A slingshot consists of a light leather cup
attached between two rubber bands. It takes
a force of 32 N to stretch the bands 1.1 cm.
a) What is the equivalent spring constant
of the rubber bands?
Answer in units of N/m.
F=kx
32=k(.011) solve for k
2909.0 N/m
To find the equivalent spring constant of the rubber bands, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement.
Hooke's Law: F = k * x
Where:
F is the force applied to the slingshot (32 N)
k is the spring constant
x is the displacement or stretch of the rubber bands (1.1 cm converted to meters)
Converting 1.1 cm to meters:
1 cm = 0.01 meters
1.1 cm = 0.011 meters
Substituting the given values into the equation, we have:
32 N = k * 0.011 m
Now, we can solve for k by dividing both sides of the equation by 0.011 m:
32 N / 0.011 m = k
Simplifying the equation gives us:
2,909.09 N/m = k
Therefore, the equivalent spring constant of the rubber bands is 2,909.09 N/m.
To find the equivalent spring constant of the rubber bands in the slingshot, you can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its equilibrium position.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the applied force (32 N in this case)
k is the spring constant (unknown)
x is the displacement (1.1 cm or 0.011 m in this case)
Rearranging the equation to solve for k, we get:
k = F / x
Substituting the values, we have:
k = 32 N / 0.011 m
k ≈ 2909.09 N/m
Thus, the equivalent spring constant of the rubber bands in the slingshot is approximately 2909.09 N/m.