GATE 2023 MN – Question 49
A dozer pushes a 100 kg cable spool at constant speed up a 20° incline. The road contact A has kinetic friction coefficient 0.15; bucket contact B has static coefficient 0.45. For the source’s sliding-contact force model, find the maximum bucket normal force in N, to one decimal. The spool radius is 400 mm as shown.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 495 to 510
Explanation
Resolve along and normal to the road. Maximum push in the source’s limiting sliding-force model occurs with bucket friction into the road, Fᵦ=0.45Nᵦ. Then Nₐ=mg cos20°+0.45Nᵦ and Nᵦ=mg sin20°+0.15Nₐ. Combining yields Nᵦ=981(sin20°+0.15cos20°)/(1−0.15×0.45)=508.0939 N, or 508.1 N. This limiting contact-force model is the one consistent with the official range; a separate no-rotation torque constraint is not specified.