Object of mass 0.75kg was hung from the end of the spring and extend the spring by 50cm. Calculate the spring constant?

To calculate the spring 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 equilibrium position.

The formula for Hooke's Law is:

F = -kx

Where:
F = force exerted by the spring (in Newtons)
k = spring constant (in N/m)
x = displacement of the spring from its equilibrium position (in meters)

Given that the mass of the object is 0.75kg and it extends the spring by 50cm (or 0.5m), we can calculate the force exerted by the spring using the formula:

F = mg
F = 0.75kg * 9.81 m/s^2
F = 7.3575 N

Now we can use Hooke's Law to find the spring constant:

7.3575 N = -k * 0.5m
k = -7.3575 N / 0.5m
k = -14.715 N/m

Therefore, the spring constant is 14.715 N/m.

Hooke's Law:

```
F = -kx
```

where:

- F is the force applied to the spring
- k is the spring constant
- x is the displacement from the spring's equilibrium position

Gravity force:

```
F = mg
```

where:

- m is the mass of the object
- g is the acceleration due to gravity

Equating forces:

```
-kx = mg
```

Solving for the spring constant:

```
k = mg/x
```

Substituting given values:

```
k = (0.75 kg)(9.81 m/s^2) / (0.5 m)
k = 14.72 N/m
```

Therefore, the spring constant is 14.72 N/m.