To find how far the rubber band stretches and its potential energy, we can use Hooke’s Law and the formula for elastic potential energy.
1. Calculate the stretch of the rubber band:
According to Hooke’s Law, the force (F) exerted by a spring is directly proportional to the distance (x) it is stretched from its original position. The equation is:
F = k * x
Where F is the force applied, k is the spring constant, and x is the distance stretched. In this case:
- F = 9.8 N
- k = 45 N/m
To find the distance x, we rearrange the formula:
x = F / k
Substituting the known values:
x = 9.8 N / 45 N/m = 0.2178 m
So, the rubber band will stretch approximately 0.22 meters or 22 cm.
2. Calculate the potential energy stored in the rubber band:
The elastic potential energy (PE) stored in a stretched or compressed spring is given by the formula:
PE = 1/2 * k * x²
Now, substitute the values we have:
PE = 1/2 * 45 N/m * (0.2178 m)²
Calculating further:
PE = 0.5 * 45 * 0.0472 ≈ 1.059 J
Therefore, the potential energy stored in the rubber band when it is pulled by a force of 9.8 N is approximately 1.06 Joules.