43. A 3.00-kg block starts from rest at the top of a 30.0° incline and slides a distance of 2.00 m down the incline in 1.50 s. Find (a) the magnitude of the acceleration of the block, (b) the coefficient of kinetic friction between block and plane, (c) the friction force acting on the block, and (d) the speed of the block after it has slid 2.00 m.
Hint
`d=1/2at^2, F=ma, v=at, f=\mun`
Answer
(a) 1.78 `m//s^2` (b) 0.368 (c) 9.37 N (d) 2.67 m/s
Show Steps
`m = 3.00 `kg `θ = 30.0° ` `t = 1.50 ` s `d=2.00` m (a) `d=1/2at^2` `a =(2d)/t^s = (2\times2.00)/1.50^2 = 1.78 s` (b) `f_k =\mu_kn` `\mu_k =f_k/n` where `f_k = mgsin(30^circ) - ma` and `n=mgcos(30^\circ)` `\mu_k = (mgsin(30^circ) -ma)/(mgcos(30^\circ)) = (gsin(30^circ) -a)/(gcos(30^\circ)) = (9.8sin(30^\circ) - 1.78)/(9.8cos(30^\circ))=0.368 ` (c) `f_k = mgsin(30^circ) - ma` `f_k = (mgsin(30^circ) -ma) = (3.00\times9.8sin(30^\circ) - 3.00\times1.78)=9.37 `N (d) `v=at = 1.78 \times 1.50 = 2.67 m//s`