How am I wrong? (ie, speed after a certain distance)?

A 5.73 kg block initially at rest is pulled to the right along a horizontal surface by a constant horizontal force of 15.8 N. The coefficient of friction is 0.107. Gravity is 9.8

Find the speed of the block after it has moved 2.13 m. Answer in m/s.

I did it two ways:

1. W=FD

W= 15.8 X 2.13

W = 33.654

33.654 = 1/2(5.73)v^2

v^2 = 33.654/2.865

v^2 = 11.74

v = 3.42 m/s

2. V = sqrt(2 X F X D / M)

V = sqrt(2 X 15.8 X 2.13 / 5.73)

V = sqrt(31.6 X 2.13 / 5.73)

V = sqrt (67.308/5.73)

V = sqrt (11.74)

V = 3.42 m/s

What am I doing wrong?

How am I wrong? (ie, speed after a certain distance)?microsoft net framework

The opposing friction force is 0.107(9.8m/s^2)(5.73kg) = 6.008478N

15.8N - 6.008478N = 9.791522N

F/m = a = 9.791522N/5.73kg = 1.709m/s^2

Distance = 1/2at^2

2Distance/a = t^2

4.26m/1.709m/s^2 = t^2 = 2.493s^2

t = 1.579s

vf = at = 1.709m/s^2(1.579s) = 2.698m/s

You could also do it like this using W = Fd

Wtotal = Wforce - Wfriction

Wtotal = 15.8N(2.13m) - 6.008478N(2.13m)

Wtotal = 33.654J - 12.798J = 20.856J

Now convert it to K

Wtotal = K = 1/2mv^2

2K/m = v^2 = 41.71J/5.73kg = 7.28m^2/s^2

v = 2.698m/s

Note:

1N = 1kg.m/s^2

1J = 1kg.m^2/s^2