Homework Help: Kinetics, force and acceleration

1. The problem statement, all variables and given/known data

The crate has a mass of 80 kg and is being towed by a chain which is always directed at 20º from the horizontal has shown. Determine the crate's acceleration in t = 2 s if the coefficient of static friction is μ_s = 0.4, the coefficient of kinetic friction is μ_k = 0.3, and the towing force is P = (90t²) N, where t is in seconds.



2. Relevant equations

ΣF = ma

3. The attempt at a solution

ΣF_x = ma_x
Pcos(20º) - μ_kmg = ma
84.57t² - 235.44 = (80 kg)a

solving for a when t = 2
a = 1.29 m/s²

The answer at the back of my book is a = 1.75 m/s². I think I'm supposed to consider that static friction force is greater than kinetic friction force, but I can't figure out how to do that.

 

Then N = mg*cos(20°)?
But that gives a = 1.46 m/s², not a = 1.75 m/s².

 

Thank you, Doc Al.