A 3.00-kg box is sliding along a frictionless horizontal surface with a speed of 1.8 m/s when it encounters a spring. (a) Determine the force constant of the spring, if the box compresses the spring 5.20 cm before coming to rest. N/m (b) Determine the initial speed the box would need in order to compress the spring by 1.60 cm.

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:

       

       where

       and

Simplifying and replacing by the values, we get:

               

Solving for k:

k = 3594.7 N/mb)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:

       

v = 0.55 m/s

Idon’t know wish i could