Question

6. A van of mass 1200 kg was moving at a velocity of 8 m/s when it was involved in a head-on collisionwith a lorry moving in the opposite direction. Assuming that the van came to a stop after the collision...(a) calculate the momentum of the van before the collision;(b) calculate the momentum of the van after the collision(c) find the change in momentum of the van (d) if the van took .30 s to stop, calculate the force that acted on each driver

Answer 1

Given data:

* The mass of the van is 1200 kg.

* The velocity of the van before the collision is 8 m/s.

* The velocity of the van after the collision is 0 m/s.

Solution:

(a). The momentum of the van before the collision is,

`p_i=mv_i`

where m is the mass of van, p_i is the momentum of van before the collision, and v_i is the velocity of van before the collision,

`\begin{gathered} p_i=1200*8 \\ p_i=9600kgms^{-1^{}} \end{gathered}`

Thus, the momentum of the van before the collision is 9600 kgm/s.

(b). The momentum of the van after the collision is,

`p_f=mv_f`

weere p_f is the final momentum, and v_f is the final velocity of the van,

Substituting the known values,

`\begin{gathered} p_f=1200*0 \\ p_f=0^{} \end{gathered}`

Thus, the momentum of the van after the collision is 0 kgm/s.

(c). The change in the momentum of the van is,

`\begin{gathered} dp=p_f-p_i \\ dp=0-9600 \\ dp=-9600kgms^(-1) \end{gathered}`

Here, the negative sign indicates that the momentum of van is decreasing with time.

Thus, the change in the momentum of the van is -9600 kgm/s.

(d). According to the Newton's second law, the force acting on the van in terms of the change in momentum is,

`F=(dp)/(dt)`

where dt is the time interval in which the momentum of the van changes,

Substituting the known values,

`\begin{gathered} F=-(9600)/(0.30) \\ F=-32000\text{ N} \\ F=-32*10^3\text{ N} \\ F=-32\text{ kN} \end{gathered}`

Here, the negative sign is indicating the direction of force acting on the van is opposite to the direction of motion of van before the collision.

Thus, the force acting on the van is -32 kN.