Body A weighs 104 N, and body B weighs 32 N. The coefficients of friction betwee
ID: 1916780 • Letter: B
Question
Body A weighs 104 N, and body B weighs 32 N. The coefficients of friction between A and the incline are ?s = 0.56 and ?k = 0.25. Angle ? is 40
Explanation / Answer
m1a = w1sin? - T + µ(s)n-----> (1) n is the normal force which acts perpendicular to the incline. It can be found from the net forces on A, perpendicular to the incline: m2a = 0 = n - w1cos? n = w1cos?-----> (2) Here, w1cos? is the component of gravity perpendicular to the incline. Substituting (2) into (1): m1a = w1sin? - T + µ(s)w1cos?-----> (3) Now, the net forces on B (which are only vertical) are tension(T, and has the same value as T in the equations above, but opposite in direction, therefore it is positive) and weight (w2). The equation for B is: m2a = T - w2 ------> (4) Adding (3) and (4) together eliminates T, you can then solve for acceleration: m1a + m2a = [w1sin? - T + µ(s)w1cos?] + (T - w2 ) (m1+ m2)a = w1sin? - w2 + µ(s)w1cos? a = [ w1sin? - w2 + µ(s)w1cos?] / (m1+ m2)-----> (5) The mass of A (m1) can be found from: w1= m1g a = [104Nsin26° - 39N + 0.58(100N)cos26°] / (10.6kg +3.27kg)