Question

For a given initial velocity, how does the time td it takes to stop on dry snow differ from the time tw it takes to stop on wet snow

Answer 1

let the friction coefficient on dry ice and wet ice is different and given as

$\mu_d$ = on dry ice

$\mu_w$ = on wet ice

now by friction force formula we can say

$F_f = -\mu mg$

so the deceleration due to friction force is given as

$a = -\mu g$

now the deceleration due to friction force on both surface is given as

$a_1 = -\mu_d * g$

$a_2 = -\mu_w * g$

now the time to stop the two blocks can be calculated by kinematics

$v_f - v_i = a t$

$0 - v_0 = -\mu_d * g * t_d$

$t_d = \frac{v_0}{\mu_d* g}$

also for other block on wet ice we can say similarly

$t_w = \frac{v_0}{\mu_w*g}$

now the ratio of two time on two surfaces is given as

$\frac{t_d}{t_w} = \frac{\mu_w}{\mu_d}$

so this is the ratio of time on two surfaces