Will a block move under the influence of force?

Question

A block whose weight is 45.0N rests on a horizontal table. A horizontal force of 36.0N is applied to the block. The coefficients of static and kinetic force are 0.650 and 0.420, respectively. Will the block move under the influence of the force, and, if so, what will be the block's acceleration? Explain your reasoning.

While working through this problem I was able to find that Fnorm=(45.0N)(9.8m/s^2)=441N
also that fstatic^max=(.650)(441)=286.65N and fkinetic=(.420)(441)=185.22N.
However, when I calculated a using fkinetic=ma then I get the answer as being a=4.116, which my book says is incorrect (correct answer is 3.72m/s^2). Where are my calculations wrong?

Answer 1

First, the weight is given, not the mass. The weight is the normal force, so to get the block moving requires a force of
45*.650
=29.25 N, which is less than the 36N force being applied.

Once moving the FBD has friction working against the force, with the net being =m*a

m*a=36-45*.420
m=45/9.81

a=(36-45*.420)*9.81/45
=3.728 m/s^2

using g=9.80 I get
3.724 m/s^2

j

Answer 2

Right in the beginning, you analyze the problem as if 45 N is its mass, when in fact it is its weight. Therefore, you do not need to multiply by 9.8 m/s^2 to get the weight.

Its mass actually is M = W/g
= 45 N/9.8m/s^2
= 4.59 kg

You know it will move because 45 N x .65 = 29.25 N <36 N

The net force acting is 36 N - 45N x .420 = 17.1 N
using F=ma,
17.1 N = (4.59kg)a
a = 3.724 m/s^2