A 12 kg box sliding on a horizontal floor has an initial speed of 4.0 m/s. the coefficient of friction between the box and the floor is 0.20

General
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a 12 kg box sliding on a horizontal floor has an initial speed of 4.0 m/s. the coefficient of friction between the box and the floor is 0.20. the box moves a distance of 4.0 m in 2.0 s. the magnitude of the change in momentum of the box during this time is most nearly

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LectureNotes said:

To find the magnitude of the change in momentum of the box during this time, we need to calculate the initial momentum and the final momentum of the box and then find the difference between them.

  1. Calculate the initial momentum:

    • The initial speed of the box is given as 4.0 m/s.
    • The mass of the box is 12 kg.
    • Therefore, the initial momentum = mass x initial velocity = 12 \, kg \times 4.0 \, m/s = 48 \, kg \cdot m/s.

  2. Calculate the final momentum:

    • The box moves a distance of 4.0 m in 2.0 s.
    • Using the given distance and time, we can calculate the final velocity using the equation v = \frac{d}{t} .
    • v = \frac{4.0 \, m}{2.0 \, s} = 2.0 \, m/s .
    • The final momentum = mass x final velocity = 12 \, kg \times 2.0 \, m/s = 24 \, kg \cdot m/s .

  3. Calculate the change in momentum:

    • Change in momentum = final momentum - initial momentum.
    • Change in momentum = 24 \, kg \cdot m/s - 48 \, kg \cdot m/s = -24 \, kg \cdot m/s .

Therefore, the magnitude of the change in momentum of the box during this time is approximately 24 kg∙m/s.