A 3.2 kg block with a speed of 11 m/s collides with a 11 kg block that has a speed of 3.3 m/s in the same direction. After the collision, the 3.2 kg block is observed to be traveling in the original direction with a speed of 6.4 m/s. (a) What is the velocity of the 11 kg block immediately after the collision? (b) By how much does the total kinetic energy of the system of two blocks change because of the collision? (c) Suppose, instead, that the 3.2 kg block ends up with a speed of 4.7 m/s. What then is the change in the total kinetic energy?
I got that a. is 4.64Ns, but I'm not sure how to go about the other two parts.
To solve part (b) and (c), we need to first calculate the initial and final kinetic energies of the system of two blocks.
The initial kinetic energy of the system is given by the sum of the kinetic energies of the two blocks before the collision. The kinetic energy of an object is given by the formula KE = (1/2) * mass * velocity^2.
For the 3.2 kg block, its initial kinetic energy is:
KE1 = (1/2) * 3.2 kg * (11 m/s)^2
For the 11 kg block, its initial kinetic energy is:
KE2 = (1/2) * 11 kg * (3.3 m/s)^2
To calculate the final kinetic energy of the system, we need to use the principle of conservation of momentum and the fact that kinetic energy is related to the square of velocity.
The principle of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. Mathematically, it can be written as:
(mass1 * velocity1) + (mass2 * velocity2) = (mass1 * velocity1') + (mass2 * velocity2')
where mass1 and mass2 are the masses of the two blocks, velocity1 and velocity2 are their initial velocities, and velocity1' and velocity2' are their final velocities.
Using this equation, we can solve for velocity2', which is the velocity of the 11 kg block immediately after the collision (part a of the question).
Now, to calculate the final kinetic energy of the system, we can use the formula KE = (1/2) * mass * velocity^2, where mass is the total mass of the two blocks and velocity is the final velocity of the system after the collision.
For part (b), the change in total kinetic energy is given by:
change in KE = final KE - initial KE
For part (c), we need to calculate the initial kinetic energy and final kinetic energy using the new final velocity of the 3.2 kg block (4.7 m/s) and proceed with the same calculations as in part (b).
I hope this explanation helps you understand the steps needed to solve parts (b) and (c) of the question.