Linear Momentum and Collisions

What is linear momentum?

The product of an object's mass and velocity, \vec{p}=m\vec{v}

Is momentum a scalar or vector quantity?

Vector quantity.

What is the direction of linear momentum?

Same direction as the object's velocity.

What are the SI units of momentum?

kg\cdot m/s

What does Newton’s Second Law look like when expressed in terms of momentum?

\Sigma \vec{F} = \frac{\Delta \vec{p}}{\Delta t}

What is impulse?

The change in momentum due to a force applied over a time interval, \vec{J} = \vec{F}\Delta t

What are the SI units of impulse?

Newton-seconds (N·s), which equals kg⋅m/s .

Is impulse a scalar or vector?

Vector quantity.

What is the impulse-momentum theorem?

Impulse equals change in momentum: \vec{F}\Delta t = \Delta \vec{p}

What happens to the force if the collision time is longer?

The force is smaller.

Define an isolated system in terms of momentum.

A system with zero net external force acting on it.

What does conservation of momentum state for an isolated system?

The total momentum remains constant.

Write the conservation of momentum equation for two objects before and after collision.

m_1\vec{v}_{10}+m_2\vec{v}_{20}=m_1\vec{v}_{1f}+m_2\vec{v}_{2f}

What are the two main types of collisions?

Elastic and inelastic collisions.

What characterizes an elastic collision?

Both momentum and kinetic energy are conserved.

What characterizes an inelastic collision?

Momentum is conserved but internal kinetic energy is not.

What is a perfectly inelastic collision?

A collision in which objects stick together after impact.

Why is internal kinetic energy not conserved in inelastic collisions?

Some internal kinetic energy is transformed into other forms like heat or sound.

What does the term "internal kinetic energy" refer to?

The sum of the kinetic energies of objects in the system.

What kind of diagram helps visualize the directions and magnitudes of velocities in a collision?

A velocity sketch showing each object with labeled masses and velocity arrows before and after the collision.

What condition must be met for momentum to be conserved in a system?

The system must be isolated—there is no net external force.

What does an impulse graph (force vs. time) represent?

The area under the curve equals the impulse.

What does a zero net external force imply about momentum?

The total momentum does not change.

What physical quantity is conserved during all collisions in an isolated system?

Momentum

Give an example of a real-world situation where impulse reduces injury.

Wearing airbags or padded helmets increases collision time, reducing force.

How can you reduce the force during a collision?

Increase the time over which the force acts.

What is the significance of the direction of impulse?

It points in the direction of the change in momentum.

What does \Delta \vec{p} = 0 indicate?

Momentum is conserved; no net change.

Why are elastic collisions idealized?

Because perfectly elastic collisions rarely occur in everyday macroscopic events.

Can kinetic energy increase during an inelastic collision?

No, kinetic energy decreases or transforms to other forms.

What role does friction play in collisions?

It usually makes collisions inelastic by converting kinetic energy to heat.

What happens to momentum if an external force acts on the system?

Momentum changes according to the impulse applied.

How do you find the final velocities in elastic collisions of two equal masses?

They exchange velocities.

What principle explains why two carts of equal mass exchange velocities in an elastic collision?

Conservation of momentum and kinetic energy.

Why is momentum considered more fundamental in collision problems than kinetic energy?

Because momentum is always conserved in isolated systems, while kinetic energy may not be.