Q18DQ 鈥淚t鈥檚 not the fall that hurt... [FREE SOLUTION]

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University Physics with Modern Physics

Hugh D. Young, Roger A. Freedman

Physics

14th edition Edition 路 1596 pages

ISBN: 9780321973610

Chapter 1: Q18DQ (page 123)

鈥淚t鈥檚 not the fall that hurts you; it鈥檚 the sudden stop at the bottom.鈥� Translate this saying into the language of Newton鈥檚 laws of motion.

Short Answer

Expert verified

It鈥檚 not the $v = u + a t$ that hurts you; it鈥檚 the sudden change in the momentum i.e. $F = - \frac{m u}{t}$ at the bottom.

Step by step solution

Newton’s Second law

A body accelerates when a net force acts on it and travels in the same direction as the net force. The product of mass and acceleration vector is equal to the force vector.

$鈭� \overset{鈫�}{F} = m \overset{鈫�}{a}$

Kinematic equation in terms of acceleration, velocity, and initial velocity.

For constant acceleration, the final velocity v is related to the initial velocity u by the expression given below,

$v = u + a t$

The statement means that the high final velocity vdoes not hurt you in a fall, but the sudden change in velocity to zero hurts. The force acted on the body at the end of the fall will depend on the de-acceleration and the time it took to stop the fall completely.

$F = m a = m (\frac{v - u}{t}) = m (\frac{0 - u}{t}) = - \frac{m u}{t}$

Hence, it can be said that It鈥檚 not the $v = u + a t$ that hurts you; it鈥檚 the sudden change in the momentum, i.e. $F = - \frac{m u}{t}$ at the bottom.