# Find Stretched Length of Spring - 8.5kg Board at 50°

• rasputin66
In summary, a 8.5 kg board is wedged into a corner and held by a spring with a spring constant of 184 N/m at a 50.0° angle. To find the amount by which the spring is stretched from its unstrained length, we need to use the formula x = (mg/k). The forces acting on the board are gravity and the spring, which must be equal to zero for equilibrium. However, in this case, we also need to consider the condition for rotational equilibrium.
rasputin66
A 8.5 kg board is wedged into a corner and held by a spring at a 50.0° angle, as the drawing shows. The spring has a spring constant of 184 N/m and is parallel to the floor. Find the amount by which the spring is stretched from its unstrained length.

(The picture shows a spring sticking out of the wall horizontally, and it is attached to one end of the board. The spring is holding the board up from falling flat on the floor. So the board is pulling on the spring.)

I know how to do some spring questions, but I don't know how to plug in the angle in this question. Please help! I know I need to find N to find x.

00000 <~~ spring
| / <~~~ board
| /
|/

m= 8.5 kg
angle= 50 degrees
k= 184 N/m

What forces act on the board? What are the conditions for equilibrium?

Gravity? And the spring?

They equal zero? I think I'm missing something. Like how to figure in this angular business.

x = (mg/k)
x=(9.8x8.5)/184
x=0.565 m<~~~ not right

Last edited:
rasputin66 said:
Gravity? And the spring?
Yes, those are the two most important forces.
They equal zero? I think I'm missing something. Like how to figure in this angular business.
What is the condition for rotational equilibrium?

x= amount of stretch

To solve this problem, we can use the equation F = kx, where F is the force applied to the spring, k is the spring constant, and x is the amount of stretch. In this case, the force applied to the spring is the weight of the board, which can be calculated using the formula F = mg, where m is the mass of the board and g is the acceleration due to gravity (9.8 m/s^2). So, the force applied to the spring is:

F = (8.5 kg)(9.8 m/s^2) = 83.3 N

Now, we can plug this force into the equation F = kx and solve for x:

83.3 N = (184 N/m)(x)

x = 83.3 N / 184 N/m = 0.452 m

Therefore, the amount by which the spring is stretched is 0.452 m. This means that the spring has stretched 0.452 meters from its unstrained length in order to support the 8.5 kg board at a 50 degree angle.

## 1. How do you calculate the stretched length of a spring?

The stretched length of a spring can be calculated using the formula: L = (mg sinθ)/k, where m is the mass of the object attached to the spring, g is the acceleration due to gravity, θ is the angle at which the spring is held, and k is the spring constant.

## 2. What is the spring constant and how does it affect the stretched length?

The spring constant is a measure of the stiffness of a spring. It is represented by the letter k and is measured in units of force per unit distance. A higher spring constant means that the spring is stiffer and will require more force to stretch it to a certain length. Therefore, a higher spring constant will result in a shorter stretched length for a given mass and angle.

## 3. How does the mass of the object attached to the spring affect the stretched length?

The mass of the object attached to the spring directly affects the stretched length. The heavier the mass, the more force it will exert on the spring, resulting in a longer stretched length. This relationship is represented by the variable m in the formula for calculating the stretched length.

## 4. Does the angle at which the spring is held impact the stretched length?

Yes, the angle at which the spring is held does impact the stretched length. The greater the angle, the more force will be exerted on the spring, resulting in a longer stretched length. This relationship is represented by the variable θ in the formula for calculating the stretched length.

## 5. What is the significance of finding the stretched length of a spring?

Finding the stretched length of a spring is important for understanding the behavior of elastic materials and their ability to store and release energy. It is also useful in various fields such as engineering, physics, and material science for designing and analyzing structures that use springs. Additionally, knowing the stretched length of a spring can help determine its durability and potential for failure under certain conditions.

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