Question

A 200 g set of keys , sitting at rest on a table falls 175 cm to the ground. Ignoring frictional forces. How much is the initial kinetic energy of the keys ? How much is the initial potential energy ? How much is the final kinetic energy ? How much is the final potential energy ? How much is the velocity right before it hits the ground ?

Answer 1

a) Initial kinetic energy of the keys equals zero.

$$KE_i=0.$$

b) Let's calculate the initial potential energy of the keys:

$$PE_i=mgh=0.2\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot 1.75\ m=3.43\ J.$$

c) According to the law of conservation of energy final kinetic energy equals initial potential energy:

$$KE_f=PE_i=3.43\ J.$$

d) Final potential energy equals zero:

$$PE_f=0.$$

e)

$$PE_i=KE_f,$$ $$mgh=\dfrac{1}{2}mv^2,$$ $$v=\sqrt{2gh}=\sqrt{2\cdot9.8\ \dfrac{m}{s^2}\cdot1.75\ m}=5.86\ \dfrac{m}{s}.$$