Question

A girl is sledding down a slope that is inclined at 30.00 with respect to the horizontal. The wind is aiding the motion by providing a steady force of 105 N that is parallel to the motion of the sled. The combined mass of the girl and the sled is 65.0 kg, and the coefficient of kinetic friction between the snow and the runners of the sled is 0.150. How much time is required for the sled to travel down a 175 m slope, starting from rest?

Answer 1

perpendicular to incline , force equation is given as

F_n = mg Cos30

kinetic frictional force is given as

f_k = u_k F_n

f_k = u_k mg Cos30

F = applied force = 105 N

parallel to incline , force equation is given as

F + mg Sin30 - f_k = ma

105 + (65 x 9.8) Sin30 - (0.15) (65 x 9.8) Cos30 = 65 a

a = 5.24 m/s²

v_o = initial velocity = 0 m/s

X = displacement = 175 m

t = time taken

using the equation

X = v_o t + (0.5) a t²

175 = 0 t + (0.5) (5.24) t²

t = 8.2 sec