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 figure block b is hanging down and block A is on inclined.
The increased (and total) kinetic energy equals the lost potential emergy. If block B has fallen 0.27 m vertically, block A has moved up the incline for an altitude change of 0.27 sin 26 = 0.1184 m
Total P.E. lost = 2.7*9.8*0.27 - 1.3*9.8*0.1184 = 7.14 - 1.51 J = 5.63 J
That equals the total K.E. increase,
(1/2)(MA + MB)*V^2
thank u so much for help Drwls!!!!!!!!!!1
The increased (and total) kinetic energy equals the lost potential emergy. If block B has fallen 0.27 m vertically, block A has moved up the incline for an altitude change of 0.27 sin 26 = 0.1184 m
Total P.E. lost = 2.7*9.8*0.27 - 1.3*9.8*0.1184 = 7.14 - 1.51 J = 5.63 J
That equals the total K.E. increase,
(1/2)(MA + MB)*V^2
jonga am dead
In the figure, the pulley has negligible mass, and both it and the inclined plane are frictionless. Block A has a mass of 1.0 kg, block B has a mass of 2.0 kg, and angle θ is 30°. If the blocks are released from rest with the connecting cord taut, what is their total kinetic energy in Joules when block B has fallen 7 cm? (take g = 10 m/s2).
To determine the total kinetic energy of the system when block B has fallen 27 cm, we need to break down the problem into steps and apply the laws of physics. Let's go through the steps:
Step 1: Find the acceleration of the system.
Since the system is frictionless, we can use the force of gravity to determine the acceleration. The force due to gravity acting on block B is given by the equation:
F_gravity = mass * gravity
Given that the mass of block B is 2.7 kg and gravity is approximately 9.8 m/s^2, we can calculate the force:
F_gravity = 2.7 kg * 9.8 m/s^2 = 26.46 N
Since the system is connected by an inextensible string, the tension in the string is the same on both sides. Therefore, the force acting on block A is also 26.46 N.
Next, we can break down the force acting on block A into its components. The force can be divided into two perpendicular directions: one parallel to the inclined plane and one perpendicular to it. The force parallel to the inclined plane will cause the block to move down the slope, while the force perpendicular to it will cause normal force against the inclined plane.
Considering the angle è to be 26°, we can find the force parallel to the inclined plane:
F_parallel = F_gravity * sin(è)
F_parallel = 26.46 N * sin(26°) = 11.33 N
Step 2: Determine the acceleration of block A.
The force parallel to the inclined plane causes acceleration along the slope. We can use the formula:
acceleration = force parallel / mass of block A
acceleration = 11.33 N / 1.3 kg = 8.715 m/s^2
Step 3: Calculate the distance traveled by block B.
Given that block B has fallen 27 cm (0.27 m), we can use the equation:
distance = 0.5 * acceleration * time^2
Since the initial velocity is zero, and we're looking for the distance traveled by block B, the equation simplifies to:
distance = 0.5 * acceleration * time^2
Step 4: Find the time taken by block B.
Since we know the distance and acceleration, we can rearrange the above equation to solve for time:
time = sqrt(2 * distance / acceleration)
time = sqrt(2 * 0.27 m / 8.715 m/s^2)
time = 0.2836 s
Step 5: Calculate the final velocity of block B.
Using the equation:
Final velocity = initial velocity + acceleration * time
Since the initial velocity is zero, the equation simplifies to:
Final velocity = acceleration * time
Final velocity = 8.715 m/s^2 * 0.2836 s
Final velocity = 2.472 m/s
Step 6: Calculate the total kinetic energy.
The total kinetic energy is the sum of the kinetic energies of both blocks. The kinetic energy of each block can be calculated using the formula:
kinetic energy = 0.5 * mass * velocity^2
For block A:
kinetic energy of block A = 0.5 * 1.3 kg * (acceleration * time)^2
For block B:
kinetic energy of block B = 0.5 * 2.7 kg * (Final velocity)^2
Finally, the total kinetic energy is:
total kinetic energy = kinetic energy of block A + kinetic energy of block B
Now you can substitute the values obtained from the previous steps and calculate the total kinetic energy of the system when block B has fallen 27 cm.