physics help?

Question

A 2.86 kg block starts from rest at the top of a 30° incline and accelerates uniformly down the incline, moving 1.85 m in 1.70 s.

(a) Find the magnitude of the acceleration of the block.
m/s2
(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.
N
(d) Find the speed of the block after it has slid a distance 1.85 m.
m/s

Answer 1

Start by considering a FBD of the block of forces parallel to the incline in the direction of motion

gravity
m*g*sin(30)
friction
-m*g*cos(30)*µk

this is equal to m*a

g*(sin(30)-cos(30)*µk)=a

two unknowns: µk and a

the equations of motion of the block in the reference frame of the incline are
s(t)=.5*a*t^2
v(t)=a*t

a)
s(1.70)=1.85=.5*a*1.70^2
solve for a
a=1.28 m/s^2

b) the a from above can be plugged into
g*(sin(30)-cos(30)*µk)=a
solve for µk
µk=0.427

c) The magnitude of friction is
m*g*cos(30)*µk
10.4 N

d) using
v(t)=a*t
v(1.7)=1.28*1.7
2.18 m/s

j

Answer 2

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