Question

If the spring of a jack in the box is compressed a distance of 8.00 cm from its relaxed ninth and then released what is the mechanical energy of the system and what is its speed of the toy head when is spring returns to its natural light assume that the mass of the toy is 50.0 geez the spring constant is 80.09/M in the toilet head moves on the end vertical direction also disregard the mass of the spring

Answer 1

The mechanical energy of the system can be calculated using the potential and kinetic energy equations. Once the spring is released, the potential energy is converted into kinetic energy. The speed of the toy head can be calculated by equating the potential and kinetic energy and solving for velocity.

Step-by-step explanation:

The mechanical energy of the system can be calculated by considering the potential and kinetic energy at the initial and final states of the spring. When the spring is compressed, it has potential energy given by the equation:

PE = (1/2) * k * x^2
where PE is the potential energy, k is the spring constant, and x is the compression distance. Given that the spring constant is 80.09 N/m and the compression distance is 0.08 m, we can calculate the potential energy. Once the spring is released and returns to its natural length, all the potential energy is converted into kinetic energy. Since the mass of the toy is given as 0.050 kg, the kinetic energy can be calculated using:

KE = (1/2) * m * v^2
where KE is the kinetic energy and v is the velocity of the toy head. Equating the potential energy and kinetic energy, we can solve for the velocity of the toy head. The mechanical energy of the system is the sum of the potential and kinetic energy.