A pan of negligible mass is attached to two springs ofnormal lengths as 0.5m each and having stiffnessesk, = 250(N/m) and k2 = 500(N/m). If a 10kgbox is dropped from a height of Im above the pan,1 m1 mks=250N/mk=500N/m1mdetermine the maximum vertical displacement d. andelongation of each spring (s1 and s2).wwwww

Answered: A pan of negligible mass is attached to…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

A pan of negligible mass is attached to two springs of
normal lengths as 0.5m each and having stiffnesses
k, = 250(N/m) and k2 = 500(N/m). If a 10kg
box is dropped from a height of Im above the pan,
1 m
1 m
ks=250N/m
k=500N/m
1m
determine the maximum vertical displacement d. and
elongation of each spring (s1 and s2).
wwwww

Expert Solution

Step 1

Given:

$K_{1} = 250 \frac{N}{m} K_{2} = 500 \frac{N}{m} i n i t i a l l e n g t h o f s p r i n g = 0.5 m$

We need to calculate the maximum vertical displacement of the system and elongation in each spring.

Step 2

The maximum displacement will occur when the block velocity becomes zero, so let that value of maximum displacement be d.

So,

The initial extension in spring:

$I n i t i a l e x t e n s i o n i n s p r i n g s d_{i} = 1 - 0.5 = 0.5 m F i n a l e x t e n s i o n i n s p r i n g s d_{f} = (\sqrt{1^{2} + d^{2}}) - {(0.5)}^{2}$

Step 3

Apply the work-energy theorem:

$\{m g h\} - \{\frac{1}{2} K_{1} (d_{f}^{2} - d_{i}^{2})\} - \{\frac{1}{2} K_{2} (d_{f}^{2} - d_{i}^{2})\} = \{\frac{1}{2} m v_{f}^{2}\} - \{\frac{1}{2} m v_{i}^{2}\} w h e r e, m = 10 K g v_{f} = v_{i} = 0 h = (1 + d) m$

Step by step

Solved in 6 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions