Question

A father pulls his child on a sled by pulling on a rope over his shoulder as shown. Using the coefficient of friction for steel on ice from table 1, calculate the acceleration of the sled if its mass plus the child is 22 kg, assuming the sled is already in motion.

Table 1 Approximate Coefficients of Friction of Some Common Materials Materials rubber on concrete (dry) rubber on asphalt (dry) steel on steel (dry) steel on steel (greasy) leather on rock (dry) ice on ice steel on ice rubber on ice wood on dry snow wood on wet snow TeflonR on Teflon near-frictionless carbon, NFC (in air) synovial joints in humans 1.0 1.0 0.40 0.05 0.8 0.03 0.01 0.005 0.18 0.10 0.04 0.02 to 0.06 0.003 1.1 1.1 0.60 0.12 1.0 0.1 0.1 0.22 0.14 0.04 0.01

Answer 1

Sigma F_y = 0 N = mg = 45 sin 35 degree n = 22 times 9.8 - 45 sin 35 degree N = 189.789 N Sigma F_x = ma 45 cos 35 degree - mu_k N = 22 a acceleration a = 45 cos 35 degree - 0.01 times 189.789/22 a = 1.589 m/s^2 almostequalto 1.6 m/s^2