a 755g mass is at rest on the end of a spring (k=124N/m). a force is applied to

Question

a 755g mass is at rest on the end of a spring (k=124N/m). a force is applied to the spring, which compresses the spring a distance of 5cm from its equilibrium position. given this information, determin the following:
a)the total energy
b)the kinetic and potential energies of the system when the spring is compressed to 5 cm to the left of its equlibrium position.
c)what is the maximum velocity of the mass during the motion
d)what is the maximum velocity of the mass at x=+1.5cm
e)what are the kinetic and potential energies at x=+1.5cm

Explanation / Answer

The total energy is:

EKinetic + EPotential = Etotal

1) 1/2*mv2 + 1/2*kxmax2 = Etotal

When the spring is fully compress the kinetic energy is zero and so the potential energy is equal to the total energy:

2) 1/2*kxmax2 = Etotal

When the spring is not compress at all, the potential energy is zero, which results in the kinetic energy being a maximum, which requires the velocity to be a maximum as well.

The velocitiy at any given point, such as in part d) can be solved by evaluating equation 2) to get the total energy, algebraically solving equation 1) for velocity, v. Once the velocity is known the knietic energy can be directly evaluated.

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