Respuesta :
ANSWER:
1. 0.00031 N
2. 8.6 m/s
STEP-BY-STEP EXPLANATION:
Given:
Spring constant (k) = 11 N/m
Speed (v) = 4.7 m/s
x = 1 cm = 0.01 m
1.
We can determine the mass by conservation of energy and then calculate the weight in the following way:
[tex]\begin{gathered} \frac{1}{2}kx^2=\frac{1}{2}mv^2 \\ \\ \text{ We replacing} \\ \\ 11\cdot \left(0.01\right)^2=m\cdot \left(5.9\right)^2\: \\ \\ m=\frac{11\cdot(0.01)^2}{(5.9)^2} \\ \\ m=3.16\cdot10^{-5}\text{ kg} \\ \\ W=m\cdot g \\ \\ W=3.16\cdot10^{-5}\cdot9.8 \\ \\ W=0.00031\text{ N} \end{gathered}[/tex]2.
The speed can also be determined by the conservation of energy, thus:
[tex]\begin{gathered} \frac{1}{2}mu^2=mgh+\frac{1}{2}mv^2 \\ \\ \text{ We relaplacing:} \\ \\ \frac{1}{2}u^2=(9.8)(2)+\frac{1}{2}(5.9)^2 \\ \\ u^2=2\cdot((9.8)(2)+\frac{1}{2}(5.9)^2) \\ \\ u=\sqrt{74.01} \\ \\ u=8.6\text{ m/s} \end{gathered}[/tex]