Question

a)A heavy sled is being pulled by two people, as shown in the figure. The coefficient of static friction between the sled and the ground is ?s=0.643 , and the kinetic friction coefficient is ?k=0.459 . The combined mass of the sled and its load is ?=306 kg . The ropes are separated by an angle ?=26° , and they make an angle ?=32.7° with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension required to get the sled moving? (Answer: 839.4)

b)If this rope tension is maintained after the sled starts moving, what is the sled's acceleration?

Answer 1

Acceleration,

2*T*cos(Φ/2) * cos(θ) - uk * (m*g - 2*T*cos(Φ/2) * sin(θ)) = m*a

Substituting values in the above eq,

2*839.4*cos(13) * cos(32.7) - 0.459 * (306*9.8 - 2*839.4*cos(13) * sin(32.7)) = 306*a

a = 2.45 m/s^2