Question

State the principle or principles that can be used to calculate the velocity of the 8-kilogram block at the instant the spring regains its original length.

a) Conservation of energy
b) Newton's second law
c) Hooke's law
d) Both a and c

Answer 1

To calculate the block's velocity when the spring returns to its original length, you apply the conservation of energy and Hooke's Law. The transfer from potential to kinetic energy and the spring's force relation to its displacement allows for this calculation.

Step-by-step explanation:

To calculate the velocity of the 8-kilogram block at the instant the spring returns to its original length, you can use two principles:

• Conservation of energy (a): This principle states that the total mechanical energy (potential plus kinetic) in the system remains constant if there are no non-conservative forces at work like friction. Since the block is moving without friction and is attached to a spring, its potential energy at maximum compression or extension will convert into kinetic energy at the point where the spring is neither stretched nor compressed.
• Hooke's Law (c): it dictates that the force exerted by a spring is directly proportional to its displacement from the equilibrium position. Hooke's Law allows you to calculate the potential energy stored in the spring when it is compressed or stretched.

Thus, the correct answer is d: Both a and c, as you will use both the conservation of energy and Hooke's Law to calculate the block's velocity at the equilibrium position.