<span>The ball with an initial velocity of 2 m/s rebounds at 3.6 m/s
The ball with an initial velocity of 3.6 m/s rebounds at 2 m/s
There are two principles involved here
Conservation of momentum and conservation of energy.
I'll use the following variables
a0, a1 = velocity of ball a (before and after collision)
b0, b1 = velocity of ball b (before and after collision)
m = mass of each ball.
For conservation of momentum, we can create this equation:
m*a0 + m*b0 = m*a1 + m*b1
divide both sides by m and we get:
a0 + b0 = a1 + b1
For conservation of energy, we can create this equation:
0.5m(a0)^2 + 0.5m(b0)^2 = 0.5m(a1)^2 + 0.5m(b1)^2
Once again, divide both sides by 0.5m to simplify
a0^2 + b0^2 = a1^2 + b1^2
Now let's get rid of a0 and b0 by assigned their initial values. a0 will be 2, and b0 will be -3.6 since it's moving in the opposite direction.
a0 + b0 = a1 + b1
2 - 3.6 = a1 + b1
-1.6 = a1 + b1
a1 + b1 = -1.6
a0^2 + b0^2 = a1^2 + b1^2
2^2 + -3.6^2 = a1^2 + b1^2
4 + 12.96 = a1^2 + b1^2
16.96 = a1^2 + b1^2
a1^2 + b1^2 = 16.96
The equation a1^2 + b1^2 = 16.96 describes a circle centered at the origin with a radius of sqrt(16.96). The equation a1 + b1 = -1.6 describes a line with slope -1 that intersects the circle at two points. Those points being (a1,b1) = (-3.6, 2) or (2, -3.6). This is not a surprise given the conservation of energy and momentum. We can't use the solution of (2, -3.6) since those were the initial values and that would imply the 2 billiard balls passing through each other which is physically impossible. So the correct solution is (-3.6, 2) which indicates that the ball going 2 m/s initially rebounds in the opposite direction at 3.6 m/s and the ball originally going 3.6 m/s rebounds in the opposite direction at 2 m/s.</span>
Explanation:
The work done equals the change in energy.
W = ΔKE
W = 0 − ½mv²
W = -½ (0.270 kg) (-7.50 m/s)²
W = -7.59 J
Work is force times displacement.
W = Fd
-7.59 J = F (-0.150 m)
F = 50.6 N
Answer:
Although the wave slows down, its frequency remains the same, due to the fact that its wavelength is shorter. When waves travel from one medium to another the frequency never changes.
1) The correct answer is
<span>C) The particles are not able to move out of their positions relative to one another, but do have small vibrational movements.
In solids, in fact, particles are bound together so they cannot move freely. However, they can move around their fixed position with small vibrational movements, whose intensity depends on the temperature of the substance (the higher the temperature, the more intense the vibrations). For this reason, we say that matter moves also in solid state.
2) The correct answer is
</span><span>A) increase the concentration of both solutions
In fact, when we increase the concentration of both solutions, we increase the number of particles that react in both solutions; as a result, the speed of the reaction will increase.
3) The correct answer is
</span><span>C) gas → liquid → solid
In gases, in fact, particles are basically free to move, so the intermolecular forces of attraction are almost negligible. In liquids, particles are still able to move, however the intermolecular forces of attraction are stronger than in gases. Finally, in solids, particles are bound together, so they are not free to move and the intermolecular forces of attraction are very strong. </span>
Yes it does ! Uh huh. Right you are. Truer words are seldom written.
You have quoted the law quite accurately but also incompletely.
Do you have a question to ask ?
