A force of 2-Newtons will stretch a rubber band 2/100 meters. Assuming that Hooke’s Law applies, how far with a force of 4-Newtons stretch the rubber band? How much work does it take to stretch the rubber band this far?
K = 2N./(2/100)m = 100 N/m.
d = 4N. * 1m/100N = 0.04 m.
Work = 2 * 0.04 = 0.08 J.
According to Hooke's Law, the stretch or extension of a spring or rubber band is directly proportional to the force applied. Therefore, if a force of 2 Newtons stretches the rubber band by 2/100 meters, we can use this information to answer your questions.
Step 1: Determine the constant of proportionality (spring constant):
According to Hooke's Law, the force (F) exerted on a spring or rubber band is equal to the spring constant (k) multiplied by the displacement or stretch (x), expressed mathematically as F = kx.
From the given information, we have:
Force = 2 Newtons
Displacement = 2/100 meters
Rearranging the equation, we get:
k = F / x
Substituting the values, we have:
k = 2 N / (2/100) m
k = 2 N / (1/100) m
k = 2 N * (100/1) m
k = 200 N/m
Step 2: Calculate the stretch for a force of 4 Newtons:
Using the same formula, we can calculate the stretch (x) for a force of 4 Newtons:
F = kx
Rearranging the equation, we get:
x = F / k
Substituting the values, we have:
x = 4 N / 200 N/m
x = 0.02 m
Therefore, a force of 4 Newtons will stretch the rubber band by 0.02 meters.
Step 3: Calculate the work done to stretch the rubber band:
In physics, work is defined as the force applied over a certain distance. Therefore, we can calculate the work done to stretch the rubber band using the formula:
Work (W) = Force (F) * Displacement (d)
Substituting the values, we have:
W = 4 N * 0.02 m
W = 0.08 Joules
Therefore, it will take 0.08 Joules of work to stretch the rubber band by 0.02 meters with a force of 4 Newtons.
To determine how far a force of 4 Newtons will stretch the rubber band, we can use Hooke's Law, which states that the force applied on a spring or elastic material is directly proportional to the displacement it produces.
Let's first convert the given information into a mathematical equation using Hooke's Law:
F = k * x
Where:
F is the force applied on the rubber band (in Newtons)
k is the spring constant (a measure of the stiffness of the rubber band)
x is the displacement or stretch of the rubber band (in meters)
We know that a force of 2 Newtons stretches the rubber band by 2/100 meters. So, we can set up the equation as:
2 = k * (2/100)
Simplifying this equation, we can find the value of the spring constant (k):
k = 2 / (2/100)
k = 2 * (100/2)
k = 100 Newtons/meter
Now that we have the spring constant (k), we can calculate how far a force of 4 Newtons will stretch the rubber band:
4 = 100 * x
Solving for x (the stretch):
x = 4 / 100
x = 0.04 meters
Therefore, a force of 4 Newtons will stretch the rubber band by 0.04 meters.
Now, let's calculate the work done to stretch the rubber band by this distance:
The work done (W) is given by the equation:
W = F * x
Substituting the values:
W = 4 * 0.04
W = 0.16 Joules
Therefore, it would take 0.16 Joules of work to stretch the rubber band by the distance of 0.04 meters.