An object with mass 500g less hang from the spring with force constant 20N/m.How far in cm would the spring stretch?
To calculate the distance the spring stretches, we will use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. Mathematically, this can be written as:
F = -kx
Where F is the force exerted by the spring, k is the force constant, and x is the displacement from the equilibrium position.
In this case, the force exerted by the spring is the weight of the object hanging from it, given by:
F = mg
Where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given that the mass of the object is 500g (or 0.5kg) less than the weight, we can write the equation as:
F = (m - 0.5g)g
Now, setting this equal to the force exerted by the spring and solving for x:
-kx = (m - 0.5g)g
x = -(m - 0.5g)g / k
Substituting the given values:
m = 0.5 kg
g = 9.8 m/s^2
k = 20 N/m
x = -(0.5 - 0.5(9.8)) * 9.8 / 20
Simplifying the expression:
x = -(0.5 - 4.9) * 9.8 / 20
x = -(4.4) * 9.8 / 20
x = -43.12 / 20
x = -2.156 m
Converting to centimeters:
x = -2.156 m * 100 cm/m
x ≈ -215.6 cm
Therefore, the spring would stretch approximately 215.6 cm.
To find how far the spring would stretch, 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.
Hooke's Law equation:
F = k * x
where:
F is the force (in Newtons),
k is the force constant or spring constant (in N/m),
x is the displacement (in meters).
In this case, we have:
F = 500g = 0.5 kg (since mass is given in grams)
k = 20 N/m
We need to convert the mass to weight, since weight is the force due to gravity and it acts downward. The weight is given by the formula:
weight = mass * g
where g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
So, the weight of the object is:
weight = 0.5 kg * 9.8 m/s^2 = 4.9 N
Now we can rearrange Hooke's Law equation to solve for x:
x = F / k
Substituting the values:
x = 4.9 N / (20 N/m)
x = 0.245 m
To convert the displacement to centimeters, we multiply by 100:
x (in cm) = 0.245 m * 100 = 24.5 cm
Therefore, the spring would stretch approximately 24.5 cm.
To find the distance the spring stretches, 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 = Force exerted by the spring (N)
k = Force constant or spring constant (N/m)
x = Displacement of the spring (m)
In this case, we need to find the displacement of the spring when an object with a mass of 500g (0.5 kg) is hung from it.
Step 1: Convert the mass from grams to kilograms.
Given mass = 500g
Converting to kg: 500g ÷ 1000 = 0.5 kg
Step 2: Apply Hooke's Law to find the displacement.
Given force constant (k) = 20 N/m
Given mass (m) = 0.5 kg
The force exerted by the spring is equal to the weight of the object, which is given by:
Force (F) = mass (m) * acceleration due to gravity (g)
Where acceleration due to gravity (g) is approximately 9.8 m/s^2.
F = m * g = 0.5 kg * 9.8 m/s^2 = 4.9 N
Now, substitute the known values into Hooke's Law formula:
4.9 N = 20 N/m * x
Solve for x (displacement):
x = 4.9 N / 20 N/m = 0.245 m
Step 3: Convert the displacement from meters to centimeters.
x = 0.245 m * 100 cm/m = 24.5 cm
Therefore, the spring stretches by 24.5 cm when the object with a mass of 500g is hung from it.