Question

Под действием упругости 10Н пружина удлинилась на 3мм. Найти длину пружины под действием силы 25Н.

Answer 1

1) По закону Гука F1=k*X1, где k - коэффициент жёсткости пружины; k=F1/X1 2) F2=k*X2 => X2=F2/k => X2=F2*X1/F1=25*0,003/10=0,0075м=7,5мм

Answer 2

Calculation of the Length of the Spring

To find the length of the spring under the action of a force of 25 N, 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 (25 N in this case) - k is the spring constant (unknown) - x is the displacement of the spring (3 mm in this case)

To find the spring constant (k), we can rearrange the equation as follows:

k = F / x

Substituting the given values, we have:

k = 25 N / 3 mm

Now, we need to convert the displacement from millimeters to meters, as the SI unit for length is meters.

1 millimeter (mm) is equal to 0.001 meters (m). Therefore, the displacement is:

x = 3 mm = 3 * 0.001 m = 0.003 m

Substituting the values into the equation, we have:

k = 25 N / 0.003 m

Calculating the value of k:

k = 8333.33 N/m

Now that we have the spring constant, we can find the length of the spring under the action of a force of 25 N.

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

x = F / k

Substituting the values, we have:

x = 25 N / 8333.33 N/m

Calculating the value of x:

x = 0.003 m

Therefore, the length of the spring under the action of a force of 25 N is 0.003 meters or 3 millimeters.

Answer:

The length of the spring under the action of a force of 25 N is 3 millimeters.