Question

Какую силу надо приложить к пружине жесткостью 100 н/м, чтобы сжать пружину от 10 см до 3 см, до какой длины растянется эта пружина от недеформированного состояния под действием сила 5 н.

Answer 1

L=l1-l2=10-3=7см=0.07м
F=kl=100×0.07=7Н
расстянется:
F=kl ; l=F/k= 5/ 100=0.05 м

Answer 2

Calculation of the Force Required to Compress the Spring:

To calculate the force required to compress a spring, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.

Hooke's Law can be expressed as:

F = kx

Where: - F is the force applied to the spring, - k is the spring constant (also known as the stiffness or the force constant) in units of N/m, - x is the displacement of the spring from its equilibrium position.

In this case, we are given that the spring constant (k) is 100 N/m and the displacement (x) is from 10 cm to 3 cm. We need to find the force required to compress the spring.

Let's calculate the force using the given values:

F = k * x

F = 100 N/m * (10 cm - 3 cm)

Converting the displacement from centimeters to meters:

F = 100 N/m * (0.1 m - 0.03 m)

F = 100 N/m * 0.07 m

F = 7 N

Therefore, the force required to compress the spring from 10 cm to 3 cm is 7 N.

Calculation of the Length of the Stretched Spring:

To calculate the length to which the spring will stretch from its undeformed state under the influence of a force, we can use Hooke's Law again.

Hooke's Law can be rearranged to calculate the displacement (x) of the spring:

x = F / k

Where: - x is the displacement of the spring, - F is the force applied to the spring, - k is the spring constant.

In this case, we are given that the force applied to the spring is 5 N and the spring constant (k) is 100 N/m. We need to find the displacement (x) of the spring.

Let's calculate the displacement using the given values:

x = 5 N / 100 N/m

x = 0.05 m

Converting the displacement from meters to centimeters:

x = 0.05 m * 100 cm/m

x = 5 cm

Therefore, the spring will stretch by 5 cm from its undeformed state under the influence of a force of 5 N.

Note: The calculation assumes that the spring is linear and obeys Hooke's Law within the given range of displacement and force.