A girl is pulling her little brother on a sled. The rope of the sled is at a 20

Question

A girl is pulling her little brother on a sled. The rope of the sled is at a 20 degree angle from the ground. The mass of the brother is 30 kg, the mass of the sled is 5 kg, the of the boy is .3; k=.1. Find how many seconds it takes for the brother to get pulled off the sled. A girl is pulling her little brother on a sled. The rope of the sled is at a 20 degree angle from the ground. The mass of the brother is 30 kg, the mass of the sled is 5 kg, the of the boy is .3; k=.1. Find how many seconds it takes for the brother to get pulled off the sled.

Explanation / Answer

The rope of the sled is at a angle = 20o from the ground The mass of the brother is M = 30 kg and the mass of the sled is m = 5 kg The coefficient of friction of the boy is = 0.3 and the coefficient of kinetic friction is k = 0.1 The forces acting on the sled in the x and y directions are Fx = w * sin - f = (M + m) * g * sin - k * n -------------(1) where f is the friction force on the sled and Fy = n + (-w * cos) = 0 or n = w * cos = (M + m) * g * cos ------------(2) From equations (1) and (2),we get Fx = (M + m) * g * sin - k * (M + m) * g * cos = (M + m) * g * (sin - k * cos) or (M + m) * ax = (M + m) * g * (sin - k * cos) or ax = g * (sin - k * cos) where g = 9.8 m/s2 and k = (0.3 + 0.1) = 0.4 Let the time taken for the brother to get pulled off the sled be t We know from the relation S = ut + (1/2)axt2 where S is the distance travelled by the sled and u = 0 or t2 = (2S/ax) or t = (2S/ax)1/2 or t = (2S/g * (sin - k * cos))1/2 or t = (2S/g * (sin - k * cos))1/2

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