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 find the total kinetic energy of the blocks when block B has fallen 27 cm (or 0.27 m), you can use the principle of conservation of mechanical energy. According to this principle, the total mechanical energy (the sum of potential energy and kinetic energy) of a system remains constant if no external forces act on it.
In this case, the potential energy of block A is given by m_A * g * h_A, and the potential energy of block B is given by m_B * g * h_B, where m_A and m_B are the masses of blocks A and B, g is the acceleration due to gravity, h_A is the height of block A, and h_B is the height of block B.
Since the inclined plane is frictionless, the total mechanical energy of the system will be conserved. At the initial position, both blocks are at rest, so their total mechanical energy is equal to the potential energy.
When block B has fallen 27 cm, block A will also move and its height will decrease. Let's say the height of block A is h_A' and the height of block B is h_B'.
Now, the potential energy for block A is m_A * g * h_A' and for block B it is m_B * g * h_B'. The total kinetic energy of the system at this position is the difference between the initial potential energy and the final potential energy:
Total KE = (m_A * g * h_A + m_B * g * h_B) - (m_A * g * h_A' + m_B * g * h_B')
Substituting the values given in the question, we have:
Total KE = (1.3 kg * 9.8 m/s^2 * h_A + 2.7 kg * 9.8 m/s^2 * h_B) - (1.3 kg * 9.8 m/s^2 * h_A' + 2.7 kg * 9.8 m/s^2 * h_B')
Since block B has fallen 27 cm, the new height h_B' is calculated by subtracting 0.27 m from the initial height h_B. However, the height h_A' needs to be calculated separately because block A also moves. To find the new height h_A', you need to use trigonometry.
The new height h_A' can be calculated using the equation h_A' = h_A - (0.27 m * cos(26°)). Here, h_A is the initial height of block A.
Once you have calculated the new heights h_A' and h_B', you can substitute them into the Total KE equation and solve for the total kinetic energy.
Please note that the accuracy of the answer depends on the accuracy of the given measurements and any assumptions made about the system.
To calculate the total kinetic energy of the blocks when block B has fallen 27 cm, we need to consider the change in potential energy of each block.
In this case, block A moves along the inclined plane, while block B moves vertically downward. The potential energy of each block can be calculated using the formula:
Potential Energy (PE) = mass * gravity * height
1. Calculate the change in potential energy for block A:
PE_A = mass_A * gravity * height_A
Since block A moves along the inclined plane, the height_A can be calculated using the vertical distance traveled by block A, which is the same as the vertical distance traveled by B, multiplied by the sine of the angle è:
height_A = 27 cm * sin(26°)
2. Calculate the change in potential energy for block B:
PE_B = mass_B * gravity * height_B
Since block B moves vertically downward, the height_B can simply be taken as the vertical distance traveled, which is 27 cm.
3. Calculate the total kinetic energy when block B has fallen 27 cm:
Total KE = PE_A + PE_B
Substitute the values into the formulas and calculate the result.
Please note that in the formula you mentioned (mass_A * gravity * h - mass_B * gravity * h * sin(26°)), you forgot to multiply the height of block A by cos(26°). This is because the vertical distance traveled by block A is h * cos(26°). Additionally, the potential energy needs to be subtracted from the initial value, not added to it.