Lecture16

# Lecture16 - Example The Ballistic Pendulum A ballistic...

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Example: The Ballistic Pendulum A ballistic pendulum is a device used to measure the speed of a projectile. As a result of the collision the pendulum-projectile system start swinging. Find the relation between the speed of the projectile and the maximum height the pendulum reaches. before collision after Part I Collision Part II Swinging Conservation momentum only Conservation energy only Note : because of gravity F ext non zero. P is not conserved M m

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What happens if the pendulum is made of an empty box, and the projectile comes out with ½ of its initial velocity? How high will the block swing? In this case you ‘ll need to write a separate eq. for the final momentum of the bullet and block In this case you only need the conservation of energy for the block.

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Systems of variable mass dM M u v M+dM v + dv Beginning Tot. system Σ F ext dP dt = = v dM dt - u dM dt + dv dM dt + M dv dt dP = (M+dM) (v+dv) – Mv – dM u = Mv +dM v + dM dv – Mv – dM u + Mdv Σ F ext = v dM dt - u dM dt + M dv dt = (v – u) dM dt + M dv dt -(u – v) dM dt = M dv dt Σ F ext v rel of dM with respect to M + v rel dM dt Σ F ext M dv dt =
Example of Rocket Find the velocity of a rocket of mass M, after it had emitted some gas. Assume that the fuel is burnt at constant rate, R. v rel = velocity of exhausting gas Projecting this vector equation along the direction of v (tangent to the path) v rel v This term is called the thrust of the rocket. Can be interpreted as an additional force on the rocket due to gas expulsion (in the direction of motion)

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Lecture16 - Example The Ballistic Pendulum A ballistic...

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