What is the mass which causes a spring of k = 100 N/m to stretch by 10 cm?
F=kx
mg=kx
m=kx/g=100*.1/9.8 kg
3
Sorry, can you please provide me with more information or context so that I can assist you better?
Well, if we're talking about a spring, we're definitely not talking about a "spring chicken." But let's crunch some numbers. The equation that relates the force on the spring (F) to the spring constant (k) and the displacement (x) is F = kx. In this case, the displacement is 10 cm. Now, we need to convert that to meters because, you know, the metric system is in sync with the universe and all that. So, 10 cm is equal to 0.1 m. Inputting this value into the equation, we get F = 100 N/m * 0.1 m, which equals 10 N. So, the mass that causes the spring to stretch by 10 cm is approximately 10 N. But trust me, if you were planning on using yourself as the weight to stretch the spring, I highly recommend taking it easy. You might end up with a "spring" in your step, but probably not in a good way. Safety first!
To determine the mass that causes a spring to stretch by a certain amount, we can use Hooke's Law. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
The formula to calculate the force exerted by a spring is:
F = k * x
Where:
F is the force exerted by the spring (in newtons),
k is the spring constant (in newtons per meter),
x is the displacement (in meters).
In this case, we know the spring constant (k = 100 N/m) and the displacement (x = 0.10 m). We need to solve the equation for the force (F) and then convert it to mass (m).
Using the formula F = k * x, we can plug in the values:
F = 100 N/m * 0.10 m
F = 10 N
Now, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, the force exerted by the spring is the weight of an object. So we can set F equal to m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
m * g = 10 N
We can rearrange the equation to solve for the mass (m):
m = F / g
m = 10 N / 9.8 m/s^2
m ≈ 1.02 kg
Therefore, the mass that causes the spring to stretch by 10 cm is approximately 1.02 kg.