APPC Unit 7: Momentum and Impulse Test on Monday Dec. 3rd!!

Let’s review from Physics 1 Momentum 𝑝=𝑚𝑣 Units: kg*m/s Impulse 𝐽=∆𝑝=𝑚∆𝑣=𝐹𝑡 Units: kg*m/s or Ns Momentum is conserved 𝑝 𝑖 = 𝑝 𝑓 unless there is an external force 𝑝 𝑖 +𝐹𝑡= 𝑝 𝑓 ** Don’t forget about Rotation**

Example Problem #1 An 80 kg stuntman jumps out of a window that’s 45m above the ground. How fast is he falling when he reaches the ground? He lands on a large, air-filled target, coming to rest in 1.5s. What average force does he feel while coming to rest? What if he had instead landed on the ground (impact time= 10ms)?

What can you tell me about the slopes and/or the areas of these graphs? 𝐽=∆𝑝=𝑚∆𝑣=𝐹𝑡

𝐹= 𝑑𝑝 𝑑𝑡 𝐽= 𝐹 𝑡 𝑑𝑡 Let’s Calculus! The force is the time derivative of momentum. Also the slope of a momentum vs time graph! The impulse can be found by integrating under the curve of a Force vs. Time graph

Example Problem #2 A force acting on an object varies as a function of time according to the equation 𝐹=𝑘 𝑡 2 , where k is a constant. If the object had an initial momentum of 0 at t=0, what is the momentum of the object at time t?

Several Types of collisions Sometimes objects stick together or blow apart. In any case, momentum is ALWAYS conserved. Collide and DON’T stick Collide and stick together 1 object breaks into 2 objects Elastic Collision = Kinetic Energy is Conserved Inelastic Collision = Kinetic Energy is NOT Conserved

2-D Collisions You will have a separate horizontal equation and vertical equation. Then you will combine the equations to solve for the final answer.

Example Problem #3 A 2-kg sliding puck whose initial velocity magnitude is v1 = 10 m/s strikes a wall at a 30 degree angle and bounces off. If it leaves the wall with a velocity magnitude of v2 = 10 m/s, and if the collision takes a total of 0.02 seconds to complete, what was the average force applied to the puck by the wall?

Example Problem #4 A 1600-kg pickup truck traveling east at 20 m/s collides with a 1300-kg car traveling north at 16 m/s. The vehicles remain tangled together after the collision. Determine the velocity (magnitude and direction) of the combined wreck immediately after the collision

The ballistic pendulum problem… so common it has it’s own name

Example Problem #5 A 16 g bullet is fired into the bob of a ballistic pendulum of mass of 1.5 kg. When the bob is at its maximum height, the strings make an angle of 60º with the vertical. The length of the pendulum is 2.3 m. Find the speed of the bullet. Ans. 450 m/s Using the initial velocity of the bullet from a, find the maximum height attained by the bob if the bullet passes through the bob and emerges with a speed of 225 m/s. Ans. 0.294 m.