A 5.0 kg block with a speed of 2.9 m/s collides with a 10 kg block that has a speed of 2.1 m/s in the same direction. After the collision, the 10 kg block is observed to be traveling in the original direction with a speed of 2.6 m/s.
Suppose, instead, that the 10 kg block ends up with a speed of 4.0 m/s. What then is the change in the total kinetic energy?
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I used m1v1 + m2v2 = m1v1f + m2v2f
to find v1, which I found to be -.9
Then I used 1/2mv^2 in place of each m1v1 term and found the change in KE to be (80-2.025 = 77.975) = (21.025+24.2 = 45.225), or 32.75J, which is incorrect.
huh?
.5*5 *2.9^2+.5*10*2.1^2 = 43.1 Joules
.5*5 *0.9^2 + .5*10* 4^2 = 81.1
81.1-43.1 = 38 Joules more
Something exploded :)
It seems 38J is incorrect too. Thanks though :)
Pay attention to PrfDamon's note: something exploded, which means, energy was added to the system during the collision.
In other words unless there was energy input from a explosion on impact or something, no way the big block took off at 4.0 m/s
To find the change in total kinetic energy, let's first calculate the initial and final kinetic energy of each block separately and then determine the difference.
1. Calculate the initial and final kinetic energy of the 5.0 kg block:
Initial kinetic energy of the 5.0 kg block:
KE1i = 1/2 * m1 * v1^2
KE1i = 1/2 * 5.0 kg * (2.9 m/s)^2
KE1i = 23.725 J
Final kinetic energy of the 5.0 kg block:
KE1f = 1/2 * m1 * (v1f)^2
We are given that the 5.0 kg block ends up at rest (v1f = 0 m/s), so the final kinetic energy is zero.
KE1f = 0 J
2. Calculate the initial and final kinetic energy of the 10 kg block:
Initial kinetic energy of the 10 kg block:
KE2i = 1/2 * m2 * v2^2
KE2i = 1/2 * 10 kg * (2.1 m/s)^2
KE2i = 22.05 J
Final kinetic energy of the 10 kg block:
KE2f = 1/2 * m2 * (v2f)^2
We are given that the final speed of the 10 kg block is 4.0 m/s.
KE2f = 1/2 * 10 kg * (4.0 m/s)^2
KE2f = 80.0 J
3. Calculate the change in the total kinetic energy:
Change in total kinetic energy = (KE1f + KE2f) - (KE1i + KE2i)
Change in total kinetic energy = (0 J + 80.0 J) - (23.725 J + 22.05 J)
Change in total kinetic energy = 77.975 J - 45.775 J
Change in total kinetic energy = 32.2 J
Thus, the change in the total kinetic energy is 32.2 Joules.