A sledge of mass 8.0\text{ kg} sliding on ice with an initial velocity of 15\text{ m s}^{-… — JAMB UTME

A sledge of mass $8.0\text{ kg}$ sliding on ice with an initial velocity of $15\text{ m s}^{-1}$ enters a rough patch that exerts a constant retarding force of $24\text{ N}$ . Calculate the time, in seconds, required for the sledge to come to a complete stop.

Answer: 5 s

Answer

The time required for the sledge to come to a complete stop is

5.0\text{ s}

By Newton's second law in terms of momentum, the rate of change of momentum is equal to the applied net force (

F = \frac{\Delta p}{\Delta t}

). Rearranging gives

\Delta t = \frac{m(v - u)}{F}

. Substituting

m = 8.0\text{ kg}

u = 15\text{ m s}^{-1}

v = 0\text{ m s}^{-1}

, and retarding force

F = -24\text{ N}

yields

\Delta t = \frac{8.0 \times (0 - 15)}{-24} = 5.0\text{ s}

Step-by-Step Solution

Determine the change in linear momentum of the sledge.

The change in linear momentum is

\Delta p = m(v - u) = 8.0\text{ kg} \times (0\text{ m s}^{-1} - 15\text{ m s}^{-1}) = -120\text{ kg m s}^{-1}

Linear momentum is defined as the product of mass and velocity.

Apply the impulse-momentum theorem to determine the time duration.

\Delta t = \frac{\Delta p}{F} = \frac{-120\text{ kg m s}^{-1}}{-24\text{ N}} = 5.0\text{ s}

Impulse delivered by a net force over a time interval equals the change in linear momentum.

Key Concept

Newton's Second Law and Impulse-Momentum Theorem

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