Direction of friction force?Watch
Exercise D, Question 19
The only thing I'm confused by is that in the worked solution they've stated that friction is acting down the slope. The box is on the point of moving down the slope, so what I'm gathering from this is that the friction is acting in the direction of motion (whereas I thought that friction always opposed the direction of movement, so shouldn't it act up the slope to oppose the forces acting down the slope)? Also the diagram is confusing me since I can't identify any forces acting up the slope to prevent it from moving down the slope.
Yes you're right, they're wrong to draw the frictional force down the slope instead of up it. Apart from that, though, they don't actually state in words that the friction is down the slope, as you've claimed. Once you turn that downward force into an upward one, the friction force equation and its solution are correct.