A slingshot consists of a light leather cup attached between two rubber bands. It takes a force of 33 N to stretch the bands 1.3 cm.
A) what is the equivalent spring constant of the rubber bands? Answer in n/m
B) how much force is required to pull the cup of the slingshot 4.2 cm from its equilibrium position? Answer in units of N
Use same procedure as
http://www.jiskha.com/display.cgi?id=1329443884
but note that the numbers are different.
A) To find the equivalent spring constant of the rubber bands, we need to 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 equation:
F = k * x
Where:
F is the force applied (in Newtons)
k is the spring constant (in N/m)
x is the displacement from the equilibrium position (in meters)
Given:
Force (F) = 33 N
Displacement (x) = 0.013 m (1.3 cm)
Using the equation, we can rearrange it to solve for the spring constant (k):
k = F / x
Substituting the given values:
k = 33 N / 0.013 m
k ≈ 2538.46 N/m
Therefore, the equivalent spring constant of the rubber bands is approximately 2538.46 N/m.
B) The force required to pull the cup of the slingshot 4.2 cm from its equilibrium position can be calculated using the same Hooke's Law equation.
Given:
Displacement (x) = 0.042 m (4.2 cm)
Using the equation, we can rearrange it to solve for the force (F):
F = k * x
Substituting the given values:
F = 2538.46 N/m * 0.042 m
F ≈ 106.47 N
Therefore, the force required to pull the cup of the slingshot 4.2 cm from its equilibrium position is approximately 106.47 N.
A) To find the equivalent spring constant of the rubber bands in the slingshot, we 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: F = k * x
Where:
F = force (in N)
k = spring constant (in N/m)
x = displacement (in m)
In this case, the force required to stretch the rubber bands 1.3 cm (which is equal to 0.013 m) is 33 N.
Plugging these values into Hooke's Law, we get:
33 N = k * 0.013 m
To find the spring constant, we can rearrange the equation as follows:
k = 33 N / 0.013 m
Calculating this gives us:
k = 2538.46 N/m
Therefore, the equivalent spring constant of the rubber bands in the slingshot is 2538.46 N/m.
B) To calculate the force required to pull the cup of the slingshot 4.2 cm (which is equal to 0.042 m) from its equilibrium position, we can use Hooke's Law again.
Using the same equation as before, F = k * x, we can substitute the given values:
F = 2538.46 N/m * 0.042 m
Calculating this gives us:
F = 106.47 N
Therefore, the force required to pull the cup of the slingshot 4.2 cm from its equilibrium position is approximately 106.47 N.