Question

A smooth block is released at rest on a 45⁰ incline and then slides a distance d. The time taken to slide is n times a much to slide on a rough incline plane than on a smooth incline. The coefficient of friction is

• A. μ_k = 1 - $\frac { 1 } { \mathrm { n } ^ { 2 } }$
• B. μ_k = $\sqrt { 1 - \frac { 1 } { \mathrm { n } ^ { 2 } } }$
• C. μ_s = 1 - $\frac { 1 } { \mathrm { n } ^ { 2 } }$
• D. μ_s = $\sqrt { 1 - \frac { 1 } { \mathrm { n } ^ { 2 } } }$

Answer 1

Answer: (A)

μ_k = 1 - $\frac { 1 } { \mathrm { n } ^ { 2 } }$

Answer 2

case (i) Without friction d = g/2 sin 45 t² ….. (i)

case (ii) With friction d = g/2 [sin 45 - μ_k cos 45] t²n² …. (ii)

From (i) and (ii) μ_k = 1 - $\frac { 1 } { \mathrm { n } ^ { 2 } }$ .