Question

In a crash test, a truck with mass 1900 kg traveling at 24 m/s smashes head-on into a concrete wall without rebounding. The front end crumples so much that the truck is 0.60 m shorter than before. (a) What is the average speed of the truck during the collision (that is, during the interval between first contact with the wall and coming to a stop)? m/s (b) About how long does the collision last? (That is, how long is the interval between first contact with the wall and coming to a stop?) s (c) What is the magnitude of the average force exerted by the wall on the truck during the collision? N (d) It is interesting to compare this force to the weight of the truck. Calculate the ratio of the force of the wall to the gravitational force mg on the truck. This large ratio shows why a collision is so damaging. (e) What approximations were necessary in making this analysis? (Select all that apply.) Neglect the horizontal component of the force of the road on the truck tires. The deceleration of the truck is approximately equal to . Assume a nearly constant force exerted by the wall, so the speed changes at a nearly constant rate.

Answer 1

Answer:

12 m/s

0.05 s

912000 N

48.9296636086

Assume a nearly constant force exerted by the wall, so the speed changes at a nearly constant rate

Explanation:

t = Time taken

u = Initial velocity = 24 m/s

v = Final velocity = 0

s = Displacement = 0.6 m

m = Mass of truck = 1900 kg

Average velocity is given by

$v_a=\dfrac{v+u}{2}\\\Rightarrow v_a=\dfrac{0+24}{2}\\\Rightarrow v_a=12\ m/s$

The average velocity is 12 m/s

Time is given by

$t=\dfrac{s}{v}\\\Rightarrow t=\dfrac{0.6}{12}\\\Rightarrow t=0.05\ s$

The time taken is 0.05 s

Force is given by

$F=m\dfrac{v-u}{t}\\\Rightarrow F=1900\times \dfrac{24}{0.05}\\\Rightarrow F=912000\ N$

The force is 912000 N

The ratio is

$\dfrac{912000}{1900\times 9.81}=48.9296636086$

The deceleration must be constant.

Hence, the answer is

Assume a nearly constant force exerted by the wall, so the speed changes at a nearly constant rate.

Answer 2

The average speed, time and magnitude of the average force are respectively;

A) v_avg = 12 m/s

B) t = 0.05

C) F_avg = 912 kN

Momentum

We are given;

• Mass of truck; m = 1900 kg

• Speed of truck; v = 24 m/s

• Crumbled distance; d = 0.6 m

A) Since the concrete is stationary before collision, the average speed of the truck during collision is;

v_avg = (u- v)/2

v_avg = (24 - 0)/2

v_avg = 12 m/s

B) From newtons first equation of motion, we know that;

v = u + at

Thus;

0 = 24 + at

a = -24/t

From newton's second equation of motion;

v² = u² + 2ad

Thus;

0² = 24² + (2 × (-24/t) × 0.6)

0 = 576 - 28.8/t

28.8/t = 576

t = 28.8/576

t = 0.05 s

C) The expression for the magnitude of average force exerted by wall on truck is;

F_avg = mu/t

F_avg = (1900 * 24)/0.05

F_avg = 912 kN

D) The approximation that was necessary in making this analysis is;

Assume a nearly constant force exerted by the wall, so the speed changes at a nearly constant rate.

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