A spiral spring extends from a lend of 10.00cm to 10.01cm when a force of 20N is applied on Newton calculate the force constant of the spring?
Force = constant * extension distance
If you really mean delta x = 0.01 centimeters
(and not 0.01 meters)
then
20 newtons = k * 0.0001 meters
k = 20 / 0.0001 = 200000/1 = 200,000 Newtons/meter
To calculate the force constant of a spring, you can use Hooke's law, which states that the force exerted by a spring is directly proportional to the amount it is stretched or compressed. The formula for Hooke's law is:
F = -k * x
Where:
F is the force applied to the spring
k is the force constant of the spring
x is the displacement of the spring from its equilibrium position
In this case, the displacement of the spring is the difference in length between its extended and compressed states, which is 10.01 cm - 10.00 cm = 0.01 cm = 0.01 m. The force applied to the spring is 20 N.
Rearranging the formula, we have:
k = -F / x
k = -20 N / 0.01 m
k = -2000 N/m
The force constant of the spring is -2000 N/m. The negative sign indicates that the force exerted by the spring is in the opposite direction of the displacement.
To calculate the force constant of the spring, you 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 is the force applied (in Newtons),
k is the force constant (also known as the spring constant),
x is the displacement of the spring (in meters).
In this case, the spring extends from a length of 10.00 cm to 10.01 cm, which corresponds to a displacement of:
x = (10.01 cm - 10.00 cm) = 0.01 cm = 0.01 m
Plugging in the given values, we have:
20 N = k * 0.01 m
Now, we can solve for k by dividing both sides of the equation by 0.01 m:
k = 20 N / 0.01 m
k = 2000 N/m
Therefore, the force constant of the spring is 2000 N/m.