Question

(a) In Problem 5, what is the speed of the flake when it reaches the bottom of the bowl? (b) If we substituted a second flake with twice the mass, what would its speed be? (c) If, instead, we gave the flake an initial downward speed along the bowl, would the answer to (a) increase, decrease, or remain the same?

Short answer

a)$v=2.08\frac{m}{s}$

b)$v=2.08\frac{m}{s}$

c) Speed of the bowl at the bottom will increase.

Step-by-step solution

 Step 1: Given

Mass of ice flake,

_{$m=2.0\times {10}^{-3}\text{\hspace{0.17em}kg}$}

Radius,

_{$\left(r\right)=0.22\text{m}$}

To understand the concept

The problem deals with the law of conservation of energy. The law of conservation of energy states that, total energy of an isolated system remains constant.

Formula:

_{$\text{Initialtotalenergy}=\text{Finaltotalenergy}$}

(a) Calculate the speed of the flake when it reaches the bottom of the bowl

According to the law of conservation of energy:

_{$K{E}_i+P{E}_i=K{E}_f+P{E}_f$}

_{$\frac{1}{2}m{v}^2+0=0+mgr$}

Hence,

_{$v=\sqrt{\left(2gr\right)}$}

_{$v=\sqrt{2\times 0.22\times 9.8}$}

_{$\text{v}=2.08\text{m/s}$}

(b) Calculate the speed if we substituted a second flake with twice the mass

If the mass of flake is doubled, then there would be no change in speed, because the speed of flake doesn’t depend on the mass.

Hence,

_{$v=2.08\text{m/s}$}

(c) Figure out if the answer to (a) would increase, decrease, or remain the same if the flake is given an initial downward speed along the bowl

According to law of conservation of energy:

_{$K{E}_f=K{E}_i+P{E}_i-P{E}_f$}

This indicates that if initial speed is greater, the final speed must increase.