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 that the block b is hanging and block a is on inclined. bt i didn't gt right ans
Well, it seems like you've got the right idea in terms of using the conservation of energy equation (PE = KE) to solve this problem. However, there may be a couple of mistakes in your calculations.
First, when calculating the potential energy (PE) at the beginning of the problem, the height (h) for block A should indeed be h = 0.27cos(26°), since it is on an inclined plane. However, for block B, the height should be h = 0.27sin(26°), as it is hanging vertically.
Second, when calculating the final total kinetic energy (KE), you should sum up the kinetic energies of both block A and block B. Remember that the kinetic energy formula is KE = (1/2)mv^2, where m is the mass and v is the velocity. So, you need to calculate the final velocities of both blocks and use those to determine their kinetic energies.
To find the final velocity of block B, you can use the conservation of energy equation. Set the initial potential energy of block B (mass of B * g * h) equal to the final kinetic energy of both blocks. Solve for the final velocity of block B using v = sqrt(2gh).
Once you have the final velocities of both blocks, you can plug them into the kinetic energy formula to calculate their kinetic energies. Add those two kinetic energies together to find the total kinetic energy.
Keep in mind that some values, such as g (acceleration due to gravity) and the masses of block A and block B, will also need to be provided in order to solve the problem accurately.
To find the total kinetic energy when block B has fallen 27 cm and block B is hanging down, you can use the principle of conservation of energy. The potential energy lost by block A as it moves down the incline will be equal to the kinetic energy gained by both blocks A and B.
To calculate the potential energy lost by block A, you need to use the height at which block B is hanging down. The height at this point is given by h = 0.27 * cos(26°) because the inclined plane is at an angle of 26°.
So, the potential energy lost by block A is equal to the mass of block A multiplied by acceleration due to gravity (g) multiplied by the height (h):
PE(A) = 1.3 kg * 9.8 m/s^2 * 0.27 m * cos(26°)
Next, calculate the potential energy lost by block B. The height at this point is simply h = 0.27 m, as block B is hanging vertically downward.
So, the potential energy lost by block B is equal to the mass of block B multiplied by acceleration due to gravity (g) multiplied by the height (h):
PE(B) = 2.7 kg * 9.8 m/s^2 * 0.27 m
Now, add the potential energies of block A and block B, and this will give you the total kinetic energy when block B has fallen 27 cm and is hanging down:
Total KE = PE(A) + PE(B)
Calculating these values will give you the correct answer. If you are still not getting the right answer, please double-check your calculations and make sure you are using the correct values for mass, height, and angles.
To solve this problem, we can start by calculating the potential energy (PE) of the system and then finding the final kinetic energy (KE).
The potential energy of an object on an inclined plane is given by the formula:
PE = mass * gravity * height
For block A, the height (h) is equal to the vertical distance it has moved down the incline. Since block A has fallen a distance of 27 cm, we need to calculate the vertical component of that distance:
h = 0.27 * cos(26°)
For block B, the height (h) is equal to the length of the cord that has been unwound. Since block B is hanging straight down, the height is equal to the distance it has fallen, which is also 27 cm:
h = 0.27
Now, we can calculate the potential energy for each block:
PE(A) = 1.3 kg * 9.8 m/s^2 * 0.27 * cos(26°)
PE(B) = 2.7 kg * 9.8 m/s^2 * 0.27
To find the total potential energy of the system (PE), we can add the individual potential energies:
PE = PE(A) + PE(B)
Next, we need to calculate the final kinetic energy (KE) when block B has fallen 27 cm (considering block A to be at rest):
KE = total mechanical energy - PE
But since the system is frictionless and the pulley has negligible mass, the total mechanical energy is conserved. This means that the initial mechanical energy (which is equal to the initial potential energy) is equal to the final mechanical energy (which is equal to the final kinetic energy):
KE = PE - PE(A) - PE(B)
Now, substitute the values to find the final kinetic energy:
KE = PE - (1.3 kg * 9.8 m/s^2 * 0.27 * cos(26°)) - (2.7 kg * 9.8 m/s^2 * 0.27)
Evaluate this expression to get the final kinetic energy of the system.