It took 1800 J of work to stretch a spring from its natural length of 2m to a length of 5m. Find the spring's force constant.
Please help. Thanks in advance.
Start with the definition of spring constant
F(x)=kx
From the definition of work,
W=∫F(x)dx
W=∫F(x)dx=kx²/2 + C
The spring has stretched from its natural length (x=0) to 3 m longer:
1800=(k/2)[3²-0²]
Finally, solve for k
k=2*1800/9=400 j/m
why F(x) = K x ?
Why did the spring go on a diet? Because it wanted to become a light spring!
Now, to solve your problem. The work done to stretch a spring is given by the formula:
W = (1/2)kx^2
where W is the work done, k is the spring constant, and x is the displacement from the natural length of the spring.
In your case, W = 1800 J and x = 5 m - 2 m = 3 m. Plugging these values into the formula, we get:
1800 J = (1/2)k(3 m)^2
Let's do some math to find k:
1800 J = (1/2)k(9 m^2)
3600 J = 9k
k = 3600 J / 9 m^2
k = 400 J/m^2
So, the spring's force constant is 400 J/m^2.
To find the spring's force constant, 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 natural length.
First, we need to find the displacement of the spring. The spring is stretched from its natural length of 2m to a length of 5m.
Displacement = Final length - Initial length
Displacement = 5m - 2m
Displacement = 3m
Now, we can calculate the force constant using Hooke's Law formula:
Work = (1/2) * k * x^2
Where:
Work is the amount of work done (1800 J),
k is the force constant (what we are trying to find),
x is the displacement (3m).
Rearranging the formula for k, we get:
k = (2 * Work) / (x^2)
Plugging in the values, we have:
k = (2 * 1800 J) / (3m)^2
k = 3600 J / 9m^2
k = 400 J/m^2
Therefore, the spring's force constant is 400 J/m^2.
To find the spring's force constant, we can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law is given by the equation: F = -kx
Where:
F is the force exerted by the spring
k is the spring's force constant
x is the displacement from the equilibrium position
In this case, we know that it took 1800 J of work to stretch the spring from its natural length of 2m to a length of 5m. Work is defined as the product of force and displacement, so we have:
Work = Force * Displacement
Therefore, we can rewrite the equation as:
1800 J = (-k) * (5 m - 2 m)
Now, let's solve for k.
1800 J = (-k) * 3 m
Divide both sides by 3 m:
600 J/m = -k
Finally, to find the spring's force constant, we need to take the negative of both sides to make it positive:
k = -600 J/m
Therefore, the spring's force constant is 600 J/m.