DYNAMICS (Newton's Laws, Momentum, and Collisions)

Flashcards covering Newton's laws, momentum, impulse, and collisions as presented in the lecture notes.

What does Newton's First Law describe about motion when there is no resultant force acting on a body?

A body at rest stays at rest and a body in uniform straight-line motion continues in that state.

What is inertia?

The tendency of a body to resist changes in its motion; mass is a measure of this inertia.

How is weight defined in physics?

The force on a mass due to a gravitational field; weight = mg.

Define linear momentum and give its units and direction.

p = mv; unit is kg·m/s (or N·s); it is a vector directed along the velocity.

Define impulse and its relation to momentum.

Impulse equals the product of force and time (FΔt) and equals the change in momentum Δp; it is a vector.

State the general form of Newton's Second Law.

For constant mass, F = ma; in general, F = d(mv)/dt, i.e., net force equals the rate of change of momentum.

What direction are acceleration and the resultant force relative to each other?

They are in the same direction.

What is the principle of conservation of momentum?

In a closed system with no external forces, the total momentum before a collision equals the total momentum after; m1u1 + m2u2 = m1v1 + m2v2.

What is an elastic collision?

A collision in which momentum and kinetic energy are both conserved.

What is a perfectly elastic collision and a key related property?

A collision in which momentum and kinetic energy are conserved; the relative speed of approach equals the relative speed of separation.

In a closed system, what can happen to kinetic energy during interactions?

Kinetic energy may be converted to internal energy, sound, etc.; KE is not necessarily conserved in all collisions.

How does inertia produce the bus-box scenario when the bus accelerates or turns?

The box tends to maintain its motion; when the bus starts, the box slides backward; when it stops, it slides forward; on a curve, it slides tangentially.

What are the steps to solve Newton's laws problems using a free-body diagram?

1) Isolate the body, 2) draw its free-body diagram, 3) resolve forces along the direction of acceleration, 4) apply Fnet = ma.

How do you set up equations for a block on a horizontal surface with friction?

Horizontal: F − f = ma; Vertical: N − mg = 0; solve for friction f and normal N.

State the impulse–momentum relationship when the force varies with time.

Impulse equals the change in momentum: FΔt = Δp; the average force satisfies Δt = Δp as well.

Name three everyday examples that illustrate impulse.

(a) Tennis follow-through increases contact time, increasing impulse; (b) Seat belts increase stopping time to reduce force; (c) Crumple zones increase stopping time.

What is Newton's Third Law?

For every action, there is an equal and opposite reaction; action-reaction forces act on two different bodies and are of the same type.

Why are weight (mg) and the normal force not an action‑reaction pair?

Because they act on the same body and are different types of forces; action–reaction pairs act on different bodies.

Give examples of action–reaction pairs.

Ground on a person and person on ground; table on a book and book on table; rocket thrust and exhaust; Earth on Moon and Moon on Earth.

What is apparent weight in an accelerating lift, and how does it change with acceleration direction?

Upward acceleration: N = m(g + a); downward acceleration: N = m(g − a); constant velocity: N = mg; free fall: N = 0.

State the impulse–momentum theorem.

Impulse equals the change in momentum: FΔt = Δp, and the net force times time equals the momentum change of the body.

What does the area under a force–time graph represent?

The impulse; equal to the change in momentum; the average force times Δt equals the impulse.

Name the three types of collisions and their kinetic energy behavior.

Elastic: momentum and kinetic energy conserved; Inelastic: momentum conserved, KE not conserved; Completely inelastic: momentum conserved, bodies stick together.

In a head-on elastic collision between masses m and M, what relation holds for relative velocity of separation and approach?

The relative speed of separation equals the relative speed of approach.

What happens when two bodies have equal mass in a one-dimensional elastic collision?

They exchange their velocities.

How do you determine the recoil velocity of a rifle when a bullet is fired?

By momentum conservation: mgun vgun = mbullet vbullet, so vgun = −(mbullet vbullet)/mgun.

What is the rocket thrust formula in terms of mass flow and exhaust velocity?

Thrust = ṁ v_exhaust (relative to the rocket); exhaust momentum leaves the rocket, producing forward thrust.

What are the units of momentum and impulse?

Momentum: kg·m·s^-1 (also N·s); Impulse: N·s (equivalently kg·m·s^-1).

What happens to momentum when there is zero net external force on a system?

The total momentum of the system remains constant; objects continue with constant velocity or at rest.

How do seat belts and airbags influence the impulse experienced by a passenger in a crash?

They increase the time over which the passenger’s momentum is brought to zero, reducing the average force.

How do you relate average force to a varying force during an impact?

The average force is the constant force that would produce the same impulse over the same time interval; area under F–t curves is the impulse.