If a force of 100N stretches a spring by 0.1m,find: the workdone in stretching the spring 0.3cm if the elastic limit is not exceeded
Do you mean 0.3 m? If so:
100/0.10 = F/0.3
F = 300 N.
W = F*d = 300*0.3 = 90 Joules.
the spring constant is ... 1 N/cm
work = 1/2 k x^2 = 1/2 * 1 * 0.3^2 = 0.045 N⋅cm = 45 dyne⋅cm = 45 ergs
To find the work done in stretching the spring by 0.3 cm, we need to use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
The formula for work done is given by:
Work = (1/2) * k * x^2
Where:
- Work is the work done in stretching the spring (in joules)
- k is the spring constant (in N/m)
- x is the displacement (in meters)
Given that a force of 100 N stretches the spring by 0.1 m, we can use Hooke's Law to find the spring constant:
F = k * x
100 N = k * 0.1 m
Solving for k, we get:
k = 100 N / 0.1 m = 1000 N/m
Now, let's calculate the work done in stretching the spring by 0.3 cm (0.003 m):
Work = (1/2) * 1000 N/m * (0.003 m)^2
= (1/2) * 1000 N/m * 0.000009 m^2
= 0.0045 Joules
Therefore, the work done in stretching the spring by 0.3 cm, without exceeding the elastic limit, is 0.0045 Joules.
To find the work done in stretching the spring by 0.3cm, we need to use Hooke's Law and the formula for work done.
Hooke's Law states that the force needed to stretch or compress a spring is directly proportional to the displacement (change in length) of the spring from its equilibrium position. Mathematically, it can be expressed as:
F = k * x
Where:
F is the force applied to the spring,
k is the spring constant (a measure of how stiff the spring is), and
x is the displacement of the spring from its equilibrium position.
In this case, we know that a force of 100 N stretches the spring by 0.1 m. Therefore, we can calculate the spring constant (k) using the following equation:
k = F / x
k = 100 N / 0.1 m
k = 1000 N/m
Now that we know the spring constant, we can find the work done. The formula for work done is:
Work = (1/2) * k * x^2
Substituting the given values:
Work = (1/2) * 1000 N/m * (0.003 m)^2
Work = (1/2) * 1000 N/m * 0.000009 m^2
Work = 0.0045 J
Therefore, the work done in stretching the spring by 0.3 cm is 0.0045 Joules.