I'm wondering as to why I got this physics question wrong, despite it being quite simple in nature. I believe that I missed something while working on the problem.
Basically, the question involves two workers moving a 52 kg crate with a coefficient of friction of 0.52. One pushes at a force of 340 N, while the other pulls with a force of 170 N. The workers push at an angle of 25 degrees.
My goal is to find the acceleration of the crate. Since one worker is pushing and the other is pulling on the crate, I thought that it made sense to combine both the pushing and pulling forces together into a single force. Then, I could just subtract the force of friction to find the system's acceleration.
The 340 N push adds to the normal force on the crate (increasing friction) and the 170N subtracts from the normal force on the crate (reducing friction).
applied force - force of friction = mass of system * acceleration (340cos25 + 170cos25) - (0.52)(9.8*52 + 340sin25 - 170sin25) = 52a a = 3.07 m/s^2
The textbook's answer is 4.5 m/s^2, which I believe comes by omitting 340sin25:
(340cos25 + 170cos25) - (0.52)(9.8*52 - 170sin25) = 52a a = 4.5 m/s^2
Why does the book omit the downwards force applied by the first man?