Object of mass 0.75kg was hung from the end of a spring and extend the spring by 50cm. Calculate how much elastic potential energy is stored in the spring?

To calculate the elastic potential energy stored in the spring, we can use the formula:

Elastic potential energy = 0.5 * k * x^2

Where:
k = spring constant
x = extension of the spring

Given that the mass of the object is 0.75kg and it extends the spring by 50cm (0.5m), we first need to calculate the spring constant (k).

The force exerted by the object on the spring is equal to the weight of the object:
F = m * g
F = 0.75kg * 9.81 m/s^2
F = 7.3575 N

The force exerted by the spring is given by Hooke's Law:
F = k * x
7.3575 N = k * 0.5m
k = 14.715 N/m

Now we can calculate the elastic potential energy stored in the spring:
Elastic potential energy = 0.5 * 14.715 N/m * (0.5m)^2
Elastic potential energy = 0.5 * 14.715 N/m * 0.25m
Elastic potential energy = 1.8394 J

Therefore, the elastic potential energy stored in the spring is 1.8394 Joules.

Given:

- Mass (m) = 0.75 kg
- Extension (x) = 50 cm = 0.5 m

Formula for Elastic Potential Energy:

```
Elastic Potential Energy (E) = 1/2 - k - x^2
```

where:

- k is the spring constant

Finding the Spring Constant (k):

We can use Hooke's Law:

```
F = -kx
```

where:

- F is the force applied to the spring
- k is the spring constant

In this case, the force is the weight of the object:

```
F = mg = (0.75 kg) - (9.8 m/s^2) = 7.35 N
```

Substituting the values of F and x into Hooke's Law, we get:

```
7.35 N = -k - 0.5 m
```

Solving for k:

```
k = 14.7 N/m
```

Calculating the Elastic Potential Energy:

Now that we know the spring constant, we can calculate the elastic potential energy:

```
E = 1/2 - 14.7 N/m - (0.5 m)^2
```

```
E = 2.28 J
```

Therefore, the elastic potential energy stored in the spring is 2.28 J.