A sphere with a mass of 2 kg moves in a straight line on a smooth and flat surface at a speed of 5 ms-1. It strikes a vertical surface and bounces back in the opposite direction at... A sphere with a mass of 2 kg moves in a straight line on a smooth and flat surface at a speed of 5 ms-1. It strikes a vertical surface and bounces back in the opposite direction at a speed of 3 ms-1. Calculate the change in momentum of the sphere (due to the collision).
Understand the Problem
The question asks to calculate the change in momentum of a sphere after it collides with a vertical surface and bounces back. We need to consider the mass of the sphere, its initial velocity, and its final velocity after the collision. The change in momentum is calculated as the final momentum minus the initial momentum.
Answer
16 kg ms$^{-1}$
Answer for screen readers
C) 16 kg ms$^{-1}$
Steps to Solve
- Calculate the initial momentum
The initial momentum $p_i$ is the product of the mass $m$ and the initial velocity $v_i$. $$ p_i = m \cdot v_i $$ Given $m = 2 \text{ kg}$ and $v_i = 5 \text{ m/s}$, $$ p_i = 2 \text{ kg} \cdot 5 \text{ m/s} = 10 \text{ kg m/s} $$
- Calculate the final momentum
The final momentum $p_f$ is the product of the mass $m$ and the final velocity $v_f$. Since the sphere bounces back in the opposite direction, we must consider the final velocity as negative. $$ p_f = m \cdot v_f $$ Given $m = 2 \text{ kg}$ and $v_f = -3 \text{ m/s}$, $$ p_f = 2 \text{ kg} \cdot (-3 \text{ m/s}) = -6 \text{ kg m/s} $$
- Calculate the change in momentum
The change in momentum $\Delta p$ is the difference between the final momentum $p_f$ and the initial momentum $p_i$.
$$ \Delta p = p_f - p_i $$ $$ \Delta p = -6 \text{ kg m/s} - 10 \text{ kg m/s} = -16 \text{ kg m/s} $$ Since the question asks for the magnitude of the change in momentum, we take the absolute value. $$ | \Delta p | = |-16 \text{ kg m/s}| = 16 \text{ kg m/s} $$
C) 16 kg ms$^{-1}$
More Information
The change in momentum represents the impulse experienced by the sphere during the collision.
Tips
A common mistake is forgetting to account for the change in direction (or sign) of the velocity after the collision. Another common mistake is subtracting the final momentum from the initial momentum instead of the other way around.
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