Question

A meter stick whose mass is $\mathbf{300}\mathbf{}\mathit{g}$lies on ice (Figure 9.49). You pull at one end of the meter stick, at right to the stick, with a force of $\mathbf{6}\mathbf{}\mathit{N}$. The ensuing motion of the meter stick is quite complicated, but what are the initial magnitude and direction of the rate of change of the momentum of the stick, ${}^{{\mathbf{dp}}_{\mathbf{sys}}}\mathbf{/}_{\mathbf{dt}}$, when you first apply the force? What is the magnitude of the initial acceleration of the center of the stick?

Short answer

The initial magnitude and direction of the rate of change of the momentum of the stick,${}^{{\mathrm{dp}}_{\mathrm{sys}}}/_{\mathrm{dt}}$ is $\mathbf{6}\mathbf{}\mathit{N}$

The magnitude of the initial acceleration of the center of the stick is $\mathbf{20}\mathbf{}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$

Step-by-step solution

Identification of given data

• The mass of a stick is $300 g(0.3kg)$
• The length of a stick is$1m$
• The force applied on a stick is$6N$

Definition of the rate of change of the momentum

According to Newton’s second law, the rate of change of momentum is equated to the applied force.

Calculation of the initial magnitude and direction of the rate of change of the momentum of the stick,

We know that,

The rate of change of momentum is

$\frac{{\mathbf{dp}}_{\mathbf{sys}}}{\mathbf{dt}}\mathbf{=}\mathit{F}$

Where $F=6N$

$\frac{d{p}_{sys}}{dt}=6N$

Hence, the initial magnitude of the rate of change of the momentum of the stick, ${}^{{\mathbf{dp}}_{\mathbf{sys}}}\mathbf{/}_{\mathbf{dt}}$ is $\mathbf{6}\mathbf{}\mathit{N}$

The initial magnitude of the rate of change of the momentum of the stick, is positive (towards the right side).

Calculation of the magnitude of the initial acceleration

The force,

$$\begin{gathered} \mathit{F}\mathbf{=}\mathit{m}\mathit{a} \\ a=\frac{F}{m} \\ =\frac{6kg·m/s^2}{0.3kg} \\ =\frac{6}{0.3}·\left[\frac{1kg·m/s^2}{1kg}\right] \\ =\frac{6}{0.3}·\left[1m/s^2\right] \\ =20m/s^2 \end{gathered}$$

Hence, the magnitude of the initial acceleration is $\mathbf{20}\mathbf{}\mathit{m}\mathbf{/}{\mathit{s}}^{\mathbf{2}}$