Answer:
μ= 0.408 : coefficient of kinetic friction
Explanation:
Kinematic equation for the box:
Formula( 1)
a= acceleration
v_i= initial speed =0
v_f= final speed= 20 m/s
t= time= 5 s
We replace data in the formula (1):
a= - 4m/s²
Box kinetics: We apply Newton's laws in x-y:
∑Fx=ma : second law of Newton
-Ff= ma Equation (1)
Ff is the friction force
Ff=μ*N Equation (2)
μ is the coefficient of kinetic friction
N is the normal force
Normal force calculation
∑Fy=0 : Newton's first law
N-W=0 W is the weight of the box
N=W= m*g : m is the mass of the box and g is the acceleration due to gravity
N=9.8*m
We replace N=9.8m in the equation (2)
Ff=μ*9.8*m
Coefficient of kinetic friction ( μ) calculation
We replace Ff=μ*9.8*m and a= -4m/s² in the equation (1):
-μ*9.8*m: -m*4 : We divide by -m on both sides of the equation
9.8*μ=4
μ=4 ÷ 9.8
μ= 0.408