Answer to Question #191530 in Mechanics | Relativity for steven

Question #191530

A 50 kg mass moving to the right at 8 m s−1 collides with a 25 kg mass moving to the right at 3 m s−1. After the collision, the velocities of the masses are v1 and v2, where v2 > v1 and 15% of the original kinetic energy is lost during the collision. Assume that no external forces are acting.

(a) Show that v2 = 19 − 2v1.

(b) Show that 3v 2 1 − 38v1 + 100 ≈ 0 is a good approximation of the equation for v1.

(c) Calculate v1 and v2.

(d) What happened to the 15% lost energy? 


1
Expert's answer
2021-05-11T09:07:18-0400

before collision\text{before collision}

m1=50;u1=8m_1 = 50;\vec{u_1}=8

m2=25;u2=3m_2=25;\vec{u_2}=3

m1u1+m2u2=475m_1*\vec{u_1}+m_2*\vec{u_2}=475

Ek1=m1u122+m2u222=1712.5E_{k1}=\frac{m_1u_1^2}{2}+\frac{m_2u_2^2}{2}=1712.5

after collision\text{after collision}

m1=50;v1m_1 = 50;\vec{v_1}

m2=25;v2m_2=25;\vec{v_2}

m1v1+m2v2=m1u1+m2u2=475(1)m_1*\vec{v_1}+m_2*\vec{v_2}=m_1*\vec{u_1}+m_2*\vec{u_2}=475(1)

Ek=m1v122+m2v222E_{k}=\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}

Ek=Ek10.15Ek1=1455.625E_k= E_{k1}-0.15*E_{k1}=1455.625

Ek=m1v122+m2v222=1455.625(2)E_{k}=\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}=1455.625(2)

(a) from the equation(1)(a)\text{ from the equation(1)}

m1v1+m2v2=475m_1*\vec{v_1}+m_2*\vec{v_2}=475

50v1+25v2=47550*\vec{v_1}+25*\vec{v_2}=475

2v1+v2=192*\vec{v_1}+\vec{v_2}=19

v2=192v1(3)\vec{v_2}=19-2*\vec{v_1}(3)

(b) from the equation(2)(b)\text{ from the equation(2)}

m1v122+m2v222=1455.625\frac{m_1v_1^2}{2}+\frac{m_2v_2^2}{2}=1455.625

m1v12+m2v22=2911.25m_1v_1^2+m_2v_2^2=2911.25

50v12+25v22=2911.2550v_1^2+25v_2^2=2911.25

2v12+v22=116.452v_1^2+v_2^2=116.45

 from the equation(3)\text{ from the equation(3)}

2v12+(192v1)2=116.452v_1^2+(19-2v_1)^2=116.45

6v1276v1+244.55=06v_1^2-76v_1+244.55=0

3v1238v1+122.75=03v_1^2-38v_1+122.75=0

3v1238v1+1000(4)3v_1^2-38v_1+100\approx0(4)

(c) from the equation(4)(c)\text{ from the equation(4)}

3v1238v1+100=03v_1^2-38v_1+100=0

v1=3.8;v2=192v1=11.4v_1 =3.8;v_2=19-2*v_1=11.4

Decision v1=8.9 is not taken by the condition of the task v2>v1\text{Decision } v_1'=8.9 \text{ is not taken by the condition of the task }v_2>v_1

Answer: v1=3.8;v2=11.4\text{Answer: }v_1 =3.8;v_2=11.4


(d) Part of the translational kinetic energy is transferred into the internal energyof the colliding bodies.(d)\text{ Part of the translational kinetic energy is transferred into the internal energy}\newline \text{of the colliding bodies.}

 As an example, deformation and heating of bodies.\text{ As an example, deformation and heating of bodies.}














Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment