Kevin S. Huang

2009: Problem 1

Topic: Collisions
Concepts: Conservation of energy, General Newton’s 2nd law

Solution:

By conservation of energy, the velocity of the apple right before it hits the ground is

mgh=\frac{1}{2}mv^2

v=\sqrt{2gh}

By Newton’s 2nd law, the average force exerted on the apple is

F=\frac{\Delta p}{\Delta t}=\frac{mv}{\Delta t}

since the apple comes to rest. The average pressure is then

P=\frac{F}{A}=\frac{m\sqrt{2gh}}{A\Delta t}=\frac{(0.3\,\mathrm{kg})\sqrt{2(10\,\mathrm{m/s^2})(0.4\,\mathrm{m})}}{(0.0004\,\mathrm{m^2})(0.1\,\mathrm{s})}=21000\,\mathrm{Pa}

so the answer is B.