Question

A skater with an initial speed of 5.70 m/s stops propelling himself and begins to coast across the ice, eventually coming to rest. Air resistance is negligible. (a) The coefficient of kinetic friction between the ice and the skate blades is 0.0850. Find the deceleration caused by kinetic friction. (b) How far will the skater travel before coming to rest? a = , x =

Answer 1

a) a = - 0.833 m/s² and b) x = 19.5 m

Step-by-step explanation:

a) As we are asked about the acceleration created by the force of friction, let's write Newton's equation for the system

X axis

-fr = ma

Y Axis

N-W = 0

N = W = mg

The equation for the force of friction is

fr = μ N

fr = μ mg

-μ mg = m a

a = - μ g

a = - 0.0850 9.8

a = - 0.833 m/s²

b) ask what distance it travels before stopping, at this point the speed is zero (vf = 0)

Vf² = v₀² - 2 a x

0 = v₀² - 2 a x

x = - v₀² / 2 a

x = 5.7² / (2 0.833)

x = 19.5 m