Uday M. answered • 09/27/19
M.S. Engineering, 5+ years of teaching experience
The best way to approach this is to first draw a picture. This is a problem about forces, so in this case you'll draw a free body diagram. You have a slope at 30 degrees, and a sled that weighs 3kg at some point on the slope.
Before we consider the forces, just to make the math easier, it's wise to change our coordinate system. Instead of the conventional horizontal x-axis and vertical y-axis, we can choose our "x" axis to be along the incline of the slope and the "y" axis to be perpendicular to that (normal to the slope). The reason we have chosen this is because we are trying to find the acceleration of the sled, and that acceleration would be in the direction of the incline of the slope (our new "x" axis). Remember that the new coordinate system we choose must be perpendicular so that we can take advantage of the fact that motion in a direction does not affect motion in the perpendicular direction.
Now let's account for our forces. The slope is ice, meaning that there is no friction. We have gravity (G) which goes straight down, so we have to convert it into our new coordinate system (you can use trig for that if you draw out the angles and vectors). Gravity will be split into Gx and Gy. We also have the normal force which acts in the new y-direction, but we don't care about that for the purposes of this problem.
All we care about is Gx, because that's effectively what is 'pushing' the sled. So if you were to write a sum of the forces equation (Newton's 2nd Law) in the new x-direction, it would be
Gx = m*a
I'll let you figure out the trigonometry of how you get to Gx. From there it's just plugging in values and doing algebra.
