Dynamics: Question 5

Worked solution

Step 1: Recall the impulse-momentum relationship

Force is defined as the rate of change of momentum, $F = \dfrac{\Delta p}{\Delta t}$. Rearranging, the impulse of a constant force gives the change in momentum directly: $\Delta p = F \Delta t$

Step 2: Substitute the given values

$\Delta p = (4.0)(3.0) = 12\text{ kg m s}^{-1}$

Step 3: Relate this to the ball’s actual momentum

Since the ball starts at rest, its initial momentum is zero, so the change in momentum equals the final momentum: $p_{\text{final}} = p_{\text{initial}} + \Delta p = 0 + 12 = 12\text{ kg m s}^{-1}$

Note that the ball’s mass ($0.50\text{ kg}$) is not actually needed to answer this question. The impulse $F\Delta t$ gives the momentum change directly, without needing to convert to a velocity first.

Why the other options are wrong

• A ($2.0\text{ kg m s}^{-1}$): this comes from multiplying the force by the mass ($4.0\times0.50$) instead of by the time.
• B ($4.0\text{ kg m s}^{-1}$): this is just the force itself, with the time interval never applied.
• D ($24\text{ kg m s}^{-1}$): this comes from finding the change in velocity, $\Delta v = F\Delta t/m = 12/0.50=24\text{ m s}^{-1}$, and mistaking this speed for the momentum, but momentum and velocity are different quantities.

Final answer

• The ball’s momentum is $\boxed{12}\text{ kg m s}^{-1}$, option C.