Question

A block of mass m = 1kg moving on horizontal surface with speed u = 2m/s enters a rough horizontal patch ranging from x = 0.10 m to x = 2.00m. If the retarding force f_r on the block in this range is inversely proportional to x over this range i.e.

f_r = $\frac{- k}{x}$ 0.10 < x < 2.00 = 0 for x < 0.10 and x > 2.00

If k = 0.5 J then the speed of this block as it crosses the patch is (use ln 20 = 3)

• A. 2.65 m/s
• B. 1 m/s
• C. 1.5 m./s `
• D. 2 m/s

Answer 1

Answer: (A)

2.65 m/s

Answer 2

As there is no friction, horizontal force on B is therefore F = 100 N

 a = $\frac{100}{20}$ = 5m/s²

but no horizontal force on A acts therefore T = 0