Please show work, Thanks! A 3.00 kg block starts from rest at the top of a 30° i
ID: 1364717 • Letter: P
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