Question

A 1.50 kg piece of cheese is placed on a vertical spring of negligible mass and force constant k = 1800 n/m that is compressed 17.4 cm

When the spring is released, how high does the cheese rise from this initial position?

Answer 1

When the compressed spring is released, the cheese rises approximately 1.19 meters from its initial position.

Step-by-step explanation:

To determine how high the cheese rises from its initial position, we can use the principle of conservation of mechanical energy. When the spring is compressed, it stores potential energy. When released, this potential energy is converted into kinetic energy as the cheese starts to move upward.

Using the formula for potential energy in a spring system, we have:

PE = (1/2)kx^2

where PE is the potential energy, k is the force constant of the spring, and x is the displacement of the spring from its equilibrium position. Plugging in the values, we get:

(1/2)(1800 N/m)(0.174 m)^2 = 26.160 J

This is the amount of potential energy the cheese has when it is at its highest point. To find the height it rises, we can equate this potential energy to potential energy at a height, given by:

mgh

where m is the mass of the cheese, g is the acceleration due to gravity, and h is the height. Plugging in the values, we get:

(1.50 kg)(9.8 m/s^2)h = 26.160 J

Simplifying the equation, we find that the height h is approximately 1.19 meters.