Chapter 7, Problem 18P

(a)

To determine

The average force exerted on the car by the barrier.

Answer to Problem 18P

  $F=138800\text{ N}$

Explanation of Solution

Given:

Mass of the car is $m=1500\text{ kg}$

Initial velocity of the car is $u=50\text{ km/h = }\left(50\text{ km/h}\right)\left(\frac{1000\text{ m}}{1\text{ km}}\right)\left(\frac{1\text{ h}}{3600\text{ s}}\right)=13.88\text{ m/s}$

Final velocity of the car is $v=0\text{ m/s}$

The time interval at which the car comes to rest after smashing with the barrier is, $\Delta t=0.15\text{ s}$

Formula used:

The average force acting on the car is the rate of change of its momentum. That is,

  $F=\frac{p_f-p_i}{\Delta t}=\frac{mv-mu}{\Delta t}$$\left(1\right)$

Where, $p_i$ and $p_f$ are initial and final momentum of the car.

Calculation:

Substituting the numerical values in equation $\left(1\right)$ ,

  $F=\frac{\left(1500\text{ kg}\right)\left(0\text{ m/s}\right)-\left(1500\text{ kg}\right)\left(13.88\text{ m/s}\right)}{0.15\text{ s}}$

  $=\frac{-20820\text{ kg}\text{.m/s}}{0.15\text{ s}}=-138800\text{ kg}{\text{.m/s}}^2\text{ = }-138800\text{ N}$

Negative sign indicates that the force acting on the car is in the direction opposite to its direction of motion.

Conclusion:

The average force exerted on the car by the barrier is $138800\text{ N}$ .

(b)

To determine

The average deceleration of the car.

Answer to Problem 18P

  $a=-92.53\text{ m/s}$

Explanation of Solution

Given:

Initial velocity of the car is $u=50\text{ km/h = }\left(50\text{ km/h}\right)\left(\frac{1000\text{ m}}{1\text{ km}}\right)\left(\frac{1\text{ h}}{3600\text{ s}}\right)=13.88\text{ m/s}$

Final velocity of the car is $v=0\text{ m/s}$

The time interval at which the car comes to rest after smashing with the barrier is, $t=0.15\text{ s}$

Formula used:

The average deceleration $\left(a\right)$ of the car can be obtained by using the equation of motion,

  $v=u+at$

  $\Rightarrow at=v-u$

  $\Rightarrow a=\frac{v-u}{t}$$\left(2\right)$

Calculation:

Substituting the numerical values in equation $\left(2\right)$

  $a=\frac{\left(0\text{ m/s}\right)-\left(13.88\text{ m/s}\right)}{0.15\text{ s}}=-92.53\text{ m/s}$

Conclusion:

The average deceleration of the car is $-92.53\text{ m/s}$ .