Answer to Question #182489 in Mechanics | Relativity for Rocky Valmores

Question

(1-Dimensional Collision) A 100g solid ball approaches a 1kg solid ball which is also approaching the 100g ball. If the initial speeds of both balls are 5m/s, what are the final speeds of the balls?

Answer 1

To be given in question

Motion 1D

M₁=100gm =0.1kg

M₂=1000gm=1.0kg

u₁=u₂=5 meter/sec

To be asked in question

v₁=?

v₂=?

We know that

Momentum conservation law

$m_{1}u_{1}+m_{2}u_{2} =m_{1}v_{1}+m_{2}v_{2} \rightarrow(1)$

Put value in eqution (1)

$0.1\times5+1\times5=0.1\times v_{1}+1\times v_{2}$

0.5+5.0=$(0.1v_{1}+1v_{2})$

5.5=$(0.1v_{1}+1v_{2})\rightarrow(2)$

We know that

Cofficient of restitution

$e=1$

elastic collision

$v_{1}-v_{2} =u_{2}-u_{1}\rightarrow(3)$

Put value in eqution (3)

$v_{1}-v_{2}=0$

$v_{1}=v_{2}$

equation (2)put values $v_{1}andv_{2}$

$5.5=1.1v_{1}$

$v_{1}=\frac{55}{11}$

$v_{1}=5meter /sec$

Similarly

$v_{1}=v_{2}=5meter/sec$