To calculate the change in momentum of the body when it collides with the wall, we will first find the initial and final momentum.
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Initial momentum (\( p_i \)): \[ p_i = m \cdot v_i \] Where:
- \( m = 100 , \text{g} = 0.1 , \text{kg} \) (converting grams to kilograms)
- \( v_i = 10 , \text{m/s} \) (initial velocity)
\[ p_i = 0.1 , \text{kg} \cdot 10 , \text{m/s} = 1 , \text{kg m/s} \]
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Final momentum (\( p_f \)): After colliding with the wall, the body moves in the opposite direction. Therefore, its final velocity will be: \[ v_f = -10 , \text{m/s} \]
Calculating the final momentum: \[ p_f = m \cdot v_f = 0.1 , \text{kg} \cdot (-10 , \text{m/s}) = -1 , \text{kg m/s} \]
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Change in momentum (\( \Delta p \)): \[ \Delta p = p_f - p_i \] \[ \Delta p = -1 , \text{kg m/s} - 1 , \text{kg m/s} = -2 , \text{kg m/s} \]
Thus, the change in momentum is: \[ \Delta p = -2 , \text{kg m/s} \]
The negative sign indicates that the momentum has changed direction. The magnitude of the change in momentum is \( 2 , \text{kg m/s} \).