We can start this question by figuring out our horizontal force components because that's where the acceleration is, meaning the crate will be moving in a horizontal only motion. To do this we need to draw a free body diagram for the crate:
Since we're only looking for horizontal components we only need to worry about the force of friction and the force being applied in the horizontal direction. The force of gravity will be needed when we calculate the acceleration for the different weights of the crate.
The first step is to figure out the applied force on the horizontal. We can do this by taking the cos of 38º and multiplying that by 450N. The reason for this is because if we draw a straight line down from where the worker's hand is we get a right triangle and to figure out the horizontal leg we use SohCahToa where 450N is the hypothenuse and our angle is 38.
So we now have two horizontal forces: a force of 125N going left and 354.6N going right. Let's now set the force of friction as a negative force and the applied force as positive. The difference in these two forces will give us a total applied force of:
Now that we have a force of 229.6N pulling on the crate we can calculate the acceleration.
(a) Remember that a N is actually kg*m/s2. So we need to cancel the kg out. In this case that's easy because the weight of the crate is already in kg and all we need to do is divide the force by the weight:
It's always a good idea to write the units down to keep track of whether you have the right figure or not.
(b) In this case our weight is in N. To get to kg we need to divide out the m/s2 part (acceleration). Well the way that's done is by using acceleration due to gravity which is 9.81m/s2 (recall this is what we needed from the beginning). So we now have:
Now that we have our crate's weight we can simply divide the force applied on it by the weight to get acceleration:
If you have any more questions feel free to post.