Answer:
μk = 0.488
Explanation:
Newton's second law:
∑F = m*a Formula (1)
∑F : algebraic sum of the forces in Newton (N)
m : mass s (kg)
a : acceleration (m/s²)
We define the x-axis in the direction parallel to the movement of the block on the inclined plane and the y-axis in the direction perpendicular to it.
Forces acting on the block
W: Weight of the block : In vertical direction
FN : Normal force : perpendicular to the inclined plane
fk : kinetic Friction force: parallel to the inclined plane
Calculated of the W
W= m*g
W= 4.9 kg* 9.8 m/s² = 48.02 N
x-y weight components
Wx = Wsin θ = 48.02*sin27° = 21.8 N
Wy = Wcos θ = 48.02*cos27° = 42.786 N
Calculated of the FN
We apply the formula (1)
∑Fy = m*ay ay = 0
FN - Wy = 0
FN = Wy
FN = 42.786 N
Calculated of the fk
fk = μk* FN= μk*42.786 Equation (1)
Kinematics of the block
Because the block moves with uniformly accelerated movement we apply the following formula to calculate the acceleration of the block :
d = v₀*t+(1/2)*a*t² Formula (2)
Where:
d:displacement (m)
v₀: initial speed (m/s)
t: time interval (m/s)
a: acceleration ( m/s²)
Data:
d= 2.7 m
v₀ = 0
t= 5.4 s
We replace data in the formula (2)
d = v₀*t+(1/2)*a*t²
2.7 = 0+(1/2)*a*( 5.4)²
2.7 = (14.58)*a
a = 2.7 / (14.58)
a= 0.185 m/s²
We apply the formula (1) to calculated μk:
∑Fx = m*ax , ax= a : acceleration of the block
Wx-fk= m*a , fk=μk*42.786 of the Equation (1)
21.8 - (42.786)*μk = (4.9)*(0.185)
21.8 -0.907= (42.786)*μk
20.89 = (42.786)*μk
μk = (20.89) / (42.786)
μk = 0.488
