A heavy dart and a light dart are launched horizontally on a frictionless table

Question

A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs. Both springs were initially compressed by the same amount. Which of the following statements about these darts are correct? (There could be more than one correct choice.)

A: The darts both have the same kinetic energy just as they move free of the spring. B: The heavy dart had more initial elastic potential energy than the light dart. C: The lighter dart leaves the spring moving faster than the heavy dart. D: Both darts had the same initial elastic potential energy. E: Both darts move free of the spring with the same speed.

Explanation / Answer

Solution:

When the springs are compressed by the same amount, they have equal Elastic potential energy.

The darts have the kinetic energy = 1/2 m1 v1 ^2 and 1/2 m2 v2^2

these kinetic enbergies of the respective darts are Equal to 1/2kx^2 since the springs and compressions are identical.

1/2 m1 v1^2 = 1/2kx^2

and 1/2 m2v2^2 = 1/2 kx^2

This shows that the Lighter dart will move Faster compared to the heavier dart.

=> A. The darts both have the same kinetic energy just as they move free of the spring.

     C . The lighter dart leaves the spring moving faster than the heavy dart.

     D. Both darts had the same initial elastic potential energy.

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