Diane pulls a sled at constant speed of 2.0 mph along a snowy path on level grou

Question

Diane pulls a sled at constant speed of 2.0 mph along a snowy path on level ground. Diane's little brother Jasper is riding on the sled. The total mass of Jasper and the sled is 27.2 kg. The force of friction on the sled is determined by k=0.1, and the cord makes a 20.4o angle with the ground. Diane is wearing a bracelet which is capable of calculating the amount of work done by its wearer in term of the number of kilocalories (1 cal = 4.186 J, so 1 kcal =4186 J). The bracelet shows that Diane has done a work of 0.6 kcal pulling her brother in the sled. How far along the path did Diane pull her brother?

Explanation / Answer

Let T be the tension in the rope. Normal force will be then,

N = mg - T sin(theta)

frictional force is given by:

Ff = T cos(theta)

also, Ff = uk N = uk (mg - T sin(theta))

equating two values of Ff

T cos(theta) = uk (mg 0- T sin(theta))

solving for T we get

T = uk mg/ [cos(theta) + sin(theta)]

Ff = T cos(theta) = uk mg cos(theta)/[cos(theta) + sin(theta)]

Work done is given by,

W = F x d = Ff d

d = W/Ff

d = W[cos(theta) + sin(theta)]/uk mg cos(theta)

W = 0.6 kcal = 2510 J

d = 2510 [cos20.4 + sin20.4]/0.1 x 27.2 x 9.8 x cos20.4 = 129.18 m

Hence, d = 129.18 m

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