Question

Question: A truck driver slams on the brakes and the momentum of the truck changes from toindue to a constant force of the road on the wheels of the truck. As a vector, write the net force exerted on the truck by the surroundings.

Short answer

Answer

The net force exerted on the truck by the surrounding is$\left\{-9512.2,0,0\right\}N$

Step-by-step solution

Definition and the formula of net force

The rate of change of a particular system’s momentum will be equated to the net force applied to that system.

If the system's momentum changes from initial momentum $\underset{p_1}{\to }$to final momentum $\underset{p_2}{\to }$over time $∆t$, the force acting on the system will be,

$\underset{F_{net}}{\to }=\frac{\underset{p_2}{\to }-\underset{p_1}{\to }}{∆t}$

Finding the net force on the system

Substitute $\left\{65,000,0,0\right\}kgm/s$for $\underset{p_1}{\to }$, $\left\{26,000,0,0\right\}kg.m/s$for $\underset{p_2}{\to }$and $4.1s$for $∆t$into the formula of net force acting on the system.

$$\begin{gathered} \underset{F_{net}}{\to }=\frac{\left\{26,000,0,0\right\}kg.m/s-\left\{65,000,0,0\right\}kg.m/s}{4.1s} \\ =\frac{\left\{26,000-65,000,0-0,0-0\right\}kg.m/s}{4.1s} \\ =\frac{\left\{-39,000,0,0\right\}kg.m/s}{4.1s}\left(\frac{1N}{1kg.m/s^2}\right) \\ =\left\{-9512.2,0,0\right\}N \end{gathered}$$

Therefore, the net force on the system is$\left\{-9512.2,0,0\right\}N.$