13.3 Example 3

A 1.7 kg collar is attached to a spring and can sliding in a vertical plane (no friction) along the bar ABC. The spring constant is 550 N/m and is undeformed when its length is 16 cm. If the collar is released in A (V = 0), find its speed when passing through B.

Solution with FisicaLab

Select the Dynamics group and, inside this, the Circular module. Erase the content of the chalkboard and select the SI system. And add one element Stationary reference system, one element Object in rest, one element Mobile with circular movement, two elements Spring, two elements Force, one element Initial system, one element Final system and one element Energy. As show the image below:

The element Stationary reference system write to default the gravity value. And the time is irrelevant for this problem. To the element Object in rest, which represents the collar in A, and taking this position as the horizontal reference:

Name

initialCollar

m

1.7

y

0

And for the element Spring corresponding to the initial state:

Name

initialSpring

k

550

x

7 @ cm

To the element Force applied to it:

f

initialForce

Both, the element Spring and the element Object in rest, corresponds to the initial state, so we add them to the element Initial system, that we call initial:

Name

initial

Object 1

initialCollar

Object 2

initialSpring

Object 3

0

Object 4

0

Now for the element Mobile with circular movement, representing the collar when passing through point B, we have (we do not know the data of the turning radius, but is irrelevant to this problem):

Name

finalCollar

m

1.7

vt

vt

r

0

y

-18 @ cm

For the element Spring that corresponds to the final state:

Name

finalSpring

k

550

x

2 @ cm

And to the applied force:

f

finalForce

Now add this element Spring and the element Mobile with circular movement, which represents the final state, to the element Final system, that we call final:

Name

final

Object 1

finalCollar

Object 2

finalSpring

Object 3

0

Object 4

0

Finally, add the elements initial and final system in the element Energy. And knowing that energy is conserved, we have:

System i

initial

System f

final

W

0

Now click in the icon Solve to get the answer:

vt = 2.233 m/s ;  initialForce = 38.500 N ;
finalForce = 11.000 N ;
Status = success.