Answer to Question #240522 in Mechanics | Relativity for Sachi

Question

A 8000 kg truck travelling at 4 m/s east collides with 2000 kg car moving at 16 m/s in direction 30⁰ south of west. After collision, the two vehicles remains tangled together.

i)  Find the momentum of lorry and the car before the collision.

ii)  With what speed and in what direction does the wreckage begin to move?

iii) Is this an elastic collision? Verify your answer.

Answer 1

given data;

Mass of truck= $m_{t} = 8000 kg$

Speed of truck= $V_{t} = 4 m/s$

Mass of car=$m _{c} = 2000 kg$

Speed of car$= V _{c} = 16 m / s$

so

$V_{c} = -16cos 30\degree i + ( -16 sin 30\degree) j$

$$V_{t} = 4i$$

1

- total momentum before collision

$p = m_{t} v_{t}+ m _{c} v_{c} = 800 (4 i) + 2000(-16(0.866)i-8j)$

$p = 32000 i - 27712 i - 16 000j$

$p = 4288 i - 16000j$

$|p| = 16564 m kg/s$

2-

as after collision they move together & as momentum is conserve

$|p| = |p_{f}| = 16564 = (m _{t} + m_{c}) v _{f}$ $\implies v_{f} = 1.66 m/s$

$v_{f} = p/m = 0.04288i - 1.6 j$

3-

initial total energy =$KE _{1} + KE _{2} = m_{t} v_{t}^2/2 + m_{c} v_{c}^2 /2 = E_{i}$

$E_{i} = 4000 (4)^2 + 1000(16)^2$

$E_{i} = 320000 J$

final energy = $(m_{t} + m_{c} /2) v_{f}^2$

$v_{e}^2 =5000(1.66)^2$

$E_{f}=13778 J$

as $E_{i}$ is not equal to $E_{f}$ thus not elastic collision