A man claims that he can hold onto a 10.0-kg child in a head-on collision as lon

Question

A man claims that he can hold onto a 10.0-kg child in a head-on collision as long as he has his seat belt on. Consider this man in a collision in which he is in one of two identical cars each traveling toward the other at 50.0 mi/h relative to the ground. The car in which he rides is brought to rest in 0.07 s.

(a) Find the magnitude of the average force needed to hold onto the child.
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(b) Based on your result to part (a), is the man's claim valid?

This man's claim is legitimate.

This man's claim is nonsense.

Explanation / Answer

The equation to find the force needed to hold the child is Fnet=ma. (Force = mass multiplied by acceleration). We know the mass which is 10. kg. We need to find acceleration.

I'm assuming that two cars going 50 mph and crashing into each other will be the same as one car going 100 mph and crashing into the wall. I got 100 mph by adding 50+50 =100mph.

Then use a kinematic equation. I cannot write subscripts on yahoo which makes it difficult to write a formula down. Final speed=Initial speed + acceleration mulitplied by time. The 'f' and 'i' means 'final' and 'initial'

In other words, Vf=Vi+at

Rearrange the equation to solve for acceleration.

1) Subtract Vi (initial speed), which means Vf-Vi=at

2) Then divide by t (time), which means Vf-Vi / t = a

Now, the #s in the variables for this equation. Vf (final speed) will be 0 when the car crashes. Vi is 100 mph. We need to convert to m/s (meters per second). 100 mph = 100*0.447=44.7 m/s
t was given to you= 0.07 seconds.

Acceleration and deceleration is the same in physics. This means a= -638 m/s^2

Fnet=ma

We know the mass which is 10 kg and the aceleration is -638 m/s/s, which means the Force= - 6380 Newtons.

B)
Just to let you know, the man will die in this crash because the man's organs would smash into his bones. Even if the child were in a child safety seat, the child is basically declared as dead.

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