An unstretched ideal spring hangs vertically from a fixed support. A 0.4 kg object is then attached to the lower end of the spring. The object is pulled down to a distance of 35cm below the unstretched position and released from rest at t=0s. A graph of the subsequent vertical position 'y' of the lower end of the spring as a function of 't' is shown to the right where y=0 is when the spring was initially unstretched. What is the spring's length when it is unstretched?
just calculate the velocity at all the time given in the options (there is a graph too)
To find the spring's length when it is unstretched, we need to analyze the given information and the graph.
From the graph, we can see that the object is pulled down to a distance of 35 cm below the unstretched position and then released at t=0s. The graph shows the subsequent vertical position 'y' of the lower end of the spring as a function of time 't'.
At the initial unstretched position, the object is not pulling the spring upwards or downwards. Therefore, the force exerted by the object and the force exerted by the spring are balanced, resulting in no net force.
When the object is pulled down, the spring stretches due to the force exerted by the object. As the object is then released, the spring force tries to restore the spring to its equilibrium position.
From the graph, we can observe that at t=0s, the object is released from rest. The graph shows the spring's position 'y' as 0, indicating that the spring has returned to its unstretched position.
Therefore, the spring's length when it is unstretched is equal to the distance the object was pulled down, which is 35 cm.