MasteringPhysics: Chapters 10&11-Google Chrome a https/session masteringphysics.

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MasteringPhysics: Chapters 10&11-Google Chrome a https/session masteringphysics.com/mycty/itemViewtassignmentProblemiD-5609994 itemView?assignmentProblemlD.56099994 https://session.masteringphysics.com/myc Phys201-2016-Spring Chaptecs 10511 Problem 10 40 previoUS Problem 10.40 Part A The spring in the figure (Elgure 1) (a) is compressed by length z it launches the block across a frictionless surface with speed to The two springs in the figure Figure 2) (b) are identical to the spring of the figure (a) They aro compressed by the same length and used to launch the same block What is the block's speed now? 707 Submit Incorrect, Try Again; 5 attempts remaining

Explanation / Answer

here,

Assuming,
k si spring constant
V is velocity when single spring are present
vo is velocity when spring are present
m is mass o0f block

also,
spring 1, k1
spring 2, k2
k1 = k2 = k since both springs are identical

CAse 1: When single spring is present
From Conservation fo Energy,
Pe of spring = KE of Block
0.5 * k * x^2 = 0. 5 *m * v^2

v^2 = kx^2/m ----------(1)

Case 2: WHen two spring are connected in parallel,

net k = k1*k2/(k1+k2) = k^2/2*k = 0.5*k

Stroed Energy in Spring 1, E1 = 0.5 * (0.5*k)*x1^2
Stroed Energy in Spring 2, E2 = 0.5 * (0.5*k)*x2^2

x1 = x2 = x
so, net erngy, PE = E1 + E2 = 0.25*2*k*x^2 = 0.5*k*x^2

From Conservation of Energy, Pe of Spring = KE gained by block

0.5*k*x^2 = 0.5 * m * vo^2

vo^2 = kx^2/m -------------------------(2)

Diving 1 by 2

(V/vo)^2 = kx^2/m * m/kx^2

V = Vo

or

v/vo = 1

If Spring constant were different then there would different ratio for sure.

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