To analyze the kinetic energy of the rubber ball before and after it hits the wall, we will use the formula for kinetic energy, which is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( KE \) is the kinetic energy, \( m \) is the mass of the ball, and \( v \) is the velocity of the ball.
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Before the collision:
- Mass, \( m = 1.0 , \text{kg} \)
- Velocity, \( v = 4.0 , \text{m/s} \) (traveling east)
The kinetic energy before the collision is: \[ KE_{\text{before}} = \frac{1}{2} (1.0 , \text{kg}) (4.0 , \text{m/s})^2 = \frac{1}{2} (1.0) (16) = 8.0 , \text{J} \]
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After the collision:
- The ball bounces back with a velocity of \( v = -2.0 , \text{m/s} \) (since it's moving west, we can denote westward velocity as negative).
The kinetic energy after the collision is: \[ KE_{\text{after}} = \frac{1}{2} (1.0 , \text{kg}) (-2.0 , \text{m/s})^2 = \frac{1}{2} (1.0) (4) = 2.0 , \text{J} \]
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Comparison:
- Kinetic energy before the collision: \( 8.0 , \text{J} \)
- Kinetic energy after the collision: \( 2.0 , \text{J} \)
Thus, compared to the kinetic energy of the ball before it hits the wall, the kinetic energy of the ball after it bounces off the wall is significantly reduced. Specifically, it is \( 2.0 , \text{J} \), which is only \( \frac{2.0}{8.0} = \frac{1}{4} \) of the initial kinetic energy.
In summary, the kinetic energy of the ball after it bounces off the wall is less than the kinetic energy before it hits the wall.