The spring-activated toy shown in the figure is sliding at speed v in the+x-direction across a smooth surface when it bursts into two fragments.Fragment 1 has mass m₁ and moves at speed v₁ in the -y-direction whilefragment 2 moves at speed v2 in the direction shown.V1Find the energy released by the spring, Us, if v 2.6 m/s, v1 = 6 m/s,m₁ =0.467 kg, and m2 = 0.583 kg. Consider the spring to be massless.[Hint: Conserve momentum during the "bursting" to solve for v2. Thenapply conservation of energy to find the energy stored in the compressedspring.]BeforeV비mi21U₂ = _______ JM210V2AfterxReport your answer below, assuming three significant figures. Remember to include a "-" ifnecessary.OLem

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Description: The spring-activated toy shown in the figure is sliding at speed v in the+x-direction across a smooth surface when it bursts into two fragments.Fragment 1 has mass m₁ and moves at speed v₁ in the -y-direction whilefragment 2 moves at speed v2 in the

The total mass of the toy is m1+m2=0.467+0.583=1.05 kg. Applying the conservation of momentum along x-direction before and after bursting, m1+m2v=m1×0+m2×v2cosθm1+m2v=m2v2cosθ --- (1) Applying the conservation of momentum along y-direction before and after bursting, m1+m2×0=m2×v2sinθ-m1×v1m1v1=m2×v2sinθ--- (2) Squaring and adding (1) and (2) we get, m1+m22v2+m22v12=m22v22cos2θ +m22v22sin2θm1+m22v2+m22v12=m22v22--- (3)The spring energy is the change of energy after and before bursting Us=12m1v12+m2v22-12m1+m2v2 Using equation (3) we can write Us=12m1v12+m2v22-12m1+m2v2=12m1v12+m22v22m2-12m1+m2v2=12m1v12+m1+m22v2+m22v12m2-12m1+m2v2=12m1v12+m1+m22v2+m22v12m2-m1+m2v2=120.467·62+1.052·2.62+0.5832·620.583-1.05·2.62=21.74 JoulesHence the energy stored in spring = 21.74 Joules

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The spring-activated toy shown in the figure is sliding at speed v in the +x-direction across a smooth surface when it bursts into two fragments. Fragment 1 has mass m₁ and moves at speed v₁ in the -y-direction while fragment 2 moves at speed 2 in the direction shown. Find the energy released by the spring, Us, if v 2.6 m/s, v1 =6 m/s, m1 =0.467 kg, and m2 = 0.583 kg. Consider the spring to be massless. [Hint: Conserve momentum during the "bursting" to solve for v2. Then apply conservation of energy to find the energy stored in the compressed spring.] V Before mi v1 U₂ = _______ J necessary. m2 V2 After x Report your answer below, assuming three significant figures. Remember to include a "if

The spring-activated toy shown in the figure is sliding at speed v in the +x-direction across a smooth surface when it bursts into two fragments. Fragment 1 has mass m₁ and moves at speed v₁ in the -y-direction while fragment 2 moves at speed 2 in the direction shown. Find the energy released by the spring, Us, if v 2.6 m/s, v1 =6 m/s, m1 =0.467 kg, and m2 = 0.583 kg. Consider the spring to be massless. [Hint: Conserve momentum during the "bursting" to solve for v2. Then apply conservation of energy to find the energy stored in the compressed spring.] V Before mi v1 U₂ = _______ J necessary. m2 V2 After x Report your answer below, assuming three significant figures. Remember to include a "if

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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The spring-activated toy shown in the figure is sliding at speed v in the
+x-direction across a smooth surface when it bursts into two fragments.
Fragment 1 has mass m₁ and moves at speed v₁ in the -y-direction while
fragment 2 moves at speed v2 in the direction shown.
V1
Find the energy released by the spring, Us, if v 2.6 m/s, v1 = 6 m/s,
m₁ =0.467 kg, and m2 = 0.583 kg. Consider the spring to be massless.
[Hint: Conserve momentum during the "bursting" to solve for v2. Then
apply conservation of energy to find the energy stored in the compressed
spring.]
Before
V
비
mi
21
U₂ = _______ J
M2
10
V2
After
x
Report your answer below, assuming three significant figures. Remember to include a "-" if
necessary.
OL
em

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