A contestant in a winter games event pushes a 37.0 kg block of ice across a froz

Question

A contestant in a winter games event pushes a 37.0 kg block of ice across a frozen lake with a rope over his shoulder as shown in Figure 4.29(b). The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03.

(a) Calculate the minimum force F he must exert to get the block moving.
_______ N (41.9 is incorrect acording to web assign)
(b) What is its acceleration once it starts to move, if that force is maintained?
________ m/s2

(.411 is incorrect according to web assign)

Explanation / Answer

a) normal force on the block N = mg - Fsin(25 degree) = (37*9.8) - (F*0.422)

friction force f = Us*N

to get the block moving

Fcos(25 degree) = Us*N

=> F*0.906 = 0.1*[37*9.8 - F*0.422] = 36.26 - F*0.0422

=> F = 36.26/0.948 = 38.248 N

b) F - Uk*N = M*a

=> a = [38.248 - 0.03*(37*9.8 - 38.248*0.422)]/M = 27.858/37 = 0.752 m/s^2

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