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 = (v_0)/(\mu_d* g)`

also for other block on wet ice we can say similarly

`t_w = (v_0)/(\mu_w*g)`

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

`(t_d)/(t_w) = (\mu_w)/(\mu_d)`

so this is the ratio of time on two surfaces