First, we should find the force of friction from the formula
Ff = μ * N
So we need the Normal force. As the box does not crash through to floor or levitate off the ground, the acceleration in the y direction is 0. Therefore, the normal force is equal to the weight of the box
ΣFy = N - mg = 0
N = mg
N = 28.6 * 9.8
N = 280.28 newtons
Now we can use the friction formula to find the friction force
Ff = 0.750 * 280.28
Ff = 210.21 N
Now we consider the forces in the x direction. If the force in the rightward direction is greater than the friction force, the box will accelerate to the right.
We see that this is the case, so we should write out a sum or forces in the x-direction.
ΣFx = 302 - 210.21 = mass* acceleration
91.79 = 28.6 * a
Now we solve for 'a'
a = 91.79 / 28.6
a = 3.209
We used base SI units for all the calculations, so we end up with an acceleration with base SI units.
Our answer is 3.209 m/s^2
Considering that all of the given values had 3 sig figs, our answer should have 3 as well. The final answer is
3.21 m/s^2
I hope this helps! For your next question, please format it so that there are spaces between the words and line breaks as necessary. If you have any questions about how to do that, please comment on this and I will get back to you as soon as I can.
