A number of children are playing with two sleds on a smooth, level, snow covered

Question

A number of children are playing with two sleds on a smooth, level, snow covered playground. After some thought and experimentation, they decide that the configuration shown below will give them the fastest ride if the two strongest children (Betty and Carl) pull the sleds. Carl pulls with a force of FC = 235 N at an angle of 20.0° with respect to the forward motion, and Betty pulls with a force of FB = 200 N at an angle of ?B = 23.70°, also with respect to the forward motion. David sits backwards on the trailing sled and drags his feet. The sled combination moves forward with a constant velocity across the snow for a distance of 20.0 m, as shown in the diagram below. Determine the following.

(a) the amount of work done on the leading sled by Betty = ?? kJ

(b) the amount of work done on the leading sled by Carl= ?? kJ

(c) the work done by the tension in the connecting rope on the leading sled = ?? kJ

(d) the work done by the tension in the connecting rope on the trailing sled= ??kJ

Explanation / Answer

x component of Fc = Fc*cos20 = 235*cos20 = 221 N

y component of Fc = Fc*sin20 = 235*sin20 = 80.4 N

x component of FB = FB*cos23.7 = 200*cos23.7 = 183.1 N

y component of FB = FB*sin23.7 = 200*sin23.7 = 80.4 N

here the speed is constant so acceleration of the system = 0

net force along hoizantal = Fcx + FBx - TR + TR - FD

Fnet = 221 + 183.1 - FD

from newtons law Fnet = m*a = 0

therefore

404.1 - FD = 0

Fd = 404.1

for the leading sled

Fcx + FBx - TR = 0

TR = 404.1 N

-----

(a)

WB = FBx*x = 221*20 = 4.42 kJ

(b)

WC = FCx*x = 183.1*20 = 3.66 kJ

(c)

W = -TR*x = -404.1*20 = -8.082 kJ

(d)

W = +TR*x= 404.1*20 = 8.082 kJ

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