A spiral spring stretches 4 cm when a mass of 0.5 kg is suspended from it. what is the spring constant?
k=mg/x =0.5•9.8/0.04=122.5 N/m
Why did the chicken cross the road? Because it wanted to find the spring constant, of course!
To calculate the spring constant (k), we need to use Hooke's Law: F = kx, where F is the force applied, k is the spring constant, and x is the displacement of the spring. In this case, we know that the mass (m) is 0.5 kg and the displacement (x) is 4 cm (or 0.04 m).
Now, let's plug in the values we know into Hooke's Law:
F = kx
0.5 kg * 9.8 m/s² = k * 0.04 m
Solving for k, we get:
k = (0.5 kg * 9.8 m/s²) / 0.04 m
So, the spring constant is equal to the force (0.5 kg * 9.8 m/s²) divided by the displacement (0.04 m). Crunching the numbers, we find that the spring constant is approximately 122.5 N/m. That's one bouncy spring!
To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to its extension.
Hooke's Law equation:
F = k * x
Where:
F is the force applied on the spring (in newtons)
k is the spring constant (in newtons per meter)
x is the extension or displacement of the spring from its equilibrium position (in meters)
In this case, the extension of the spring (x) is given as 4 cm, which is equivalent to 0.04 meters.
The mass (m) is given as 0.5 kg, and we can calculate the force (F) using the formula:
F = m * g
Where:
m is the mass (in kg)
g is the acceleration due to gravity (approximately 9.8 m/s²)
Substituting the values:
F = 0.5 kg * 9.8 m/s²
This gives us:
F = 4.9 N
Now, we can rearrange Hooke's Law equation to find the spring constant:
k = F / x
Plugging in the known values:
k = 4.9 N / 0.04 m
Calculating this, we get:
k ≈ 122.5 N/m
Therefore, the spring constant is approximately 122.5 N/m.
To find the spring constant, you 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.
Hooke's Law can be expressed as:
F = -kx
where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.
In this case, the spring stretches by 4 cm when a mass of 0.5 kg is suspended from it. The displacement, x, is given in centimeters (cm), so we need to convert it to meters (m) to match the SI units of the spring constant.
1 cm = 0.01 m
Therefore, x = 4 cm * 0.01 m/cm = 0.04 m
Now, we can rearrange Hooke's Law to solve for the spring constant:
k = -F / x
The force F can be calculated using Newton's second law, which states that force is equal to the mass multiplied by the acceleration:
F = m * g
where m is the mass (0.5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging the values into the equation:
F = 0.5 kg * 9.8 m/s^2 = 4.9 N
Substituting the values into the equation for the spring constant:
k = -F / x = -4.9 N / 0.04 m
Calculating the result:
k ≈ -122.5 N/m
The negative sign indicates that the spring force acts in the opposite direction of the displacement. So, the spring constant is approximately 122.5 N/m.