Answer:
a) k= 3594,7 N/m
b) v= 0.55 m/s
Explanation:
- a)
- As the surface is horizontal, the only change in energy will be the change in kinetic energy, as the box comes to an stop after compressing the spring.
- As we know that the surface is frictionless also, this change in kinetic energy must be equal to the change in the elastic potential energy of the spring.
- So we can write the following equality:
[tex]\Delta K = \Delta U[/tex]
where [tex]\Delta K = \frac{1}{2}*m*v^{2}[/tex]
and [tex]\Delta U = \frac{1}{2} * k* \Delta x^{2}[/tex]
- Simplifying and replacing by the values, we get:
[tex]3.00 kg* (1.8 m/s)^{2} = k* (0.052 m) ^{2}[/tex]
[tex]k = \frac{3.00kg*(1.8m/s)^{2} }{(0.052m)^{2}} = 3594.7 N/m[/tex]
- b)
- For this part, we can just apply the same equality, replacing the value of k by the one we got, and solving for the initial speed v:
[tex]v = \sqrt{\frac{k*\Delta x^{2}}{m} } = \sqrt{\frac{3594.7N/m*(0.016m)^{2} }{3.00kg}} = 0.55 m/s[/tex]
