Practice 5: Work & Kinetic Energy Problem 1. A box of mass m=1 kg is sliding with a constant speed of 4.5 m/s on a frictionless horizontal surface when, at point P, it encounters a rough section. The coefficient of kinetic friction there is 0.1 at P. How far this box slides before stopping. Vi m Hint: To apply the work-energy theorem, we need to know the change in kinetic energy. What is AE in this problem? Problem 2. Similar to Problem 1, but now the coefficient of kinetic friction in the rough section is not constant; it starts at 0.1 at P and increases linearly with distance past P, reaching a value of 0.6 at 12.5 m past point P. How far this box slides before stopping. Vi m P Hk (2C) Conceptual analysis: We want to calculate the work done by friction and apply work-energy theorem. Since the friction is not constant, we have to use the general expression to calculate the work. W = F . di 1. Use the problem statement to write an expression for uk. Which expression is correct? Here A represents a number. A) HK (x)= 0.6 + Ax B) MK (x) = 4.5 + Ax C) HK (x) = 0.1 + Ax 2. What is the value of A. Hint: use initial conditions to find the value. A) A = 0.04 m-! B) A = 25 m-! C) A = 0.048 m-! D) A = 1.25 m-PHYS1230: General Physics, Problems 3. Now calculate the work done by the friction force Wext = AE to find the distance d that the box travels in the rough surface before stopping. Hint: Use fr = MK mg along with the correct expression for Mk