Explosions are like sticking collisions in reverse

• Notes
• 14

This preview shows pages 9–14. Sign up to view the full content.

Explosions are like sticking collisions in reverse. Start with one body (often at rest), and it breaks into several moving pieces. Assuming F net =0 on the system, p 1 ,f + p 2 ,f + · · · = p i Common case: object at rest breaks into two moving objects: p 1 ,f + p 2 ,f = 0

This preview has intentionally blurred sections. Sign up to view the full version.

Phys 2A - Mechanics Example: An astronaut is “spacewalking” when he finds herself a few meters form the spaceship and decides it’s time to get back. She is not moving with respect to the ship and cannot walk. Her tether has broken so she cannot pull herself in. She decides to throw something away from the ship. But she knows she should not go too fast towards the ship. She can throw away a 2.0 kg- wrench from her toolbox, and she weighs 52.0 kg including suit and all tools. At what speed should she throw it if she wants to approach the ship at 1.0 m/s? ANS: Clearly F net =0 (no contact forces, no gravitational force). So she can use conservation of momentum. In the ship’s frame of reference (same as her’s, initially) her initial velocity is zero. So p 1 ,f + p 2 ,f = 0 where “1” refers to her and “2” to the tool. Now p 2 ,f = - p 1 ,f m tool v tool = - m she v she ,f (good luck!) | v tool | = m she m tool | v she ,f | = 52 - 2 2 . 0 (1 . 0) m/s = 25 m/s
Phys 2A - Mechanics Example: Rocket motion. Rocket/jet propulsion works by throwing stuff like our astronaut of the previous example. But the “throwing” is continuous and at a fixed speed with respect to the rocket. There is an additional complication: as stuff is thrown the mass of the rocket decreases.

This preview has intentionally blurred sections. Sign up to view the full version.

Phys 2A - Mechanics Example: Rocket motion (continued). x y initial (time t) final (time t+ Δ t) m - Δ m Δ m m v v + Δ v v - u Here u = velocity of ejected stuff with respect to rocket (relative motion!) Conservation of momentum: P f = P i ( m - Δ m )( v + Δ v ) + Δ m ( v - u ) = mv or Neglecting Δ m Δ v (second order in small quantities) and simplifying m Δ v + u Δ m = 0 Divide by time interval, simplify and take limit Δ t ! 0 m Δ v Δ t = - u Δ m Δ t dv dt = - u 1 m dm dt rocket propulsion equation
Phys 2A - Mechanics dv dt = - u 1 m dm dt The equation gives the acceleration of the rocket. It is positive (since the mass is decreasing in time).

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '07
• Hicks

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern