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 between the sled and the ground is mu s = 0.579, and the kinetic friction coefficient is mu k = 0.403. The combined mass of the sled and its load is m = 306 kg. The ropes are separated by an angle theta = 27 degree , and they make an angle theta = 30.1 degree with the horizontal. Assuming both ropes pull equally hard, what is the minimum rope tension required to get the sled moving? If this rope tension is maintained after the sled starts moving, what is the sled's acceleration?

Explanation / Answer

by applying newton laws

2T cos 30.1+ 2T cos 13.5 -f = 0

2T cos 30.1+ 2T cos 13.5 = µs ( mg - 2T cos30.1)

1.7303 T+ 1.9447 T = (0.579) ( 306 kg x 9.8 m/s2 – 1.7303 T)

4.6613 T = 1736.3 N

T = 372.5 N

b) by applying Newton laws

2T cos 30.1+ 2T cos 13.5 -f = ma

2T cos 30.1+ 2T cos3.54 - µk ( mg - 2T cos 30.1) = ma

2(372.5) cos 30.1+ 2(372.5) cos13.5 -0.403 (306*9.8 – 2(372.5) cos 30.1) = ma

a = 1.373 m/s2

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