An object with the mass 500g was hang from the spring with force constant 20N/m how far in cm would the spring stretch
F = kx
plug in your numbers. watch the units.
weight force = m g = 0.500 * 9.81 Newtons
x = F/k =0.500 * 9.81 N / 20 N/meter
multiply by 100 to get cm
Well, let's see here. We have a 500g object hanging from a spring with a force constant of 20N/m. To find out how far the spring would stretch, we can use Hooke's Law, which states that the force exerted by the spring is proportional to the displacement from its equilibrium position. So, by applying some mathematical humor, we have:
Why did the spring go to therapy? Because it couldn't handle the weight of the situation!
But I digress. Let's calculate the displacement now, shall we? Hooke's Law can be written as:
F = kx
Where F is the force applied (in this case, the weight of the object), k is the force constant, and x is the displacement (what we're trying to find). Rearranging the formula, we get:
x = F/k
Now, let's plug in the values. The mass of the object is 500g, which can be converted to 0.5kg. The force constant is 20N/m. Therefore:
x = (0.5kg * 9.8m/s^2) / 20N/m
Simplifying this expression, we find:
x = 0.0245m
But wait, our question asked for the displacement in centimeters, not meters! Let's convert that:
x = 0.0245m * (100cm/1m) = 2.45cm
So, the spring would stretch approximately 2.45cm. I hope this answer springs some joy into your physics journey!
To calculate the distance the spring stretches, we can apply Hooke's Law. Hooke's Law states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position.
The equation for Hooke's Law is given by:
F = k * x
Where:
F is the force exerted by the spring (in Newtons),
k is the force constant or spring constant (in N/m),
x is the displacement of the spring (in meters).
In this case, we are given:
Mass (m) = 500 grams = 0.5 kg (converted from grams to kilograms),
Force constant (k) = 20 N/m.
To find the displacement (x) in meters, we need to convert the mass to weight using the acceleration due to gravity (g).
Weight (W) = mass (m) * gravity (g)
In this case, since the object is hanging, the weight of the object is equal to the force exerted by the spring. So:
F = W = m * g
Where:
g is the acceleration due to gravity, which is approximately 9.8 m/s^2.
Now we can rearrange the equation to solve for x:
x = F / k
Substituting the values, we get:
x = (m * g) / k
x = (0.5 kg * 9.8 m/s^2) / 20 N/m
Simplifying further:
x = 0.049 m
To convert this to centimeters, we multiply by 100:
x = 0.049 m * 100 cm/m
x = 4.9 cm
Therefore, the spring would stretch approximately 4.9 cm.
To find out 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. The equation 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),
x is the displacement of the spring from its equilibrium position.
In this case, we are given:
mass = 500g = 0.5kg (since 1kg = 1000g)
force constant (k) = 20N/m
First, let's find the force applied to the spring. The force can be calculated using the equation:
force = mass * acceleration
In this case, there is no acceleration acting on the mass when it is hanging from the spring, so the force is equal to the weight of the object:
force = mass * acceleration due to gravity = m * g
where g ≈ 9.8 m/s² is the acceleration due to gravity.
Substituting the given mass:
force = 0.5kg * 9.8 m/s² = 4.9 N
Next, we can rearrange Hooke's Law to solve for x:
x = F / k
Substituting the values we have:
x = 4.9 N / 20 N/m = 0.245 m
Finally, to convert the displacement to centimeters, we multiply by 100:
x = 0.245 m * 100 cm/m = 24.5 cm
Therefore, the spring would stretch approximately 24.5 cm when a 500g object is hung from it.