posted by justin .
A 3.00 kg block starts from rest at the top of a 30° incline and accelerates uniformly down the incline, moving 1.94 m in 1.70 s.
(a) Find the magnitude of the acceleration of the block.
(b) Find the coefficient of kinetic friction between the block and the incline.
(c) Find the magnitude of the frictional force acting on the block.
(d) Find the speed of the block after it has slid a distance 1.94 m.
(a) Solve X = (1/2)a t^2 to get the acceleration, a = 1.34 m/s^2
(b) If there were no friction, the acceleration would be g sin30 = 4.9 m/s^2. There must be an opposing friction force
Ff = M(4.9 - 1.34)= 10.7 N
(That answers part (c))
The coefficient of kinetic friction is
muk = Ff/M*g*cos30 = 0.364
(d) The final speed of the block (after moving 1.94 m) is twice the average speed. The average speed is
1.94/1.70 = 1.14 m/s