Momentum

What is Momentum?

• Definition: An object in motion remains in motion (with constant velocity) unless acted upon by an external force.

• Comparison of Masses:

  • For two objects with different masses traveling at the same speed, the larger mass is harder to stop.

  • For two objects with the same mass but different speeds, the faster object is harder to stop.

• Momentum Formula:

  • Momentum (p) is defined as mass times velocity.

  • Momentum is ALWAYS CONSERVED!

Momentum as a Vector Quantity

• Units: kg*m/s

• Example 1:

  • Calculating the momentum of a 3000 kg truck traveling at 15 m/s involves using the formula: p = mass × velocity.

Application Examples

Example 2:

• A 1500 kg ferryboat has momentum of 30000 kg*m/s.

  • To find velocity: v = p/m = 30000/(1500) = 20 m/s.

Example 3:

• A car has a momentum of 28000 kg*m/s and travels at 24 m/s.

  • To find mass: m = p/v = 28000/(24) = 1166.67 kg.

Momentum of a System of Objects

• Total momentum of a system is the sum of the momenta of all objects within that system.

Example 4: Momentum Calculation

• Given two objects:

  • Object 1: 6 kg at 13 m/s

  • Object 2: 14 kg at 7 m/s

  • Calculate total momentum:

    • p_total = (m1 * v1) + (m2 * v2) = (6 * 13) + (14 * 7) = 78 + 98 = 176 kg*m/s East.

Comparing Momentum

• Consideration of two moving objects:

  • A large truck moving at 30 m/s vs a small car moving at 30 m/s. The truck (larger mass) has more momentum (Answer: A).

Momentum Change and Impulse

• Change in Momentum = Impulse.

• Newton's First Law: velocity of an object changes only under external force.

• Impulse (J): average force acting on an object over a specific time.

  • J is a vector and in the same direction as the net force (ΣF) on the object.

  • Impulse leads to changes in momentum, with units of Ns or kgm/s.

• Conditions for Momentum Conservation: If F_net = 0, momentum is conserved.

Impulse, Momentum, and Newton's Third Law

• During interactions between two objects, impulses are equal and opposite (similar to third law pairs of forces).

• If no external forces act, increase in the momentum of one object equals the decrease in the momentum of the other.

Effect of Collision Time on Force

• Force is inversely proportional to time; changing the time of impact will affect the force exerted.

• Impulse formula: J = FΔt

Real-World Applications of Momentum

• Applications in safety gear and sports:

  • Car safety design

  • Car air bags

  • Landing techniques in parachuting

  • Techniques in martial arts

  • Hitting and catching a baseball

Case Study: Car Air Bags

• Keeping Δp constant while changing Δt results in decreased F.

• Benefits of air bags: enhancing safety by increasing impact time leading to less force, thereby reducing physical harm.

Case Study: Hitting a Baseball

• Constant force during the swing, aiming to maximize Δp to send the ball flying faster.

• Importance of follow-through in maximizing time of contact.

Types of Impulse Questions and Understanding

Example 1:

• An object of mass 5 kg subjected to a constant force of 12 N for 5 s. Calculate impulse and change in momentum.

Example 2:

• A 0.050 kg tennis ball that rebounds after being struck. Determine change in momentum and impulse.

Example 3:

• A golfer's club hits a golf ball; find average force on the golf ball.

Momentum Conservation and Collisions

Theme Overview

• Momentum is conserved in isolated systems during:

  • Collisions

  • Explosions

• Note the key points relating to energy change during these events.

Classification of Collisions

• Two primary types based on kinetic energy changes:

  1. Inelastic collisions: Some kinetic energy converts to other forms; objects may stick together (perfect inelastic) or bounce apart (general inelastic).

  2. Elastic collisions: Kinetic energy is conserved; objects bounce off one another without energy loss.

Perfect Inelastic Collision

• Two objects merge upon collision, moving together as a single object.

Elastic Collision Mechanism

• Involves conservation of momentum and kinetic energy throughout the collision process.

Explosions and Energy Changes

• Energy transitions from potential to kinetic or vice-versa during explosive events.

Key Terms Regarding Momentum

• Situations where momentum is conserved:

  • Closed systems without external forces.

  • Impulse and momentum relationships emphasized in collisions.

Final Conceptual Questions

• • Momentum is conserved when no net external forces act (D).

  • In static conditions, momentum cannot change (D).

  • Conservation of momentum derives from Newton's 2nd Law (B).

  • All situations of collisions (elastic, inelastic, explosions) adhere to momentum conservation principles.