A 22.5-kg mass is attached to a horizontal frictionless spring. The system has a spring with a spring constantof 9.65 x 104N/m that is displaced 8.95 cm from its resting position, and then released. What is the maximumspeed attained by the mass?a. 5.86 m/s C. 5.52 m/sb. 6.14 m/s d. 6.48 m/s

The maximum speed of the mass can be found using the principle of conservation of energy. The total energy in the system is conserved and is a sum of kinetic and potential energy. At maximum speed, all the potential energy stored in the spring is converted into kinetic energy of the mass.

The potential energy (PE) stored in the spring when it is stretched or compressed is given by the formula:

PE = 0.5 * k * x^2

where k is the spring constant and x is the displacement from the resting position.

Substituting the given values:

PE = 0.5 * 9.65 * 10^4 N/m * (8.95 * 10^-2 m)^2 PE = 326.6 J

At maximum speed, all this potential energy is converted into kinetic energy (KE). The kinetic energy of a moving object is given by the formula:

KE = 0.5 * m * v^2

where m is the mass of the object and v is its speed. At maximum speed, KE = PE, so we can set the two equal and solve for v:

0.5 * m * v^2 = PE v^2 = 2 * PE / m v = sqrt(2 * PE / m)

Substituting the given values:

v = sqrt(2 * 326.6 J / 22.5 kg) v = 6.14 m/s

So, the maximum speed attained by the mass is 6.14 m/s (option b).

The maximum speed of the mass can be found using the principle of conservation of energy. At the maximum displacement, all the energy in the system is potential energy, which is converted into kinetic energy as the mass moves towards the equilibrium position.

The potential energy (PE) stored in a spring is given by the formula:

PE = 0.5 * k * x^2

where k is the spring constant and x is the displacement from the equilibrium position.

Substituting the given values:

PE = 0.5 * 9.65 * 10^4 N/m * (8.95 * 10^-2 m)^2 PE = 326.6 J

At the maximum speed, all the potential energy is converted into kinetic energy (KE). The kinetic energy is given by the formula:

KE = 0.5 * m * v^2

where m is the mass and v is the speed. We can set the kinetic energy equal to the potential energy and solve for v:

326.6 J = 0.5 * 22.5 kg * v^2 v^2 = 326.6 J / (0.5 * 22.5 kg) v = sqrt(326.6 J / (0.5 * 22.5 kg)) v = 6.14 m/s

So, the maximum speed attained by the mass is 6.14 m/s (option b).