A 3.00kg block starts from rest at a 30.0 degree incline and accelerates uniformly down moving 2.00m in 1.50s.

Question

a. Find the magnitude of the acceleration of the block
b. Find the coefficient of kinetic friciotn between the clock and the incline?
c. FInd the magnitude of the frictional force acting on the block?
d. Find speed of the block after it has slide 2.00m?

Answer 1

a. acceleration, a:

s=ut+1/2at^2

Substitute known values:

2=(0)1.5+1/2a*1.5^2
2=1.125a
a=1.78m/s^2

b. coefficient of friction, u:

F=Ma
F=3*1.78=5.33N

F=component of weight of block along the incline-
force of friction,f

Note that F is the net force acting on the block. Two forces are acting on this block: the component of the weight along the incline downward, and the force of friction f, upward. The difference between the two equals F.

5.33=3*9.8sin30-f
5.33=14.7-f
f=9.37N

f=uN where u is the coefficient of friction and N is the component of the weight of the block normal to the incline.
9.37=u3*9.8cos30
9.37=25.5u
u=0.37

c. frictional force,f:

Already computed above. f=9.37N

d. speed of the block:

v=u+at
v=0+1.78(1.5)
=2.67m/s