Question

A woman is holding a 7 kg baby in her arms in a car traveling 30 miles per hour. The car crashes and comes to a stop in 0.05 seconds. How much force (in metric units) must the woman use to keep hold of the baby? How much in American Standard units?

Answer 1

Let's first focus on metric. Instead of miles per hour, we want meters per second. Multiply by some conversion factors:

\[\frac {30 \space miles}{1 \space hour} \times \frac{1609.34 \space meters}{1 \space mile} \times \frac{1 \space hour}{3600 \space seconds}=13.4 \space m/s\]
Force is mass times acceleration. The acceleration here is 13.4/0.05=268 m/s^2. Keep in mind the acceleration should really be negative because really we're decelerating to a stop, but we can just use the magnitude of this acceleration to calculate the force.

That makes the force on the baby F=ma=7(268)=1876 N, which is the same force the mother must apply in the opposite direction to keep the net force on the baby 0 N.

I'm not sure what units you'd be using for American Standard Units (I'm not American) - maybe pounds, miles, and hours? - but just apply conversion factors to the appropriate variables and solve the same way as above.

Answer 2

Thank you for your help!! :)