a light elastic string attached to two points A and B on the same horizontal level has a wall picture of mass 1.4kg attached to its midpoint. The weight of the wall picture causes the elastic card of 40cm to a new length of 50cm. Draw a diagram to represent the above information. Calculate the tension in the string. The modulus of the elasticity of the string.
To represent the given information, we can draw a diagram as follows:
```
A B
|\ /|
| \ / |
| \_______/ |
| / \ |
| / \ |
|/ \|
---------------
Wall Picture
```
In this diagram, points A and B represent the two points where the light elastic string is attached at the same horizontal level. The midpoint of the string has a wall picture attached to it. The string is initially 40cm in length, and due to the weight of the wall picture, it extends to a new length of 50cm.
To calculate the tension in the string, we can use Hooke's Law, which states that the force exerted by an elastic material is directly proportional to the extension or compression of the material. In this case, the tension in the string is balancing the weight of the wall picture.
We can set up the equation as follows:
Tension = k * extension
where Tension is the tension in the string, k is the modulus of elasticity of the string, and extension is the change in length of the string.
From the given information, we know that the initial length of the string is 40cm, and the new length is 50cm. Therefore, the extension is:
extension = new length - initial length
= 50cm - 40cm
= 10cm
Now, we need to convert the extension to meters in order to use the equations. We know that 1 meter is equal to 100 centimeters, so:
extension = 10cm * (1m / 100cm)
= 0.1m
Next, we need to know the mass of the wall picture in order to calculate the tension. According to the question, the mass of the wall picture is 1.4kg.
Gravity exerts a force on the mass, given by the formula:
Force of gravity = mass * acceleration due to gravity
where acceleration due to gravity is approximately 9.8 m/s^2.
Force of gravity = 1.4kg * 9.8m/s^2
= 13.72 N
Since the tension in the string balances this force, we can write:
Tension = Force of gravity
= 13.72 N
Therefore, the tension in the string is 13.72 N.
To calculate the modulus of elasticity of the string, we can rearrange the equation for tension:
k = Tension / extension
Plugging in the values we've already obtained:
k = 13.72 N / 0.1m
= 137.2 N/m
Therefore, the modulus of elasticity of the string is 137.2 N/m.
To represent the information given, we can draw a diagram as follows:
```
A-----P------B
|
M=1.4kg
```
Where:
- A and B are the two points on the same horizontal level where the string is attached.
- P is the midpoint of the string, where the wall picture is attached.
- M is the wall picture with a mass of 1.4kg.
To calculate the tension in the string, we can use the equation:
Tension = (Mass × g) + (k × ΔL)
Where:
- Mass is the mass of the wall picture (1.4kg).
- g is the acceleration due to gravity (9.8 m/s^2).
- k is the spring constant of the elastic string.
- ΔL is the change in length of the string (from 40cm to 50cm).
First, convert the lengths to meters:
- Initial length (40cm) = 0.4m
- Final length (50cm) = 0.5m
To calculate the change in length (ΔL):
ΔL = Final length - Initial length
= 0.5m - 0.4m
= 0.1m
Now, substitute the values into the equation and solve for Tension:
Tension = (1.4kg × 9.8 m/s^2) + (k × 0.1m)
To calculate the modulus of elasticity of the string, we can use the formula:
Modulus of Elasticity = Tension / (Initial length × Strain)
Where:
- Strain = ΔL / Initial length
Substitute the values into the equation and solve for the Modulus of Elasticity.