before and after in an inelastic collision
D. Momentum conservation follows from the third law's equal and opposite internal forces
E. Objects that stick together have lost some kinetic energy

**Answer:** A. Total kinetic energy is the same before and after in an elastic collision; B. Total momentum is the same before and after; D. Momentum conservation follows from the third law's equal and opposite internal forces; E. Objects that stick together have lost some kinetic energy

**Why:** Momentum survives every collision because the internal forces cancel in pairs. Kinetic energy survives only elastic ones by definition, so the inelastic claim is false and the sticking case always loses energy to heat and deformation.

Page: https://tryals.app/practice/computer-science-i/momentum-and-collisions/select-every-statement-that-is-true-about-collisions-in-an-isolated

### 2. Momentum is conserved in every collision; kinetic energy is conserved only in elastic ones. Why does one survive an inelastic collision and the other not?

A. Because momentum is only approximately conserved, and the approximation happens to be good.
B. Because internal forces cancel, while kinetic energy can become heat.
C. Because kinetic energy is genuinely destroyed in an inelastic collision, violating conservation of energy.
D. Because momentum is a vector and kinetic energy is a scalar, and only vectors are conserved.

**Answer:** B. Because internal forces cancel, while kinetic energy can become heat.

**Why:** Momentum conservation follows directly from the third law — the internal forces are equal and opposite, so the two momentum changes cancel — and nothing about the collision's messiness touches that. Energy is still conserved in total; it simply moves into heat, sound and permanent deformation. Which is why an elastic collision gives a second equation and can be solved completely.

Page: https://tryals.app/practice/computer-science-i/momentum-and-collisions/momentum-is-conserved-in-every-collision-kinetic-energy-is-conserved

### 3. A digital sampling system reproduces a 20 kHz tone accurately and turns a 30 kHz tone into a spurious low-frequency one. What has happened?

A. The system's amplifier distorts at high frequencies
B. High frequencies decay faster and are recorded as lower ones
C. The tone exceeds the hardware's maximum representable value
D. Aliasing, the sampling rate is too low to represent 30 kHz

**Answer:** D. Aliasing, the sampling rate is too low to represent 30 kHz

**Why:** Below two samples per cycle, a high frequency produces the same sample values as a low one and is reconstructed as the impostor. It is the wagon-wheel effect in audio, and it is why every ADC has a low-pass filter in front of it, you cannot remove an alias after sampling.

Page: https://tryals.app/practice/computer-science-i/momentum-and-collisions/a-digital-sampling-system-reproduces-a-20-khz-tone-accurately-and

### 4. A crumple zone reduces the force on the occupants because the same change in momentum is spread over a longer time.

**Answer:** True

**Why:** True. The impulse $F\Delta t = \Delta p$ is fixed by the collision, so lengthening $\Delta t$ lowers F proportionally. Doubling the stopping time halves the peak force. Airbags, seatbelt pretensioners and the crumple zone all buy time rather than absorbing energy in the way the word 'cushion' suggests.

Page: https://tryals.app/practice/computer-science-i/momentum-and-collisions/a-crumple-zone-reduces-the-force-on-the-occupants-because-the-same