If there is no friction under either box, see figure 4.21, determine the acceler

Question

If there is no friction under either box, see figure 4.21, determine the acceleration of both blocks. Assume masses and P are known. Figure 4.21:

Explanation / Answer

change in length of cord between mA n mB is 0 so : xA be distance travelled by mA xB be distance travelled by mB -4xA + 3xB = 0 => double differentiating with time -4aA + 3aB = 0 => aA = 3aB/4 -equation 1 force on mA : 4T ( T is tension in cord) towards right force on mB : P - 3T towards right 4T = mA*aA - equation 2 P-3T = mB*aB - equation 3 solving for aB T = mA*aA/4 from 2 T = mA*3*aB/16 from 1 p - 9mA*aB/16 = mB*aB aB(16mB+9mA)/16 = P => aB = 16P/(16mB+9mA) => aA = 12P/(16mB+9mA)

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