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?
I have difficulty telling which is which, I assume block b is hanging straight down, and block a is on the incline.
difference PE=final KE
massa*g*h-massb*g*hsin26=totalKE
you know h (.27m) and g, solve for total KE.
To find the total kinetic energy of the blocks when block B has fallen 27 cm, we need to calculate the velocities of both blocks at that point and then compute their respective kinetic energies.
To start, we can use the principle of conservation of mechanical energy, which states that the sum of potential energy and kinetic energy remains constant in the absence of non-conservative forces like friction.
1. Calculate the potential energy of block B at the initial height:
Potential energy (PE) = mass x gravity x height
PE = 2.7 kg x 9.8 m/s^2 x (27 cm / 100 cm/m)
PE = 2.7 kg x 9.8 m/s^2 x 0.27 m
PE = 7.4482 J
2. According to the conservation of mechanical energy, the potential energy lost by block B will be entirely converted to kinetic energy when it reaches the lower point. Therefore, the kinetic energy of block B at that point will be equal to its initial potential energy, which is 7.4482 J.
3. Next, we can determine the velocity of block B. We can use the equation of motion for an object moving down an inclined plane without friction:
Velocity (v) = √(2gh)
where g is the acceleration due to gravity and h is the vertical distance fallen.
v = √(2 x 9.8 m/s^2 x 0.27 m)
v = √(5.3646 m^2/s^2)
v = 2.3130 m/s
4. Now, we need to find the velocity of block A. Since block A is connected to block B by a taut cord passing over a pulley, the velocities of both blocks will be the same.
Consequently, the velocity of block A will also be 2.3130 m/s.
5. Finally, we can calculate the total kinetic energy of the two blocks. The kinetic energy of an object is given by the formula:
Kinetic energy (KE) = 0.5 x mass x velocity^2
For block A:
KE_A = 0.5 x 1.3 kg x (2.3130 m/s)^2
KE_A = 1.7465 J
For block B:
KE_B = 0.5 x 2.7 kg x (2.3130 m/s)^2
KE_B = 6.7599 J
Total kinetic energy = KE_A + KE_B
Total kinetic energy = 1.7465 J + 6.7599 J
Total kinetic energy = 8.5064 J
Therefore, when block B has fallen 27 cm, the total kinetic energy of the blocks is approximately 8.5064 Joules.