Chapter 2: Q9P (page 82)

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

Expert verified

Answer

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

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,

$\underset{F_{n e t}}{\to} = \frac{\underset{p_{2}}{\to} - \underset{p_{1}}{\to}}{∆ t}$

Finding the net force on the system

Substitute $\{65, 000, 0, 0\} k g m / s$ for $\underset{p_{1}}{\to}$ , $\{26, 000, 0, 0\} k g . m / s$ for $\underset{p_{2}}{\to}$ and $4.1 s$ for $∆ t$ into the formula of net force acting on the system.

$\underset{F_{n e t}}{\to} = \frac{\{26, 000, 0, 0\} k g . m / s - \{65, 000, 0, 0\} k g . m / s}{4.1 s} = \frac{\{26, 000 - 65, 000, 0 - 0, 0 - 0\} k g . m / s}{4.1 s} = \frac{\{- 39, 000, 0, 0\} k g . m / s}{4.1 s} (\frac{1 N}{1 k g . m / s^{2}}) = \{- 9512.2, 0, 0\} N$