Hookes law states that the distance that a spring is stretched by hanging object varies directly as the mass of the object. If the distance is 20 cm when the mass is 3kg, what is the distance when the mass is 5 kg?
since d = km, d/m=k is constant. So, you want d such that
d/5 = 20/3
To solve this problem, we can use the formula for Hooke's Law, which states that the distance that a spring is stretched is directly proportional to the mass of the object. Mathematically, it can be represented as:
Distance = k * mass
where k is the constant of proportionality.
We are given that the distance is 20 cm when the mass is 3 kg. Let's substitute these values into the formula and solve for k:
20 cm = k * 3 kg
Divide both sides of the equation by 3 kg:
20 cm / 3 kg = k
k ≈ 6.67 cm/kg (rounded to two decimal places)
Now, we can use this value of k to find the distance when the mass is 5 kg:
Distance = k * mass
Distance = 6.67 cm/kg * 5 kg
Distance ≈ 33.33 cm (rounded to two decimal places)
Therefore, the distance when the mass is 5 kg is approximately 33.33 cm.
To solve this problem, we need to apply Hooke's Law, which states that the distance a spring is stretched (or compressed) is directly proportional to the force applied to it.
In this case, the distance that the spring is stretched is directly proportional to the mass of the object hanging from it. So, we can write the following equation:
Distance = k * Mass
Where:
- Distance is the distance the spring is stretched (in this case, we'll measure it in centimeters).
- Mass is the mass of the object hanging from the spring (in this case, we'll measure it in kilograms).
- k is the constant of proportionality that relates the distance to the mass.
To find the value of k, we need to use the given information. It states that the distance is 20 cm when the mass is 3 kg. We can substitute these values into our equation to solve for k:
20 = k * 3
Now, we can solve for k:
k = 20 / 3
k ≈ 6.67 (rounded to two decimal places)
Now that we know the value of k, we can use the equation to find the distance when the mass is 5 kg:
Distance = k * Mass
Distance = 6.67 * 5
Distance ≈ 33.35 cm
Therefore, when the mass is 5 kg, the distance the spring is stretched is approximately 33.35 cm.