A heavy sled is being pulled by two people as shown in the figure. The coefficie

Question

A heavy sled is being pulled by two people as shown in the figure. The coefficient of static friction betweern the sled and the ground is = 0.595, and the kinetic friction coefficient is = 0.411. The combined mass of the sled and its load is m= 351 kg. The ropes are separated by an angle = 28", and they make an angle -30.8" with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension required to get the sled moving? ' Number If this rope tension is maintained after the sled starts moving, what is the sled's acceleration? Number m/ s

Explanation / Answer

Tension at theta above the horizontal,

F = 2 T cos(28/2 ) = 1.94 T

in vertical,

N + F sin30.8 - (351 x 9.8) = 0

N = 3439.8 - 0.994 T

f_max = us N = 2046.7 - 0.591 T

along the horizontal,

F cos20.8 - f_max = 0

1.666 T - 2046.7 + 0.591 T = 0

T = 907 N .......Ans

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now kinetic friction will act.

fk = uk N = 0.411 ( 3439.8 - 0.994x907) = 1043.2 N

1.66 x 907 - 1043.2 = 351 a

a = 1.33 m/s^2 ........Ans

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