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Difficulty: EasyNewton's Laws of Motion and Linear Momentum

A constant net force of 20 N20\text{ N} acts on an object of mass 4 kg4\text{ kg} that is initially at rest on a frictionless horizontal surface. What is the magnitude of the linear momentum of the object after 3 s3\text{ s}?

Answer: 60 kg m s^-1

Answer

The magnitude of the linear momentum of the object after 3 s3\text{ s} is 60 kg m s−160\text{ kg m s}^{-1}.
According to Newton's Second Law in terms of momentum, force is the rate of change of linear momentum (F=ΔpΔtF = \frac{\Delta p}{\Delta t}). Rearranging gives Δp=FΔt\Delta p = F \Delta t. Since the object is initially at rest (pi=0 kg m s−1p_i = 0\text{ kg m s}^{-1}), the final momentum is pf=FΔt=20 N×3 s=60 kg m s−1p_f = F \Delta t = 20\text{ N} \times 3\text{ s} = 60\text{ kg m s}^{-1}.

Step-by-Step Solution

1
Apply the impulse-momentum theorem.
J=FΔt=ΔpJ = F \Delta t = \Delta p
The impulse of the net force acting on an object equals the change in its linear momentum.
2
Calculate the final linear momentum.
pf=20 N×3 s=60 kg m s−1p_f = 20\text{ N} \times 3\text{ s} = 60\text{ kg m s}^{-1}
Since the object starts from rest, its initial momentum is zero (pi=0p_i = 0), so the final momentum is equal to the total impulse supplied.

Key Concept

Impulse-Momentum Theorem
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Topics

Newton's Laws of Motion and Linear Momentum

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