Question

A 0.20-kg mass is oscillating on a spring over a horizontal frictionless surface. When it is at a displacement of 2.6 cm for equilibrium it has a kinetic energy of 1.4 J and a spring potential energy of 2.2 J. What is the maximum speed of the mass during its oscillation?

Answer 1

Explanation:

The given data is as follows.

                    mass = 0.20 kg

              displacement = 2.6 cm

              Kinetic energy = 1.4 J

       Spring potential energy = 2.2 J

Now, we will calculate the total energy present present as follows.

         Total energy = Kinetic energy + spring potential energy

                           = 1.4 J + 2.2 J

                            = 3.6 Joules

As maximum kinetic energy of the object will be equal to the total energy.

So,      K.E = Total energy

                = 3.6 J

Also, we know that

                  K.E = $\frac{1}{2}mv^{2}_{m}$

or,                   v = $\sqrt{\frac{2K.E}{m}}$

                        = $\sqrt{2 \times 3.6 J}{0.2 kg}$

                        = $\sqrt{36}$

                        = 6 m/s

thus, we can conclude that maximum speed of the mass during its oscillation is 6 m/s.