Answer:
a = 4.05 m/s²
Explanation:
Known data
m= 92 kg : mass of the skier
θ =30° :angle θ of the ski slope with respect to the horizontal direction
μk= 0.10 : coefficient of kinetic friction
g = 9.8 m/s² : acceleration due to gravity
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 ramp and the y-axis in the direction perpendicular to it.
Forces acting on the skier
W: Weight of the skier : In vertical direction
N : Normal force : perpendicular to the ski slope
f : Friction force: parallel to the ski slope
Calculated of the W
W= m*g
W= 92kg* 9.8 m/s² = 901,6 N
x-y weight components
Wx= Wsin θ= 901,6 N *sin 30° = 450.8 N
Wy= Wcos θ = 901,6 N *cos 30° =780.8 N
Calculated of the N
We apply the formula (1)
∑Fy = m*ay ay = 0
N - Wy = 0
N = Wy
N = 780.8 N
Calculated of the f
f = μk* N= 0.10*780.8 N
f = 78.08 N
We apply the formula (1) to calculated acceleration of the skier:
∑Fx = m*ax , ax= a : acceleration of the block
Wx - f = m*a
450.8- 78.08 = ( 92)*a
372.72 = (92)*a
a = (372.72)/ (92)
a = 4.05 m/s²
