- #1

jybe

- 41

- 1

## Homework Statement

A block slides down a frictionless incline (30 degrees above horizontal) for L=1.4m until it meets a horizontal surface with coefficient of kinetic friction 0.3 before coming to rest. Use work and energy to find the distance that the block slides on the horizontal surface before stopping.

L = 1.4 m

theta = 30 degrees

Coefficient of kinetic friction = 0.3

M = 3 kg

## Homework Equations

mgh = 0.5mv

^{2}

## The Attempt at a Solution

v = (2gh)

^{0.5}

v = (2*9.8*1.4*sin(30))

^{0.5}

v = 3.7 m/s (speed of block as it just enters the horizontal surface)

F(friction) = 0.3 * 2kg * 9.8

F(friction) = 5.88 N

a = F/m

a = 5.88 N /2 kg

a = 2.94 (opposite direction of velocity)

Vf

^{2}= Vi

^{2}+ 2a*Δx

0 = 3.7

^{2}-(2*2.94*Δx)

Δx = 2.33 m

Therefore, the distance traveled on the horizontal surface is 2.33 m.

Does this look correct? I'm doubting the way I solved for acceleration.