A horizontal slingshot consists of two light, identical springs (with spring constants of...

RESEARCH:

From the above figure, the path of the stone takes while in the slingshot is completely horizontal so that gravity is neglected.

(a) In order to determine the total mechanical energy, consider all kinetic and potential energies in the system. At the instant when the slingshot is released the mechanical energy stored in the system is potential energy stored in the spring.

. . . . . . (1)

(b) The speed of the stone at equilibrium position can be determined by conservation of energy.

SKETCH:

Figure shows the horizontal slingshot consists of two light strings and cup containing stone and they line up vertically.

SIMPLIFY:

Energy conservation requires that the total energy remains the same, that is.

(a)

From the above figure, by using Pythagorean Theorem

Then the total mechanical energy is

. . . . . . (2)

(b) From law of conservation of energy, the mechanical energy is conserved so at the position have only the potential energy, then

Thus rearranging the above equation for speed of the stone is

. . . . . . (3)

CALCULATE:

According to the given information and the origin of the coordinate system we selected

(a) By putting the values in equation (2), we get

Therefore the total mechanical energy of the system is.

(b) By putting the values in equation (3), we get

Therefore the speed of the stone at is.