Two masses mA and mB are on inclines and are connected together by an inextensib

Question

Two masses mA and mB are on inclines and are connected together by an inextensible cable running over a frictionless pulley as shown below. The coefficient of kinetic friction between each mass and its incline is the same for both masses.

(a) Derive the equation for the acceleration of the two-mass system, in terms of the variables of the problem (i.e., mA, mB, ?A, ?B, ?k, and g.) In applying the 2nd Law to the FBDs of each mass, assume that the positive direction of motion is mA moving up its incline and mB moving down its incline.

(b) Find the magnitude and direction of the acceleration if mA = 2.0 kg, mB = 5.0 kg, ?A = 51 deg, ?B = 21 deg and ?k = 0.03.

Explanation / Answer

assume B down the incline, A up the incline for B: mB*gsinB - T - kmB*gcosB = mB*a for A: T - mA*gsinA - kmA*gcosA = mA*a add 2 equations together, mB*gsinB - mA*gsinA - kg(mBcosB + mAcosA) = (mA + mB)a so a = [mB*sinB - mA*sinA - k(mBcosB + mAcosA)]g/(mA + mB) if mA = 2.0 kg, mB = 5.0 kg, A = 51 deg, B = 21 deg, k = 0.03, a = 0.084 m/s^2 a> 0 means B does go down the incline, A does go up the incline

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