A 2kg block is placed onto a vertically oriented spring whose spring constant k is 1960 N/m. Find the distance that the spring will be compressed.
To find the distance that the spring will be compressed, we need to apply Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement or compression of the spring.
Hooke's Law can be expressed as:
F = -kx
Where:
F is the force exerted by the spring,
k is the spring constant,
x is the displacement or compression of the spring.
In this case, we have the mass of the block, but we need to convert it to force. The force exerted by gravity can be calculated using Newton's second law, which states that force is equal to mass multiplied by acceleration.
Let's find the force exerted by the spring first:
Weight = m * g
Where:
m is the mass of the block, which is 2 kg,
g is the acceleration due to gravity, which is approximately 9.8 m/s².
Weight = 2 kg * 9.8 m/s² = 19.6 N
Since the block is at rest on the spring, the force exerted by the spring is equal to the weight of the block:
F = 19.6 N
Now we can substitute the force value into Hooke's Law equation:
19.6 N = -kx
Rearranging the equation to solve for x:
x = -19.6 N / k
Substituting the value of the spring constant k into the equation:
x = -19.6 N / 1960 N/m = -0.01 m
Since displacement or compression cannot be negative, the distance that the spring will be compressed is 0.01 meters (or 10 mm).