Answer to Question #191470 in Molecular Physics | Thermodynamics for Yotamu

Question

a.      shows a bead sliding on a wire, How large must height h1 be if the bead, starting at rest A, is to have a velocity of 200cm/s at point B? Ignore friction

Answer 1

When a bead has dropped a distance h it has lost potential energy = mgh, where m is the mass of the object, and g is the acceleration due to gravity, 9.8 $m/s^2$ . This potential energy will become kinetic energy $\frac{1}{2}mv^2$ .

$v = 200 \;cm/s = 2.00 \;m/s \\ m \times 9.8 \times h = \frac{1}{2} m \times 2.0^2 = m \times \frac{4.00}{ 2} = m \times 2 \\ m \times 9.8 \times h = m \times 2 \\ 9.8 \times h = 2 \\ h = \frac{2}{9.8} = 0.204 \;m = 20.4 \;cm$

Answer: 20.4 cm