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7) 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 lighter dart leaves the spring moving faster than the heavy dart.
C) The heavy dart had more initial elastic potential energy than the light dart.
D) Both darts move free of the spring with the same speed.
E) Both darts had the same initial elastic potential energy.

Please explain each answer choice

Answer :

MathPhys

Answer:

A, B, and E

Explanation:

The springs are identical, and are compressed the same amount, so they have the same initial elastic potential energy. (E is true)

Energy is conserved, so the darts have the same amount of kinetic energy. (A is true, C is false)

The lighter dart has the same energy as the heavier dart.  Since it has less mass, it must have a greater speed. (B is true, D is false)

Cricetus

Even though those who move away from the spring, this same darts have always had the similar K.E. The lightweight dart accelerates away from the spring speedier than just the heavier dart. The elastic potential of both darts was the same from the start.

  • Whenever two springs are squeezed by some of the similar amount (x), their Elastic potential energy is equivalent.

→ [tex]Darts \ K.E = \frac{1}{2} m_1 v_1^2[/tex]

and,

                     [tex]= \frac{1}{2} m_2v_2^2[/tex]

  • As nothing more than a result, the kinetic energy of the corresponding darts are therefore equal to [tex]\frac{1}{2} kx^2[/tex] since their springs as well as compressions would be the similar.

→ [tex]\frac{1}{2} m_1 v_1^2 = \frac{1}{2} m_2v_2^2[/tex]

and,

→ [tex]\frac{1}{2} m_2 v_2^2 = \frac{1}{2} kx^2[/tex]

This demonstrates that perhaps the lighter dart will have to go quickly than the bulkier dart.

Thus the above response is right.

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