In the Figure the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.3 kg, block B has a mass of 2.7 kg, and angle è is 26 °. If the blocks are released from rest with the connecting cord taut, what is their total kinetic energy when block B has fallen 27 cm and in ths block b is hanging down? i jus wanted to ask that difference PE=final KE means
mass of a*g*h-mass of b*g*hsin26=totalKE. is this right? bcause i m nt getting right answer. for a height should be h= 0.27cos26 and for b height=0.27? figure is wat u assumed that block b is hanging. bt i didn't gt right ans
To solve this problem, you can use the principle of conservation of mechanical energy. The difference in potential energy (PE) between the initial and final positions should be equal to the difference in kinetic energy (KE) between these positions.
In this case, the potential energy is given by the formula PE = m * g * h, where m is the mass, g is the acceleration due to gravity, and h is the height.
For block A, the initial position has a potential energy of m_A * g * h_A, where m_A is the mass of block A and h_A is the initial height.
For block B, the initial position has a potential energy of m_B * g * h_B, where m_B is the mass of block B and h_B is the initial height.
The final position for both blocks is when block B has fallen 27 cm and block B is hanging down. In this position, block B has a potential energy of m_B * g * h_f, where h_f is the final height of block B.
According to the conservation of mechanical energy, the total difference in potential energy is equal to the total difference in kinetic energy. Therefore, the equation becomes:
(m_A * g * h_A) - (m_A * g * h_f) + (m_B * g * h_B) - (m_B * g * h_f) = total KE.
Simplifying this equation, we have:
m_A * g * (h_A - h_f) + m_B * g * (h_B - h_f) = total KE.
Substituting the values given in the problem, you can calculate the total kinetic energy. Make sure you convert centimeters to meters before substituting the values.
It is important to note that in the equation above, the correct heights should be used for block A and block B at the initial and final positions. If you are not getting the right answer, make sure you are using the correct values for h_A, h_B, and h_f, and double-check your calculations.