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: