A spring of unknown force constant is attached to a rod so that it hangs vertically. With no mass attached, the spring has a length of 12.0 cm. When a student attaches a mass of 50 grams, the spring stretches to a length of 18.0cm. Determine the force constant for this spring.
F = m*g = 0.05kg * 9.8N/kg = 0.49 N.
d = 18-12 = 6 cm = 0.06 m.
k = 0.49N/0.06m = 8.17N/m.
Well, it sounds like this spring is really enjoying some stretching exercises! Let's see if we can determine its force constant.
To find the force constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the amount the spring is stretched or compressed.
In equation form, that would be F = k * x, where F is the force applied to the spring, k is the force constant, and x is the displacement (change in length) of the spring.
In this case, we have the displacement (18.0 cm - 12.0 cm = 6.0 cm) and the mass (50 grams). But remember, we need to convert grams to kilograms to keep the units consistent.
So, 50 grams is equal to 0.05 kilograms. And the displacement is 6.0 cm, which is equal to 0.06 meters.
Now, we can plug these values into Hooke's Law equation:
0.05 kg = k * 0.06 m
To solve for k, we divide both sides of the equation by 0.06 m:
k = 0.05 kg / 0.06 m
And if we do the math, we find that the force constant for this spring is approximately 0.833 N/m.
So, there you have it – the force constant for this stretching spring. Just remember to give it a good stretch before letting it pogo its way back to equilibrium!
To determine the force constant of the spring, 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 = k * x
Where:
F is the force applied to the spring,
k is the force constant (also known as the spring constant) of the spring,
x is the displacement of the spring from its equilibrium position.
In this case, we can derive the force constant of the spring by using the given information:
Force applied to the spring, F = m * g
Where:
m is the mass attached to the spring - 50 grams (converted to kg: 50 grams = 0.050 kg)
g is the acceleration due to gravity - approximately 9.8 m/s^2
Given that the spring stretches from a length of 12.0 cm to 18.0 cm, the displacement of the spring, x is:
x = (18.0 cm - 12.0 cm) = 6.0 cm (converted to meters: 6.0 cm = 0.06 m)
Substituting the values into Hooke's Law, we have:
F = k * x
m * g = k * x
0.050 kg * 9.8 m/s^2 = k * 0.06 m
Now we can solve for the force constant, k:
k = (0.050 kg * 9.8 m/s^2) / 0.06 m
Calculating this expression, we find that the force constant of the spring is approximately:
k = 8.167 N/m
Therefore, the force constant for this spring is 8.167 N/m.
To determine the force constant for the spring, 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 = k * x
Where:
F is the force applied to the spring.
k is the force constant (also known as the spring constant).
x is the displacement from the equilibrium position.
In this case, when no mass is attached, the spring has a length of 12.0 cm, which is its equilibrium position. When a mass of 50 grams is attached, the spring stretches to a length of 18.0 cm, resulting in a displacement of 6.0 cm (18.0 cm - 12.0 cm).
First, let's convert the mass from grams to kilograms:
Mass = 50 grams = 0.050 kg
Now, we can determine the force applied to the spring using the following equation:
F = m * g
Where:
m is the mass in kilograms.
g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
F = (0.050 kg) * (9.8 m/s^2)
F = 0.49 N
Now, we can rearrange Hooke's Law to solve for the force constant:
k = F / x
k = 0.49 N / 0.06 m
k = 8.17 N/m
Therefore, the force constant for this spring is 8.17 N/m.