A force of 2N will stretch a rubber band 2 cm. Assuming that Hooke's law applies, how far will a 4N force stretch the rubber band? How much work does it take to stretch the rubber band this far?
To determine how far a 4N force will stretch the rubber band, we can use Hooke's law, which states that the force required to extend or compress a spring is directly proportional to the displacement of the spring from its equilibrium position.
Let's calculate the spring constant (k) first using the given information. According to Hooke's law, we have:
Force = k * displacement
Rearranging the equation, we get:
k = Force / displacement
Plugging in the values, we have:
k = 2N / 2cm = 1N/cm
Now, we can use this spring constant to calculate the displacement for a 4N force. Rearranging the equation for displacement, we have:
displacement = Force / k
Plugging in the values, we get:
displacement = 4N / 1N/cm = 4cm
Therefore, a 4N force will stretch the rubber band by 4 cm.
To calculate the work done in stretching the rubber band, we can use the formula:
Work = force * displacement
Plugging in the values, we get:
Work = 4N * 4cm = 16Ncm
So, it takes 16 Ncm of work to stretch the rubber band by 4 cm.
To find out how far a 4N force will stretch the rubber band, we can use Hooke's Law formula:
F = k * x,
where F is the force applied, k is the spring constant (or stiffness) of the rubber band, and x is the displacement (stretch) of the rubber band.
First, let's find the value of k using the given information. It states that a force of 2N stretches the rubber band by 2 cm. So we have:
2N = k * 2cm.
To get rid of the cm unit, we need to convert it to meters since the force is given in Newtons:
2N = k * 0.02m.
Now, we can solve for k:
k = 2N / 0.02m,
k = 100 N/m.
Next, let's find out how far a 4N force will stretch the rubber band. Using the same formula, we have:
4N = 100 N/m * x.
Solving for x gives:
x = 4N / 100 N/m,
x = 0.04 m,
x = 4 cm.
Therefore, a 4N force will stretch the rubber band by 4 cm.
Now, let's calculate the work done to stretch the rubber band by 4 cm. The work done is equal to the product of the force applied and the displacement:
Work = Force * Distance,
Work = 4N * 0.04m,
Work = 0.16 Joules.
Therefore, it takes 0.16 Joules of work to stretch the rubber band by 4 cm.
twice as far
(1/2) k x^2
where k = force/distance