A catapult of a spring constant 100N/M contains 2.0J of elastic potential energy when it is pulled back. What is the extension of the rubber band? I know that E= F/K but I don't know how to work out the force from the information provided, help would be much appreciated, thanks
e = 1/2 k x^2 ... (kind of like KE)
2.0 = 1/2 * 100 * x^2
o.o4
To determine the extension of the rubber band, we can start by using the given information about the elastic potential energy (E) and the spring constant (K). The equation you mentioned, E = F/K, relates the elastic potential energy to the force and spring constant of the system.
To solve for the force (F) in the equation, we need to rearrange it. Multiply both sides by K to isolate F:
F = E * K
Now, we can substitute the known values:
F = 2.0 J * 100 N/M
F = 200 N
We have found the force (F) exerted by the spring when it is pulled back.
Next, we can use Hooke's Law, which states that the force (F) exerted by a spring is directly proportional to the extension (x) of the spring. The equation is:
F = k * x
Where k is the spring constant and x is the extension.
Rearranging the equation to solve for the extension (x), we have:
x = F / k
Plugging in the values:
x = 200 N / 100 N/M
x = 2 M
Therefore, the extension of the rubber band is 2 meters.