Answer to Question #198771 in Mechanics | Relativity for karen

Question #198771

Two blocks of mass 300 g and 200 g respectively are moving toward each other along a horizontal frictionless surface with velocities of 50 cm/s and 100 cm/s, respectively. a. If the blocks collide and stick together, find their final velocity. (5 pts.) b. Find the final velocity of each block if the collision is completely elastic (e =1).


1
Expert's answer
2021-05-26T21:35:25-0400

Gives

m1=300g=0.3kgm_1=300g=0.3kg

m2=200g=0.2kgm_2=200g=0.2kg

u1=50cm/sec=0.50cm/secu_1=50cm/sec=0.50cm/sec

u2=100cm/sec=1m/secu_2=100cm/sec=1m/sec

v=?v=?

Momentum conservation

m1u1+m2u2=(m1+m2)vm_1u_1+m_2u_2=(m_1+m_2)v

v=m1u1+m2u2m2+m2v=\frac{m_1u_1+m_2u_2}{m_2+m_2}


v=0.3×0.50+0.2×10.3+0.2=0.7m/secv=\frac{0.3\times0.50+0.2\times1}{0.3+0.2}=0.7m/sec

(b)

Momentum conservation in elastic collision

m1u1+m2u2=(m1v1+m2v2)m_1u_1+m_2u_2=(m_1v_1+m_2v_2)


0.3×0.50.2×1=0.3v1+0.2v20.3\times0.5-0.2\times1=0.3v_1+0.2v_2

0.3v1+0.2v2=0.150.20.3v_1+0.2v_2=0.15-0.2

0.3v1+0.2v2=0.05(1)0.3v_1+0.2v_2=-0.05\rightarrow(1)

elastic collision

e=1

v2v1=u1u2v_2-v_1=u_1-u_2

v2v1=0.5+1=1.5(2)v_2-v_1=0.5+1=1.5\rightarrow(2)

eqution (1)and(2)

v2=80cm/secv_2=80cm/sec

v1=70cm/secv_1=-70cm/sec


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Comments

Fagbolagun Oluwanifemi
23.01.23, 21:49

This is really impressive and helpful, it really helped me with my assignment. Thank you so much.

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