Question

To practice Problem-Solving Strategy 7.2 Conservation of energy with conservative forces. A basket of negligible weight hangs from a vertical spring scale of force constant 1500 N/mN/m . If you suddenly put an adobe brick of mass 3.00 kgkg in the basket, find the maximum distance that the spring will stretch.

Answer 1

When an adobe brick with a mass of 3.00 kg is added to the basket, the spring will stretch a maximum distance of 0.0196 meters or 1.96 centimeters.

Step-by-step explanation:

When an adobe brick with a mass of 3.00 kg is added to the basket, it will stretch the spring.

According to Hooke's Law, the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for the force exerted by a spring is given by:

F = kx

where F is the force, k is the force constant of the spring, and x is the displacement of the spring.

In this case, the force exerted by the spring is equal to the weight of the adobe brick, which is given by F = mg. Thus, we can equate these two forces to find the maximum displacement of the spring:

kx = mg

Plugging in the values, we have:

1500x = 3.00 * 9.8

Solving for x, we find that the maximum distance the spring will stretch is 0.0196 meters or 1.96 centimeters.

Answer 2

0.03924 m

Step-by-step explanation:

Let g = 9.81 m/s2. Let x be the maximum distance that the spring will stretch. And let the potential energy reference point be at the the lower end where the spring is stretched to the maximum. Using mechanical energy conservation we have the following:

- At the bottom end where the spring is stretched to maximum: potential and kinetic energy is 0. Elastic energy is
`kx^2/2`

- At the point where the weight is placed: potential energy is mgx, kinetic energy and elastic energy is 0 (because the spring is not stretched)

`E_p = E_e`

`kx^2/2 = mgx`

`x = 2mg/k = 2*3*9.81/1500 = 0.03924 m`