Aspring of constant 20 n/m has compressed a distance 8 m by a(n) 0.3 kg mass, then released. it skids over a frictional surface of length 2 m with a coefficient of friction 0.16, then compresses the second spring of constant 2 n/m. the acceleration of gravity is 9.8 m/s2.
how far will the second spring compress in order to bring the mass to a stop?

Explanation:

Here we will call:

1. : The energy when the first spring is compress

2. : The energy after the mass is liberated by the spring

3. : The energy before the second string catch the mass

4. : The energy when the second sping compressed

so, the law of the conservations of energy says that:

1.

2.

3.

where is the work of the friction.

1. equation 1 is equal to:

where K is the constant of the spring, x is the distance compressed, M is the mass and the velocity, so:

Solving for velocity, we get:

= 65.319 m/s

2. Now, equation 2 is equal to:

where M is the mass, the velocity in the situation 2, is the velocity in the situation 3, is the coefficient of the friction, N the normal force and d the distance, so:

Volving for , we get:

3. Finally, equation 3 is equal to:

where is the constant of the second spring and is the compress of the second spring, so:

solving for , we get:

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explanation:

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.