Answer:
μk = 0.124
Explanation:
Known data
m=5.0 kg : mass of the sled
T= 10 N : force with which the boy pulls the rope
θ =60.0° :angle of the rope with respect to the horizontal direction
g = 9.8 m/s² : acceleration due to gravity
Newton's second law to the sled :
∑F = m*a Formula (1)
∑F : algebraic sum of the forces in Newton (N)
m : mass s (kg)
a : acceleration (m/s²)
Forces acting on the sled
W: Weight of the sled : In vertical and downward direction
N : Normal force : In vertical and upwards direction
f : Friction force: parallel to the movement of the sled and in the opposite direction to the movement
T:Rope tension : forming angle 60.0° of of the rope with respect to the horizontal direction
Calculated of the W of the sled
W= m*g
W= 5.0 kg* 9.8 m/s² = 49 N
x-y components of the tension of the rope T
Tx= 10*cos60°= 5 N
Ty= 10*sin60° = 8.66 N
Calculated of the N
We apply the formula (1)
∑Fy = m*ay ay = 0
N+Ty -W = 0
N = 49 N - 8.66 N
N = 40.34 N
Calculated of the f
f = μk* N
f = μk* 40.34 Equation (1)
We apply the formula (1) to calculated f
∑Fx = m*ax the sled moves with constant velocity, then ax=0
∑Fx = 0
Tx-f = 0
5 - f = 0
f = 5N
We replace f in the equation (1)
5 = μk* 40.34
μk = 5 / 40.34
μk = 0.124
