A sled with a mass of 20 kg slides along a frictionless ice at 4.5 m/s. It then crosses a rough patch of snow that exerts a friction force of 12N.

Question

A sled with a mass of 20 kg slides along a frictionless ice at 4.5 m/s. It then crosses a rough patch of snow that exerts a friction force of 12N. How far does it slide on the snow before coming to rest?

 

need to figure out how to solve this, please help me! 

Answer 1

Use the kinematic relation

 

v_f² - v_i² = 2ax

 

v_f = final speed = 0 (comes to rest)

v_i = initial speed = 4.5 m/s

a = constant acceleration = F/m = (-12 N) / (20 kg) = -0.6 m/s² (The minus sign means the force is opposed to the driection of motion)

x = distance traveled under the constant force until it comes to rest

 

0 - v_i² = 2(F/m)x

 

x = -mv_i² / 2F = -(20)(4.5)² / [(2)(-12)] m = 16.875 m