Consider helping a friend move. They have a box with a mass of 100 kg that you are pushing along the ground by applying a force directed 30 degrees below the horizontal, as shown in the figure below:
30°
There is friction force of 50 N acting between the box and floor. You ramp up the force linearly, from 100 N to 225 N, over the first metre of motion, and then maintain a steady force of 250 N, so that
$F_{Applied}(x) = \begin{cases} 125 \frac{x}{1m} N + 100 \text{ N} & 0 \text{ m} < x < 1 \text{ m} \\ 225 \text{ N} & x \ge 1 \text{ m} \end{cases}$
a) Calculate the magnitude of the work done by you as you push the box 3 m. (5 marks)
b) Calculate the magnitude of the work done by friction as you push the box 3 m. (2 marks)
c) How fast is the box moving after it has been pushed 3 m (assuming it started from rest)? (3 marks)