a slingshot will shoot a 10 pebble 22.0 m straight up. a) how much potential energy is stored in the slingshot rubber band? B) With the same potential energy is stored in the rubber band, how high can the slingshot shoot a 25g pebble?
a. PE=mg*heightitreaches
b. =10/25 * 22m
To calculate the potential energy stored in a slingshot's rubber band, we can use the formula:
Potential Energy (PE) = 0.5 * k * x^2
where:
- PE is the potential energy
- k is the spring constant of the rubber band
- x is the displacement from the equilibrium position (how far the rubber band is stretched)
a) Finding the potential energy stored in the slingshot rubber band for a 10g pebble shot 22.0 m straight up:
To calculate the potential energy, we first need to determine the spring constant of the rubber band.
The spring constant (k) is a measure of how stiff the rubber band is. It represents the force required to stretch the rubber band, and it depends on the material and dimensions of the rubber band. Unfortunately, we don't have this information. So, I'll assume a typical value for a slingshot rubber band, which is around 25 N/m.
We also need the displacement (x) of the rubber band. Since the pebble is shot straight up, the rubber band's displacement is equal to the height reached: 22.0 m.
Now we can substitute the values into the potential energy formula:
PE = 0.5 * 25 * (22.0^2)
Calculating this, we get:
PE = 0.5 * 25 * 484
PE = 6050 Joules
Therefore, the potential energy stored in the slingshot rubber band is 6050 Joules.
b) Now, let's use the same potential energy to determine how high a 25g pebble can be shot:
To find the maximum height, we can use the potential energy equation again and solve for the height (h):
PE = 0.5 * k * h^2
This time, we need to rearrange the equation to solve for the height:
h = sqrt(2 * PE / k)
Let's substitute the values:
PE = 6050 Joules (from previous calculation)
k = 25 N/m (same as the assumed spring constant)
h = sqrt(2 * 6050 / 25)
h = sqrt(484)
h = 22.0 m
Therefore, with the same potential energy stored in the rubber band, the slingshot can shoot a 25g pebble up to a height of 22.0 meters.