+870 The energy needed to break a wooden board is about 6.5 J. The mass of a $1 coin is 8.1 g. The gravity on Earth is 9.80665 N·kg-1.
The formula to calculate the gravitational potential energy of an object is:
\(E=m \cdot \Delta h\cdot g\)
where E is the energy in J (joules), m the mass in kg (kilograms), 𝚫h the variation of height in m (meters) and g the gravity in N·kg-1 (newtons per kilogram).
Using this information, determinate the (minimal) height you would have to drop a $1 coin from in order for it to have enough energy to break a wooden board.
Hint: Be careful with measuring units!
Neglecting air friction and terminal velocity:
6.5j = 8.1/1000 kg h 9.80665 N.kg^-1
(6.5 x 1000/8.1 )/ 9.80665 = 81.83 m
+870 \(E=m\cdot \Delta z\cdot g \\\Rightarrow \Delta z=\frac{E}{m\cdot g} \\m\cdot \Delta z\cdot g\geq 6.5 \\8.1\times 10^{-3}\cdot \Delta z\cdot 9.80665\geq 6.5 \\\Delta z\geq \frac{6.5}{8.1\times 10^{-3}\times9.80665}\approx 81.829 \text{ m}\)
I got the same result; that's perfect.
20/20 and the brownie:
