QZ_04_S

QZ_04_S - Ph1a: Solution to Quiz 4 Alejandro Jenkins, Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Ph1a: Solution to Quiz 4 Alejandro Jenkins, Fall 2004 Problem 1 (6 points) - Collision on a Spring A linear spring has a free length D . When a mass m is hung on one end, the spring has an equilibrium length D + ` . While it is hanging motionless with an attached mass m , a second mass m is dropped from a height ` onto the first one. The masses collide inelastically and stick together. (a) (1 point) What is the new equilibrium length of the spring? Solution: The equilibrium length of the spring is that for which the spring’s restoring force exactly cancels the weight of the attached mass. If a linear spring with elastic constant k is stretched by an amount ` (measured from its free length D ), then the restoring force is k` . If a mass m was attached, then, at equilibrium, k` = mg . If the weight is doubled, then the spring’s restoring force at its new equilibrium length must be twice what it was before: 2 mg = k 2 ` . The spring will now be stretched by 2 ` with respect to its free length. The total length of the spring at its new equilibrium is D + 2 ` . (b) (1 point) What is the period of the resulting motion? Solution: The spring’s stiffness, characterized by the elastic constant k , has not changed. The mass attached is now 2 m . Therefore the period is T = 2 π s 2 m k . But k is not specified in the problem, so we must express it in terms of other quantities given. Since the spring stretched by an amount ` under the weight of m , we have k` = mg , or k = mg/` . Therefore, T = 2 π s 2 ` g . (c) (2 points)
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

QZ_04_S - Ph1a: Solution to Quiz 4 Alejandro Jenkins, Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online