Question

El muelle de un dinamómetro se alarga 6cm cuando aplicamos sobre él una fuerza de 10 N. Calcula el alargamiento del muelle al aplicar una fuerza de 20 N.

Answer 1

The elongation of the spring when a force of 20 N is applied is 12 cm.

Step-by-step explanation:

To calculate the elongation of the spring when a force of 20 N is applied, we can use the concept of Hooke's Law. Hooke's Law states that the elongation of a spring is directly proportional to the force applied to it.

Given that the elongation is 6 cm when a force of 10 N is applied, we can set up the following proportion:

10 N / 6 cm = 20 N / x

Solving for x, we get: x = (20 N × 6 cm) / 10 N = 12 cm

Therefore, the elongation of the spring when a force of 20 N is applied is 12 cm.

Answer 2

x = 12cm

Step-by-step explanation:

First, with the values given for the force and the displacement, you calculate the spring-constant of the dynamometer by using the following equation (primero, con los valores dados de la fuerza y el desplazamiento, calculas la constante del resorte aplicando la siguiente formula):

`F=kx`

F: force (fuerza) = 10N

k: spring constant (constante del resorte)

x: displacement of the spring (desplazamiento del resorte) = 6cm

by using these values you calculate k (usando estos valores calculas k):

`k=(F)/(x)=(10N)/(6cm)=1.66(N)/(cm)`

With this value you calculate the displacement for a force of 20N (con este valor de k calculas el desplazamiento del resorte para una fuerza de 20N):

`x=(F)/(k)=(20)/(1.66N/cm)=12cm`

hence, the displacement is 12cm