Momentum • Momentum is a vector describing how difficult it is to stop a moving object • Total momentum is the sum of individual momenta • p ⃗=mv ⃗ • Units are kg·m/s or N·s Example 1: Changing Momentum • An Aichi D3A bomber mass (3600 kg) departs from its aircraft carrier with a velocity of 85 m/s due east. What is its momentum? • After it drops its payload, its new mass is 3000 kg and it attains a cruising speed of 120 m/s . What is its new momentum? Impulse • As you observed in the previous problem, momentum can change • A change in momentum is known as an impulse (J) • J ⃗=Δp ⃗ Example 2: Impulse • The D3A bomber, which had a momentum of 3.6e5 kg·m/s, comes to halt on the ground. What impulse is applied? Relationship Between Force and Impulse • F ⃗=ma ⃗=m (dv ⃗)/dt=d/dt (mv ⃗ )=(dp ⃗)/dt Example 3: Force from Momentum • The momentum of an object as a function of time is given by p=kt2, where k is a constant. What is the equation for the force causing this motion? Impulse-Momentum Theorem Example 4: Impulse-Momentum • A 6-kg block, sliding to the east across a horizontal, frictionless surface with a momentum of 30 kg·m/s, strikes an obstacle. The obstacle exerts an impulse of 10 N·s to the west on the block. Find the speed of the block after the collision. Example 5: Water Gun • A girl with a water gun shoots a stream of water than ejects 0.2 kg of water per second horizontally at a speed of 10 m/s. What horizontal force must the girl apply on the gun in order to hold it in position? Impulse from F-t Graphs • Impulse is the area under a Force-time graph • Impulse is equivalent to a change in momentum Example 6: Impulse from Force • A force F(t)=t3 is applied to a 10 kg mass. What is the total impulse applied to the object between 1 and 3 seconds?
