A 3.4-kg object rests on a horizontal frictionless surface. It is in a position such that it is compressing a spring a distance 11.8 cm.If the object is released, the object leaves the spring at a speed of 18.3 cm/s.What is the spring constant of the spring?Express your answer in N/m, to at least one digit after the decimal point.

To find the spring constant of the spring, we can use the principle of conservation of mechanical energy.

1. First, let's convert the distance the object compresses the spring into meters. We have 11.8 cm, which is equal to 0.118 m.

2. The potential energy stored in the spring when it is compressed can be calculated using the formula: Potential energy = (1/2) * k * x^2 where k is the spring constant and x is the distance the spring is compressed.

   Plugging in the values, we have: Potential energy = (1/2) * k * (0.118)^2

3. Next, we need to find the kinetic energy of the object when it leaves the spring. The kinetic energy can be calculated using the formula: Kinetic energy = (1/2) * m * v^2 where m is the mass of the object and v is the velocity of the object.

   Plugging in the values, we have: Kinetic energy = (1/2) * 3.4 kg * (0.183 m/s)^2

4. According to the principle of conservation of mechanical energy, the potential energy stored in the spring when it is compressed is equal to the kinetic energy of the object when it leaves the spring. Therefore, we can set the two equations equal to each other:

   (1/2) * k * (0.118)^2 = (1/2) * 3.4 kg * (0.183 m/s)^2

5. Now, we can solve for the spring constant, k. Rearranging the equation, we have:

   k = (3.4 kg * (0.183 m/s)^2) / (0.118)^2

6. Calculating the expression on the right-hand side, we find:

   k ≈ 105.6 N/m

Therefore, the spring constant of the spring is approximately 105.6 N/m.

To find the spring constant of the spring, we can use the principle of conservation of mechanical energy.

1. First, let's convert the distance the object compresses the spring into meters. We have 11.8 cm, which is equal to 0.118 m.

2. The potential energy stored in the spring when it is compressed can be calculated using the formula: Potential energy = (1/2) * k * x^2 where k is the spring constant and x is the distance the spring is compressed.

   Plugging in the values, we have: Potential energy = (1/2) * k * (0.118)^2

3. Next, we need to find the kinetic energy of the object when it leaves the spring. The kinetic energy can be calculated using the formula: Kinetic energy = (1/2) * m * v^2 where m is the mass of the object and v is the velocity of the object.

   Plugging in the values, we have: Kinetic energy = (1/2) * 3.4 kg * (0.183 m/s)^2

4. According to the principle of conservation of mechanical energy, the potential energy stored in the spring when it is compressed is equal to the kinetic energy of the object when it leaves the spring. Therefore, we can set the two equations equal to each other:

   (1/2) * k * (0.118)^2 = (1/2) * 3.4 kg * (0.183 m/s)^2

5. Now, we can solve for the spring constant, k. Rearranging the equation, we have: k = (3.4 kg * (0.183 m/s)^2) / (0.118)^2

6. Calculating the expression on the right-hand side, we find: k ≈ 89.6 N/m

Therefore, the spring constant of the spring is approximately 89.6 N/m.