Please show work, Thanks! A 3.00 kg block starts from rest at the top of a 30° i

Question

Please show work, Thanks!

A 3.00 kg block starts from rest at the top of a 30° incline and slides a distance of 1.80 m down the incline in 1.70 s.

(a) Find the magnitude of the acceleration of the block.


(b) What is the coefficient of kinetic friction between block and plane?


(c) What is the frictional force acting on the block?
Magnitude
Direction

up the inclinedown the incline    normal to the incline and upwardnormal to the incline and downward

(d) Find the speed of the block after it has slid 1.80 m.

Explanation / Answer

given,

mass = 3 kg

angle = 30 degree

distance = 1.8 m

time = 1.7 sec

s = ut + 0.5 * at^2

1.8 = 0 + 0.5 * a * 1.7^2

a = 1.245 m/s^2

acceleration of the block = 1.245 m/s^2

force equation of block

mg * sin(30) - k * mg * cos(30) = ma

g * sin(30) - k * g * cos(30) = a

9.8 * sin(30) - k * 9.8 * cos(30) = 1.245

k = 0.430656

frictional force = 0.430656 * 9.8 * cos(30)

frictional force = 3.655 N at up the incline

v = u + at

v = 0 + 1.245 * 1.7

speed of the block after it has slid 1.80 m = 2.1165 m/s

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